RESPONSE-CONSEQUENCE CONTINGENCY DISCRIMINABILITY WHEN 
POSITIVE AND NEGATIVE REINFORCEMENT COMPETE 
IN CONCURRENT SCHEDULES 
 
Except where reference is made to the work of others, the work described in this 
dissertation is my own or was done in collaboration with my advisory committee.  This 
dissertation does not include proprietary or classified information. 
 
_____________________________________ 
Michael Austin Magoon 
 
 
Certificate of Approval: 
 
 
 
______________________________ ______________________________ 
Thomas S. Critchfield    M. Christopher Newland, Chair 
Associate Professor    Alumni Professor 
Psychology     Psychology 
 
 
______________________________ ______________________________ 
Martha C. Escobar    James F. McCoy 
Assistant Professor    Associate Professor 
Psychology     Psychology 
 
 
   ______________________________ 
   Stephen L. McFarland 
   Dean 
   Graduate School 
RESPONSE-CONSEQUENCE CONTINGENCY DISCRIMINABILITY WHEN 
POSITIVE AND NEGATIVE REINFORCEMENT COMPETE 
IN CONCURRENT SCHEDULES 
 
Michael Austin Magoon 
 
 
 
A Dissertation 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Doctor of Philosophy 
 
 
 
Auburn, Alabama 
December 16, 2005
iii 
RESPONSE-CONSEQUENCE CONTINGENCY DISCRIMINABILITY WHEN 
POSITIVE AND NEGATIVE REINFORCEMENT COMPETE 
IN CONCURRENT SCHEDULES 
 
Michael Austin Magoon 
 
 
 
Permission is granted to Auburn University to make copies of this dissertation at its 
discretion, upon request of individuals or institutions, and at their expense. 
The author reserves all publication rights. 
 
 
 
 ___________________________ 
 Signature of Author 
 
 ___________________________ 
 Date of Graduation 
iv 
DISSERTATION ABSTRACT 
RESPONSE-CONSEQUENCE CONTINGENCY DISCRIMINABILITY WHEN 
POSITIVE AND NEGATIVE REINFORCEMENT COMPETE 
IN CONCURRENT SCHEDULES 
 
Michael Austin Magoon 
Doctor of Philosophy, December 16, 2005 
(M.S., Auburn University, 2001) 
(B.A., The Florida State University, 1996) 
(A.A., Indian River Community College, 1994) 
208 Typed Pages 
Directed by M. Christopher Newland 
 Four experiments were conducted to test the qualitative prediction of contingency 
discriminability theory that any difference in type between the consequences of 
concurrently available discriminated operants will heighten response-consequence 
contingency discriminability and increase behavioral sensitivity to those consequences.  
In each experiment, three human subjects working under two-ply concurrent schedules of 
variable-cycle money reinforcement completed four experimental conditions in each of 
two phases.  The phases differed from each other only in terms of the type of 
reinforcement contingency and/or the way in which the consequent stimuli were 
presented.  Primary analyses were carried out via the standard conventions of the 
v 
generalized matching relation.  In Experiment 1, one phase consisted of concurrent 
schedules of positive versus positive reinforcement and the other consisted of concurrent 
schedules of positive versus negative reinforcement (avoidance).  All subjects 
demonstrated steeper matching function slopes in the phase that arranged concurrently 
available different types of consequences.  Experiments 2 and 3 were designed to test the 
necessity and/or sufficiency of two features that distinguish positive from negative 
reinforcement in Experiment 1:  money gain versus money loss; and the presentation of 
feedback after subjects met versus failed to meet the reinforcement contingency.  Both 
features were sufficient, but neither was necessary, to produce a slope effect similar to 
that seen in Experiment 1.  Experiment 4 differed from Experiments 1-3 by arranging 
concurrently available same-type consequences within each phase, but having the types 
differ across phases.  No systematic slope effects were observed in Experiment 4.  
Overall, the results supported the qualitative prediction of contingency discriminability 
theory that any difference in type between the consequences of concurrently available 
discriminated operants will heighten response-consequence contingency discriminability 
and increase behavioral sensitivity to those consequences.  These results are discussed in 
terms of the potential utility of the present methods to advance further research into the 
effects of choice-controlling variables other than reinforcement frequency, and in terms 
of some issues that must be resolved prior to doing so. 
vi 
ACKNOWLEDGEMENTS 
 The author would like to extend warmest thanks to Tom Critchfield for offering 
the opportunity for this research to take place at Illinois State University.  Without his 
conceptual, editorial, financial, and personal support, this dissertation never would have 
been completed.  Greatest thanks are also offered to Chris Newland for seeing it through 
to the end, though he was under no obligation to do so, and for providing some of his 
ICRE funds for the research.  Thanks are also due to Martha Escobar and Jim McCoy for 
agreeing to serve as committee members and for expanding the intellectual discourse.  
Pete Johnson, the outside reader, also deserves special thanks for working hard to 
expedite the dissertation completion process at the end. 
 In addition to those directly involved with development of the document, the 
author would like to thank Barry Burkhart, Chair of the Department of Psychology at 
Auburn University, for helping to secure a departmental graduate research grant, and 
David Barone, Chair of the Department of Psychology at Illinois State University, for 
offering the author a teaching position during a portion of his time there. 
 Many thanks also to Mei-Shio Jang for writing the computer program and for 
helping to extract the relevant data, to Dustin Merrill for his assistance with some 
portions of data collection, and to Chris Krageloh for his advanced empirical and 
conceptual help. 
 Finally, thanks to Thane Bryant and Alice Carroll for their usually unheralded 
help with administrative processes and paperwork.  Their help was particularly needed 
given that this research was carried out from a distance, and therefore is especially 
appreciated. 
vii 
Style manual or journal used: 
 
American Psychological Association.  (2001).  Publication manual of the American 
Psychological Association (5
th
 ed.).  Washington, DC:  Author. 
 
Computer software used: 
 
 QuickBasic 4.5 
 Microsoft Word 2002 SP3 
 Microsoft Excel 2002 SP3 
 SPSS (Release 11.5.0) 
viii 
TABLE OF CONTENTS 
LIST OF TABLES AND FIGURES............................................................................... xiv 
CHAPTER 1: 
LITERATURE REVIEW 
 Introduction............................................................................................................ 1 
 Concurrent Schedules and the Matching Relation................................................. 2 
  The strict matching relation........................................................................ 2 
  The generalized matching relation............................................................. 6 
 Contingency Discriminability Theory.................................................................. 10 
  Classical signal detection theory.............................................................. 10 
  Initial integration...................................................................................... 12 
  Testing the models and their assumptions................................................ 16 
 The Differential Outcomes Effect........................................................................ 25 
  The utility of the GMR in testing the DOE.............................................. 27 
 The Matching Relation and Negative Reinforcement.......................................... 28 
  Research with nonhumans........................................................................ 28 
  Research with humans.............................................................................. 35 
  Summary.................................................................................................. 47 
 Rationale for Current Studies............................................................................... 48 
  Magoon and Critchfield (2005) replication.............................................. 48 
ix 
  Investigation of sensitivity differences.................................................... 50 
 References............................................................................................................ 53 
 Footnote................................................................................................................ 62 
 Figure Caption...................................................................................................... 63 
 Figure................................................................................................................... 64 
CHAPTER 2: 
RESPONSE-CONSEQUENCE CONTINGENCY DISCRIMINABILITY WHEN 
POSITIVE AND NEGATIVE REINFORCEMENT COMPETE IN CONCURRENT 
SCHEDULES 
 Introduction.......................................................................................................... 65 
GENERAL METHOD 
 Subjects................................................................................................................ 72 
  Participants............................................................................................... 72 
  Money Earnings and Payment.................................................................. 72 
 Setting and Apparatus.......................................................................................... 73 
 Procedure.............................................................................................................. 73 
  Instructions............................................................................................... 73 
  Experimental task..................................................................................... 74 
  Schedules.................................................................................................. 75 
  Consequences........................................................................................... 76 
  Stability criteria........................................................................................ 76 
 Data Analysis....................................................................................................... 76 
x 
Experiment 1.................................................................................................................... 77 
 Method................................................................................................................. 77 
 Results.................................................................................................................. 79 
  Slopes (Sensitivity) 
   Visual analysis............................................................................. 80 
   Descriptive analysis..................................................................... 80 
   Normative analysis....................................................................... 80 
   Inferential statistical analysis....................................................... 82 
  Intercepts (Bias) 
   Visual analysis............................................................................. 84 
   Descriptive analysis..................................................................... 84 
   Normative analysis....................................................................... 85 
   Inferential statistical analysis....................................................... 85 
  Experiment 1 Results Summary............................................................... 87 
 Discussion............................................................................................................ 87 
Experiment 2.................................................................................................................... 89 
 Method................................................................................................................. 90 
 Results.................................................................................................................. 91 
  Slopes (Sensitivity) 
   Visual analysis............................................................................. 92 
   Descriptive analysis..................................................................... 92 
   Normative analysis....................................................................... 93 
   Inferential statistical analysis....................................................... 93 
xi 
  Intercepts (Bias) 
   Visual analysis............................................................................. 93 
   Descriptive analysis..................................................................... 94 
   Inferential statistical analysis....................................................... 94 
  Experiment 2 Results Summary............................................................... 95 
 Discussion............................................................................................................ 96 
Experiment 3.................................................................................................................... 97 
 Method................................................................................................................. 98 
 Results.................................................................................................................. 99 
  Slopes (Sensitivity) 
   Visual analysis........................................................................... 100 
   Descriptive analysis................................................................... 100 
   Normative analysis..................................................................... 100 
   Inferential statistical analysis..................................................... 101 
  Intercepts (Bias) 
   Visual analysis........................................................................... 101 
   Descriptive analysis................................................................... 101 
   Inferential statistical analysis..................................................... 102 
  Experiment 3 Results Summary............................................................. 103 
 Discussion.......................................................................................................... 103 
Experiment 4.................................................................................................................. 104 
 Method............................................................................................................... 106 
 Results................................................................................................................ 106 
xii 
  Slopes (Sensitivity) 
   Visual analysis........................................................................... 107 
   Descriptive analysis................................................................... 107 
   Normative analysis..................................................................... 108 
   Inferential statistical analysis..................................................... 108 
  Intercepts (Bias) 
   Visual analysis........................................................................... 108 
   Descriptive analysis................................................................... 108 
   Inferential statistical analysis..................................................... 109 
  Experiment 4 Results Summary............................................................. 110 
 Discussion.......................................................................................................... 110 
GENERAL DISCUSSION 
 Results Summary............................................................................................... 111 
 Implications for Quantitative Model Development of CDT.............................. 114 
 Evaluating GMR Parameter Differences........................................................... 118 
 A Methodological Concern of the Present Investigation................................... 123 
 Conclusion......................................................................................................... 125 
References...................................................................................................................... 127 
Footnotes........................................................................................................................ 134 
Tables............................................................................................................................. 135 
Figure Captions.............................................................................................................. 152 
Figures............................................................................................................................ 154 
Appendix A.................................................................................................................... 159 
xiii 
Appendix B.................................................................................................................... 164 
CHAPTER 3: 
EXTENDED GENERAL DISCUSSION 
 Introduction........................................................................................................ 176 
 Studies of Reinforcer Magnitude as a Framework for Studies 
  of Reinforcer Type................................................................................. 178 
 Comments on the DLOE.................................................................................... 184 
  On reinforcer type versus magnitude..................................................... 184 
  Reinforcer type differences and bias...................................................... 184 
  On the provisional status of the DLOE.................................................. 186 
  Concatenating the DLOE....................................................................... 187 
References...................................................................................................................... 189 
Figure Caption................................................................................................................ 192 
Figure............................................................................................................................. 193 
xiv 
TABLES AND FIGURES 
Chapter 1: Literature Review 
 Figure 1.  SDT Matrix.......................................................................................... 64 
Chapter 2: Response-Consequence Contingency Discriminability when Positive and 
 Negative Reinforcement Compete in Concurrent Schedules 
 Table 1.  Experiment 1 Conditions.................................................................... 135 
 Table 2.  Experiment 2 Conditions.................................................................... 137 
 Table 3.  Experiment 3 Conditions.................................................................... 139 
 Table 4.  Experiment 4 Conditions.................................................................... 141 
 Table 5.  Experiment 1 Independent Regressions.............................................. 143 
 Table 6.  Experiment 1 MRC Regressions......................................................... 144 
 Table 7.  Experiment 2 Independent Regressions.............................................. 145 
 Table 8.  Experiment 2 MRC Regressions......................................................... 146 
 Table 9.  Experiment 3 Independent Regressions.............................................. 147 
 Table 10.  Experiment 3 MRC Regressions....................................................... 148 
 Table 11.  Experiment 4 Independent Regressions............................................ 149 
 Table 12.  Experiment 4 MRC Regressions....................................................... 150 
 Table 13.  Overall Results Table........................................................................ 151 
 Figure 1.  Matching functions for Experiment 1................................................ 154 
 Figure 2.  Matching functions for Experiment 2................................................ 155 
xv 
 Figure 3.  Matching functions for Experiment 3................................................ 156 
 Figure 4.  Matching functions for Experiment 4................................................ 157 
 Figure 5.  Slopes and Slope Differences............................................................ 158 
Chapter 3: Extended General Discussion 
 Figure 1.  Intercept and Intercept Differences................................................... 193 
1 
CHAPTER 1 
Literature Review 
 Most operant research can be characterized as belonging to one of two broad, and 
typically mutually exclusive, categories:  stimulus control and consequence control.  
Studies of stimulus control tend to hold constant maximally different consequence 
conditions (e.g., continuous reinforcement versus extinction) and vary antecedent stimuli.  
Studies of consequence control tend to hold constant antecedent stimuli and vary one or 
more different consequence dimensions (e.g., frequency, magnitude, type, delay, etc.).  
The formulation of a unified theory capable of accounting for results from both domains 
would be a landmark achievement. 
 Unfortunately, conceptual and quantitative theory development of both stimulus 
and consequence control have not proceeded in parallel ? the study of consequence 
control has been arguably more successful (Davison, 1991).  Nevertheless, integration of 
an apparently successful theory of consequence control with the apparently equally 
successful signal detection theory (SDT) has led to the emergence of contingency 
discriminability theory (CDT) as a potential unifying theory.  The two purposes of this 
literature review are to describe the course of development of CDT and to propose 
research that might aid in its further conceptual and quantitative development.  The 
former will be accomplished by first examining the evolution of the matching relation 
and then by describing its integration with SDT.  The latter will be accomplished by
2 
reviewing research that used the matching relation to study negative reinforcement,
1
 but 
that may have unintentionally harnessed an effect predicted by CDT, and then by 
critiquing that research and offering suggestions as to how to improve it. 
Concurrent Schedules and the Matching Relation 
 Ferster and Skinner (1957) exposed pigeons to two response keys on the same 
wall of an experimental operant chamber, programmed schedules of reinforcement on 
each key such that responses on one key did not influence the schedule on the alternate 
key (i.e., they were programmed independently), and described response patterns on each 
of the keys.  Findley (1958) was the first to characterize behavior under this arrangement 
beyond mere description.  He suggested that preference and switching, rather than the 
schedule induced behavior on each key, were the two fundamental characteristics of such 
behavior.  He defined switching as an ?alternation in prepotency? of the two operants and 
preference as when an organism is ?emitting one operant to the partial exclusion of the 
other? (p. 123).  To the extent that an organism is said to choose an option it most prefers, 
concurrent schedule arrangements provide an experimental vehicle by which to quantify 
the relative reward value of different conditions of reinforcement (deVilliers, 1977). 
 The strict matching relation.  Findley (1958) set out to replicate the findings of 
Ferster and Skinner (1957).  His initial cumulative records made it apparent that pigeons? 
switches between schedules were only observable when there was a 5 s delay imposed 
between a switch and the delivery of a reinforcer on the other schedule.  As a result, he 
developed a new procedure (a) to make the switching behavior more explicit, and (b) to 
specify clearly the stimulus occasion for each response to make it more subject to the 
control of the experimenter.  His new method, the switching-key, changeover-key, or 
3 
Findley procedure also used two response keys.  However, in contrast to the traditional 
procedure, one key was specified as the response key on which responses were subject to 
the contingencies specified by the experiment and the other key was designated the 
switching or changeover (CO) key.  The function of the CO key was to alternate the 
schedules operating on the response key.  Typically, the CO key is associated with a light 
different in color from the ones associated with each of the schedules programmed on the 
response key.  A response on the CO key, then, actually has two functions:  (a) to change 
the schedule operating on the response key; and (b) to change the color of the light 
associated with the schedule on the response key.  Although the two-key procedure and 
the CO-key procedure seem to be very dissimilar methodologically, empirical evidence 
suggests that performance on the two procedures appear to be functionally identical 
(Davison & McCarthy, 1988). 
 Findley (1958) arranged his concurrent schedules so that one schedule remained 
constant across conditions and the other varied the rate of reinforcers delivered.  He 
found that under these conditions pigeons? response rates on one schedule were increased 
by increased reinforcement rates on that schedule and were decreased by increased 
reinforcement rates on the other schedule.  This relation was confounded, however, 
because the absolute reinforcement rate changed from condition to condition.  Herrnstein 
(1961) sought to rectify this problem by holding the overall reinforcement rate constant 
while varying the distribution of reinforcement delivery across the two keys via differing 
variable interval (VI) schedules.  He exposed pigeons to a two-key procedure and 
manipulated the use of a changeover delay (COD).  Only with a COD in effect did he 
find an orderly relationship between the relative rates of reinforcement delivered on the 
two keys and the relative rates of responding on the two keys.  The relationship 
conformed to the quantitative relationship, 
 
21
1
21
1
RR
R
BB
B
+
=
+
,        (1) 
where B
x
 is the number of responses to option x and R
x
 is the number of reinforcers 
delivered on option x.  This equation described the general relationship, but was later to 
be modified according to further empirical findings. 
 Herrnstein (1961) unsuccessfully attempted to fit data from several previous 
experiments to his new equation.  He found that data from single-key experiments, data 
from multiple schedule experiments, and data from experiments where there was no COD 
deviated from strict matching (Herrnstein, 1961).  Subsequent experiments validated the 
necessity of the COD (Catania, 1963a; Catania & Cutts; 1963); increased the generality 
of the relationship across subjects (Catania & Cutts, 1963; Shull & Pliskoff, 1967), 
procedures (Shull & Pliskoff, 1967), and reinforcers (Shull & Pliskoff, 1967); extended 
the relationship to matching with the relative size of reinforcers (Catania, 1963b; 
Neuringer, 1967) and with the relative delays to reinforcers (Chung & Herrnstein, 1967); 
and extended the equation to include other constants (Catania, 1963a).  Including 
constants in the equation was actually suggested by Herrnstein (1961) when he noted that 
the function was probably not linear but instead was probably concave downward (i.e., 
negatively accelerated).  In spite of these empirical validations (Catania, 1966), his 
equation was still not able to account for data obtained with single-key and multiple 
schedule arrangements. 
4 
 Herrnstein (1970) revised Equation 1 to include two free parameters that would 
better accommodate data that did not fit the original equation, particularly data from 
single-key and multiple schedule arrangements.  The new equation, 
 
o
RmRR
kR
B
++
=
21
1
1
,        (2) 
was based on new assumptions.  First, his original equation assumed that the only 
responses available to the subject were the ones explicitly programmed by the 
experimenter.  He thought this unlikely and probably the basis for the equation not being 
able to account for responding in single-key procedures.  ?A more defensible assumption 
is that at every moment of possible action, a set of alternatives confronts the animal, so 
that each action may be said to be the outcome of a choice? (Herrnstein, 1970, p. 254).  In 
essence, he was saying that just because the organism was not responding on the 
experimental manipulanda does not mean that it is doing nothing.  In all likelihood, it is 
doing something else, albeit unmeasured, that is being reinforced by something that is 
also unmeasured.  The addition of the constant k is meant to quantify all measured and 
unmeasured responses in units commensurate with the measured response (i.e., k = B
1
 + 
B
o
) and the addition of the R
o
 parameter is meant to quantify all unmeasured reinforcers 
in units commensurate with the experimenter-defined reinforcers (Herrnstein, 1970). 
 A second novel assumption had to do with the interactions of schedules over 
temporal distance (Herrnstein, 1970), that is, with multiple schedules.  In concurrent 
schedules, all sources of reinforcement can plausibly be assumed to exert their effects on 
all operating schedules, that is, a full interaction of schedules can be expected 
(Herrnstein, 1970).  However, multiple schedules do not allow for such an assumption.  
5 
In the case of multiple schedules, the organism is exposed to only one schedule at a time 
and has no control over changing them.  Therefore, it can be assumed that the further 
removed from one another the schedules are, the less each will interact with the other.  
This additional assumption was reflected in his quantitative formulation by adding 
another ?scaling? constant, m, which could range from 0 to 1 representing the degree of 
interaction between schedules.  If there were maximum interaction between schedules 
(i.e., concurrent schedules), the constant would be 1 and would reduce the equation to the 
concurrent formulation.  Any deviation from maximum interaction would reduce the 
scaling constant accordingly. 
 Rachlin (1971) criticized Herrnstein?s approach as tautological in that changing 
quantitative formulations to accommodate new assumptions has merit but does not 
describe the most appropriate way for an empirical law to evolve.  He suggested that new 
assumptions needed to be borne out from empirical validation.  Davison and McCarthy 
(1988) reviewed how the data collected to the point of their writing failed to reconcile 
Herrnstein?s (1970) quantitative formulation with his theoretical interpretation primarily 
due to the demonstrated lack of independence between response parameters and 
reinforcement parameters (Davison & McCarthy, 1988, pp. 35-38). 
 The generalized matching relation.  Baum (1974) noted that in several cases 
where strict matching (i.e., Herrnstein?s 1961 formulation) could not be found, 
reexamination of the data via an algebraic equivalent (i.e., as a ratio) brought order to 
seemingly disorderly data.  His generalized matching relation (GMR) thus took the form, 
 
a
R
R
c
B
B
?
?
?
?
?
?
?
?
=
2
1
2
1
,         (3) 
6 
and describes a power function similar to what Herrnstein (1961) originally proposed.  
The log-linear transform of Equation 3 is 
 c
R
R
a
B
B
logloglog
2
1
2
1
+
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
       (4) 
and yields linear functions to which Baum (1974) knew of ?no study of simple concurrent 
schedules in which the data fail to conform? (p. 231).  This equation uses two parameters 
that can be derived from the data and used to describe various deviations from 
Herrnstein?s equation, yet it retains the formal properties of Herrnstein?s (1961) original, 
or strict, matching relation because Equations 3 and 4 reduce to the ratio form of 
Equation 1 when the added parameters each equal one.  The additional parameters are 
described by Baum (1974) as accounting for what he called bias (log c) and sensitivity 
(a) of behavior to various experimental (or nonexperimental) conditions. 
 ?Bias means unaccounted for preference? (Baum, 1974, p. 233).  It indicates a 
stable preference between either the responses or the reinforcers within a given 
experimental arrangement.  Sometimes these preferences are unaccounted for as Baum 
described them and other times they may be manipulated to see how they vary with other 
independent variables.  Other forms of the GMR have specified the various parameters 
that may be responsible for biased matching (e.g., the concatenated matching relation, see 
Davison & McCarthy, 1988, for a discussion).  It was Baum?s contention that when 
matching is not found, it is not because the equation is inadequate, or that something is 
wrong with the organism being studied, but that the experimenter has failed to control or 
measure all of the relevant independent variables.  If, for example, the methods of an 
experiment are such that everything is held constant and the only difference that remains 
7 
8 
is a particular contingency difference (e.g., positive vs. negative reinforcement), and a 
bias is revealed, the results could be interpreted as a preference for that programmed 
difference. 
 Sensitivity is less well understood.  Baum (1974) described two types of 
sensitivity, overmatching and undermatching.  Overmatching is the situation where an 
organism responds more than predicted by strict matching to the schedule providing the 
more frequent reinforcement (i.e., the richer schedule) and less than predicted to the 
schedule providing the less frequent reinforcement (i.e., the leaner schedule).  
Quantitatively, this results in a value of a greater than one.  Undermatching is the reverse 
situation where an organism responds less than predicted to the richer schedule and more 
than predicted to the leaner schedule.  This results in a value of a less than one.  The 
reasons for sensitivity deviations from matching have not yet been fully explicated 
(Baum, 1974, 1979; Davison & McCarthy, 1988; Davison & Nevin, 1999; deVilliers, 
1977; Madden & Perone, 1999). 
 Baum (1974) offered three preliminary possibilities.  First, he thought 
undermatching likely if there were poor discrimination between alternatives.  It might be 
assumed that conversely he thought overmatching would be the product of heightened 
discrimination between alternatives although he did not say as much.  Second, he thought 
that too short a COD would result in undermatching and that increasing COD?s would 
shift the matching relation toward overmatching.  This possibility is related to the first 
because presumably a longer COD helps to differentiate the two response options from 
each other (Findley, 1958; Herrnstein, 1961).  Third, he thought that increased 
deprivation would result in undermatching and decreased deprivation would result in 
9 
shifts toward overmatching because, when satiated, there are decreases in overall 
responding and of rate of changeover.  He buttresses this point by referring to his own 
previous research where satiated pigeons conformed to the matching relation in the 
absence of a COD. 
 In a subsequent paper devoted exclusively to further understanding sensitivity in 
the matching relation, Baum (1979) evaluated the distribution of sensitivity values (i.e., a 
values) across all the data he had on hand and offered a new possible reason for 
deviations from unity.  He determined matching equation parameters using both least 
squares and nonparametric regression procedures for individual subjects from 23 
different studies varying across labs, species (rats, pigeons, and humans), responses 
(lever press, key peck, button press), dependent measures (responses and time), and 
procedures (changeover-key, two-key, and three-key under forced changeover and 
independent schedules).  His analyses revealed that time measures more closely 
approximated strict matching (a values distributed around 1.0) than response measures (a 
values distributed around 0.8).  To him this meant that local response rates on the leaner 
alternative must be different from the rates at the richer alternative.  He ascribed these 
local reinforcement rate differences to asymmetrical pausing.  If pausing is favored at the 
richer alternative, overmatching is observed.  If pausing is favored at the leaner 
alternative, undermatching is observed.  Since his own observations revealed the latter to 
be the norm, he concluded that, in addition to his previous reasons, a further possible 
reason for observed undermatching is more frequent pausing on the leaner alternative. 
 Baum (1974, 1979) believed unit sensitivity and bias (i.e., strict matching) to be 
the norm in any standard rigorously controlled concurrent schedules arrangement.  He 
10 
thought bias deviations were a function of either (a) a response bias, (b) a discrepancy 
between scheduled and obtained reinforcement, (c) qualitatively different reinforcers, or 
(d) qualitatively different schedules (Baum, 1974).  He thought sensitivity deviations 
were a function of either (a) variables responsible for differentiating operants (e.g., 
exteroceptive stimuli, COD), (b) changing or differing deprivation levels (Baum, 1974, 
1979), or (c) asymmetrical pausing (Baum, 1979).  Baum?s conclusions regarding bias 
have been generally accepted with some added parameters (see Davison & McCarthy, 
1988).  His conclusions regarding sensitivity have not proven to be fully adequate and 
have continued to be vetted though various means and methods.  SDT and its integration 
with the GMR offers a promising means by which to understand better the variables 
influencing sensitivity. 
Contingency Discriminability Theory 
 As progress was being made in the development of the matching relation, 
classical SDT (Green & Swets, 1966) was advancing a relatively successful quantitative 
model that ostensibly separated stimulus effects from other effects (e.g., consequences).  
Nevin (1969) was the first to identify the possible amalgamation of these two apparently 
disparate research domains by performing matching analyses of signal detection data.  
His work began an effort to develop an integrated quantitative model of behavioral 
detection that could account for both stimulus control and reinforcement effects that 
would eventually lead to the more general and conceptual CDT. 
 Classical signal detection theory.  Signal detection theory has its origins in 
classical psychophysics, which is concerned primarily with quantitative analyses of 
sensory thresholds.  In a most basic psychophysical absolute threshold experiment, a 
11 
stimulus is presented repeatedly at both increasing and decreasing intensities.  On each 
trial, the subject reports (verbally with humans, some other operant response with 
nonhumans) whether they sensed the stimulus.  By presenting the stimulus at both 
increasing and decreasing intensities, the experimenter can determine an average, or 
absolute threshold, for that stimulus for that subject. 
 Signal detection procedures use similar methods except that the signal is either 
presented with noise (i.e., some other distracting stimuli) (S
1
) or the noise is presented 
without the signal (S
2
) in discrete trials.  This allows four possible outcomes on each trial 
and is illustrated in Figure 1.  When the signal-with-noise (S
1
) is presented, the subject 
can report its presence (B
1
) or its absence (B
2
) corresponding to a hit (R
11
) or a miss (R
12
), 
respectively.  When the noise-without-signal (S
2
) is presented, the subject can also report 
its presence (B
1
) or its absence (B
2
) corresponding to a false alarm (R
21
) or a correct 
rejection (R
22
), respectively.  Since misses and correct rejections are the inverse counts of 
hits and false alarms, respectively, simply plotting the probability of hits as a function of 
the probability of false alarms reveals orderly relationships.  The curves generated this 
way are called receiver-operating characteristic curves. 
 Probabilities are used to generate the curves because the theory assumes that 
probability distributions (usually normal but different versions use different types), one 
representing the internally observed effects of each stimulus, interact with each other and 
with other ?subject? variables to determine the response on a particular trial.  d' is the 
measure of the distance between these hypothesized probability distributions (in standard 
deviation units under the assumption of normal distributions) and represents sensory 
sensitivity between the two stimuli.  ? is the measure of the other ?subject? variables 
12 
mentioned above.  The complete rationale for its value is beyond the scope of this paper 
(see Green & Swets, 1966, ch. 4), but it is based on assumptions revolving around the 
?rationality of maximization.?  Suffice it to say that it represents the bias a subject brings 
to the situation.  According to the theory, the bias can be the product of pre-experimental 
biases, expectations based on instructions, the consequences of responding, and/or any 
other nonstimulus variables (as defined by the experimenter).  The logic behind the 
determination of ? is, in fact, a part of the basis for Nevin?s (1969) call for integration 
with the matching relation.  More will be said on this below.  In any case, the point at 
which the bias value intersects with the overlapping probability distributions is the 
decision point.  It is further assumed that, for any given observation of a stimulus, the 
subject transforms the probability distributions into a ?likelihood ratio.?  If the likelihood 
ratio exceeds ?, one response will occur and if it is less than ?, the other will occur. 
 Initial integration.  ?The most striking achievement of the theory is that if signal 
strength is constant, d? remains the same within variations of any given 
experiment?More importantly, it remains constant across different classes of 
experiment? (Nevin, 1969, p. 477).  This feature, combined with SDT?s failure to deal 
effectively with response bias and the matching relation?s success in quantifying the 
effects of differential reinforcement, is probably what made integration of the two so 
attractive.  Signal detection theory isolated stimulus control effects while being unable to 
explain reinforcer effects, and the matching relation isolated reinforcer effects while 
being unable to account for stimulus control effects.  Several researchers thought that the 
matching relation might provide a reasonable bias function for SDT. 
13 
 Aside from the conceptual similarity of the two research domains, Nevin (1969) 
also proposed that multiple concurrent schedules were methodologically parallel to those 
used in classical signal detection research.  Typical SDT research follows each correct 
response (i.e., hits and correct rejections) with some sort of reinforcement (e.g., food, 
feedback, points) and each incorrect response (i.e., misses and false alarms) with 
punishment or extinction.  A multiple concurrent FR1 Ext. concurrent Ext. FR1 schedule 
mimics this procedure and, if arranged in discrete trials, exactly replicates it.  When one 
component of the multiple schedule, signaled by a distinct stimulus (S
1
), is presented, one 
response (B
1
) is reinforced (R
11
) and the other (B
2
) is not (R
12
).  When the other 
component, signaled by a different distinct stimulus (S
2
), is presented, the previously 
reinforced response (B
1
) is no longer reinforced (R
21
) and the other one (B
2
) is (R
22
). 
 Nevin (1981) reported a behavioral detection model, initially presented at the 
1977 meeting of the Psychonomic Society, which used Herrnstein?s (1961) strict 
matching relation for its bias function.  He started by noting that application of the strict 
matching relation to the signal detection paradigm leads to a problem.  If reinforcement is 
delivered only for B
1
 and never for B
2
 in the presence of S
1
 (i.e., R
11
 = reinforcement, R
12
 
= extinction), and only for B
2
 and never for B
1
 in the presence of S
2
 (i.e., R
22
 = 
reinforcement, R
21
 = extinction), then only B
1
 should occur in the presence of S
1
 and only 
B
2
 should occur in the presence of S
2
.  That is, there should be perfect responding, no 
errors.  In contrast to that expectation, errors are found to occur consistently under such 
circumstances (Nevin, 1981).  Nevin (1981) proposed that the effect of a reinforcer for a 
response in the presence of one stimulus generalizes to strengthen the same response in 
the presence of the other stimulus and that the subject distributes its responses to match 
the ratio of the combination of direct and generalized reinforcement.  He incorporated a 
new parameter, ?, designating the similarity of S
1
 and S
2
, to account for the generalization 
of reinforcement effects.  The resulting equations were, in the presence of S
1
, 
 
22
11
2
1
R
R
B
B
?
= ,         (5) 
and in the presence of S
2
, 
 
22
11
2
1
R
R
B
B ?
= .         (6) 
He suggested that 1/? was an index of discriminability closely related to Green and 
Swet?s (1966) d?.  Furthermore, from his new equations he could easily derive an 
isosensitivity curve equation and an isobias curve equation that were identical to a 
previously developed linear learning model based on ?rather abstract considerations of 
choice theory? (Nevin, 1981, p. 12).  He described his model as leading ?to predictions 
that cannot readily be distinguished from those of the elaborate conceptual machinery of 
classical signal detection theory? (Nevin, 1981, p. 14). 
14 
 At the same time as Nevin was presenting his model in 1977, Davison and Tustin 
(1978) independently developed their own version of the behavioral detection model.  
The primary difference between the models was that Davison and Tustin (1978) used 
Baum?s (1974) GMR as the basis for their bias function instead of the strict matching 
relation.  Furthermore, they proposed a different conceptual mechanism through which 
differential stimuli influenced response distribution.  In their model, differential stimuli 
did not influence responding simply through stimulus generalization as proposed by 
Nevin (1981), but more specifically, it assigned a biasing role for stimuli much like that 
for reinforcers.  In the presence of S
1
, responding became more biased toward B
1
, and in 
the presence of S
2
, responding became more biased toward B
2
.  Their new equations 
were, in the presence of S
1,
 
a
R
R
cd
B
B
?
?
?
?
?
?
?
?
=
22
11
2
1
,        (7) 
and in the presence of S
2
, 
 
a
R
R
d
c
B
B
?
?
?
?
?
?
?
?
=
22
11
2
1
.        (8) 
The log-linear transform of Equations 7 and 8 are, in the presence of S
1
, 
 dc
R
R
a
B
B
R
loglogloglog
22
11
1
2
1
++
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
,     (9) 
and in the presence of S
2
, 
 dc
R
R
a
B
B
R
loglogloglog
22
11
2
2
1
?+
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
.     (10) 
a
Rx
 represents sensitivity to changes in reinforcement rate in the presence of stimulus x.  
At this point in the development of their model, they assumed sensitivity to reinforcement 
to be the same in the presence of S
1
 as it is in the presence of S
2
 (i.e., a
R1
 = a
R2
).  This 
assumption would later prove to be the source of an important change in their model.  
Log d is the bias caused by the signaling stimulus.  Equations 9 and 10 both have the 
same response in the response ratio numerator (B
1
), thus log d is added in Equation 9, 
reflecting a bias toward that response in the presence of S
1
, and is subtracted in Equation 
10, reflecting a bias away from that response in the presence of S
2
.  It is easier to see in its 
log-linear form that they were treating stimulus effects similarly to reinforcement effects 
15 
16 
in that they each biased responding.  It was the first suggestion that no distinction 
between the discriminative and reinforcing functions of stimuli is logically necessary. 
 Two points are clear from Equations 9 and 10.  First, when there is no 
discrimination between stimuli (i.e., log d = 1) Equations 7 and 8 and Equations 9 and 10 
reduce to Equations 3 and 4 (the GMR), respectively, thus preserving the fundamental 
matching relationship.  Second, stimulus biases (log d) are independent of both inherent 
bias (log c) and reinforcement effects [a log (R
11
/R
22
)] thus preserving the fundamental 
SDT discriminability and bias independence.  Furthermore, the isosensitivity curve and 
isobias curve equations derived from Davison and Tustin?s (1978) equations (p. 333 
Equation 10 and p. 334 Equation 13) are mathematically identical to those found by 
Nevin (1981) (and by extension to a previous linear learning model) and Green and Swets 
(1966).  That the same equations were independently derived from several different 
perspectives is, indeed, of interest. 
 Testing the models and their assumptions.  Subsequent research extended the 
Davison-Tustin model to account for procedures that arranged reinforcement for ?errors? 
(Davison & McCarthy, 1980) following the suggestion of the Nevin (1981) model.  Thus, 
the Davison-Tustin model seemed to integrate successfully the considerations of all 
research perspectives (but see Nevin, Jenkins, Whittaker, & Yarensky, 1982 for a 
critique).  That is, until Miller, Saunders, and Bourland (1980) provided evidence that the 
Davison-Tustin assumption of reinforcement sensitivity invariance across stimulus 
disparity differences (McCarthy & Davison, 1979, 1980) was invalid. 
 The research done by Davison and McCarthy up to Miller et al.?s (1980) paper 
used discrete-trials methods (e.g., Davison & McCarthy, 1980; McCarthy & Davison, 
17 
1979, 1980).  Outside the context of Davison, McCarthy, and Nevin?s work, Miller et al. 
(1980) investigated the role of varying stimulus disparity in a free-operant changeover-
key procedure (Findley, 1958) using Baum?s (1974) original GMR.  They exposed three 
groups of pigeons to different line orientations on the response key.  Group 1 was the 0-
degree disparity group, that is, the line orientations indicating which component of the 
concurrent schedule was operating were not different from each other within subject but 
were different across subjects within group.  Group 2 was the 15-degree disparity group 
and Group 3 was the 45-degree disparity group.  All subjects were exposed to 
comparable relative reinforcement rate conditions.  Their results clearly showed that 
Baum?s (1974) measure of sensitivity (a) increased with increasing stimulus disparity and 
with increased absolute rates of reinforcement (see also Nevin, et al., 1982 for more on 
absolute rates of reinforcement).  The fundamental problem was that the Davison-Tustin 
model did not address the factors that determine sensitivity to reinforcement.  They 
simply continued to include it, as Baum (1974) had originally proposed, as a free 
parameter to be derived from the data.  In light of the evidence from Miller, et al. (1980) 
this position no longer was tenable. 
 Subsequent research tended to refute the assumptions that sensitivity to changes 
in relative reinforcement was independent of stimulus disparity (i.e., a
R1
 = a
R2
) and 
absolute rates of reinforcement (Davison, McCarthy, & Jensen, 1985; Logue, 1983; 
McCarthy, Davison, & Jenkins, 1982; White, Pipe, & McLean, 1984).  Consequently, 
Davison and Jenkins (1985) proposed a replacement for Baum?s (1974) GMR using a 
measure of response-consequence contingency discriminability in place of Baum?s free 
parameter a.  The proposed equation was 
 
?
?
?
?
?
?
?
?
+
+
=
12
21
2
1
RRd
RRd
c
B
B
br
br
,        (1) 
where d
br
 measures the discriminability of the operant classes signaled by the reinforcing 
stimuli.  Thus, this version of the matching relation has no free parameters; it has only a 
measure of inherent bias (log c) and a measure of reinforcement bias that is a function of 
frequency of reinforcement moderated by the ?confusability? of the response-
consequence contingency.  The confusability they defined as being partly due to the 
subject?s sensory ability and partly due to the stimuli signaling the reinforcement 
contingencies. 
 The process described by Equation 11 is similar to the generalized strengthening 
effect across stimuli proposed by Nevin (1981).  d
br
 varies between 1 (no response-
consequence contingency discriminability) and infinity (perfect response-consequence 
contingency discriminability).  When d
br
 = 1 the subject cannot discriminate which 
reinforcers resulted from which response.  Consequently, reinforcers for B
2
 (i.e., R
2
) 
affect B
1
 to the same degree as reinforcers for B
1
 (i.e., R
1
) and vice-versa, the effective 
reinforcement ratio reduces to 1, and the slope of the log-linear regression line (i.e., the 
matching function) is zero indicating no differential responding despite changes in 
relative rates of reinforcement.  When d
br
 = infinity, the effects of R
2
 on B
1
 and the 
effects of R
1
 on B
2
 are minimized, effectively to zero, resulting in a relative reinforcement 
ratio determined solely by R
1
 and R
2
.  The resulting equation is Baum?s (1974) GMR 
with no sensitivity parameter (i.e., a = 1).  This model does not allow for overmatching. 
18 
 Using their version of the matching relation in place of Baum?s (1974) GMR, 
Davison and Jenkins (1985) proposed a new version of the Davison and Tustin (1978) 
model of behavioral detection.  The resulting equations were, in the presence of S
1
, 
 
?
?
?
?
?
?
?
?
+
+
=
1122
2211
2
1
RRd
RRd
cd
B
B
br
br
sb
,       (12) 
and in the presence of S
2
, 
 
?
?
?
?
?
?
?
?
+
+
=
1122
2211
2
1
RRd
RRd
d
c
B
B
br
br
sb
,       (13) 
where d
sb
 serves the same function as d does in the Davison-Tustin model, but is 
subscripted to differentiate stimulus-response contingency discriminability from 
response-consequence contingency discriminability.  These equations maintain the 
independence of inherent bias, stimulus bias, and reinforcement bias and maintain the 
fundamental matching relationship, but are more specific regarding the measure of 
behavioral sensitivity to changes in relative rates of reinforcement.  Furthermore, by 
treating stimulus effects and reinforcement effects similarly mathematically, this 
formulation extends Davison and Tustin?s (1978) earlier contention that discriminative 
stimuli and reinforcers act on behavior in similar ways. 
 Although the Davison-Jenkins model appeared to be conceptually defensible, 
Alsop (1991) and Davison (1991) revealed a quantitative logical flaw.  Equations 12 and 
13 assume independent effects of d
sb
 and d
br
 which they contend ?is not a reasonable 
prediction? (Alsop, 1991, p. 43).  The Davison-Jenkins formulation mathematically 
asserts that if there is no response-consequence contingency discriminability (i.e., d
br
 = 
1), stimulus-response contingency discriminability will still exert its own independent 
19 
effect on behavior.  That is, the model predicts differential responding to two distinct 
stimuli even if the subject cannot discriminate differential reinforcement between the two 
responses.  It is not reasonable to predict, for example, that a red light signaling one 
reinforcement contingency and a green light signaling another reinforcement contingency 
could differentially affect behavior if the reinforcement contingencies themselves were 
indiscriminable from each other. 
 To remedy the quantitative flaw of Davison and Jenkin?s (1985) model, Alsop 
(1991) proposed the following modifications:  in the presence of S
1
, 
 
?
?
?
?
?
?
?
?
+
+
=
2211
2211
2
1
RdRd
RRdd
c
B
B
brsb
brsb
,       (14) 
and in the presence of S
2
, 
 
?
?
?
?
?
?
?
?
+
+
=
1122
1122
2
1
RRdd
RdRd
c
B
B
brsb
brsb
.       (15) 
Like the Davison-Jenkins detection model, when d
sb
 = 1 Equations 14 and 15 reduce to 
Davison and Jenkin?s (1985) matching relation (Equation 11).  However, unlike the 
Davison-Jenkins model, when d
br
 = 1, Equations 14 and 15 predict equal responding to 
B
1
 and B
2
. 
 Alsop (1991) provided the mathematical justification for the new version of the 
behavioral detection model, but Davison (1991) provided the initial conceptual 
justification.  To better illustrate its implications it is helpful to perform some simple 
mathematical operations and rewrite the equations as, in the presence of S
1
, 
20 
 
?
?
?
?
?
?
?
?
?
?
?
?
+
+
=
sbbr
brsb
d
R
d
R
dd
R
R
c
B
B
2211
22
11
2
1
,       (16) 
and in the presence of S
2
, 
 
?
?
?
?
?
?
?
?
?
?
?
?
+
+
=
22
11
2211
2
1
R
dd
R
d
R
d
R
c
B
B
brsb
brsb
.       (17) 
Davison (1991) argued that every ?stimulus/response/reinforcer combination?is 
discriminable from other such combinations as a function of the joint stimulus[-response 
contingency] and [response-consequence] contingency discriminabilities of the two 
combinations? (pp. 65-66).  Referring to Equation 16, it can be seen that, in the limits of 
perfect stimulus-response and response-consequence contingency discriminability (i.e., 
d
sb
 = d
br
 = infinity), the only effective reinforcement to influence B
1
 is R
11
; the other 
terms in the reinforcement bias portion of the equation functionally reduce to zero.  
Consequently, in the presence of S
1
, only B
1
 responses would be expected to occur 
(assuming no inherent bias, log c).  To extend the example to Equation 17, perfect 
stimulus-response and response-consequence contingency discriminability would result 
in a reinforcement bias of zero.  Thus, in the presence of S
2
, there is no effective 
reinforcement for B
1
 and therefore no such responses would be expected to occur.  In the 
other extreme, the limits of zero stimulus-response and response-consequence 
contingency discriminability (i.e., d
sb
 = d
br
 = 1) lead to reinforcement bias values of 1 in 
both Equations 16 and 17.  Accordingly, response ratio values in the presence of each of 
the stimuli would only be a function of inherent bias (log c). 
21 
22 
 It is also important to understand how stimulus-response and response-
consequence contingency discriminabilities function independently of one another.  If 
there were no stimulus-response discriminability and perfect response-consequence 
contingency discriminability (i.e., d
sb
 = 1 and d
br
 = infinity), Equations 16 and 17 would 
both reduce to Herrnstein?s (1961) strict matching equation with Baum?s (1974) bias 
parameter.  In effect, response distributions would be expected to be a strict function of 
relative reinforcement distribution independent of any stimulus effects.  In the case of 
perfect stimulus-response discriminability and zero response-consequence contingency 
discriminability (i.e., d
sb
 = infinity and d
br
 = 1), reinforcement bias effects would reduce 
to 1 in the presence of both stimuli and response distributions would only be a function of 
inherent bias.  That inherent bias is the only factor responsible for unequal response 
distributions whenever d
br
 = 1 demonstrates the presumed primacy of consequences by 
the Law of Effect (Thorndike, 1911).  Stimulus differences can only exert an effect (i.e., 
stimulus control) if there is some degree of response-consequence contingency 
discriminability. 
 Davison and Nevin (1999) reviewed and developed the model under a signal-
detection (i.e., conditional discrimination) paradigm and then extended it to see how well 
it described existing data in the areas of complex conditional discriminations, 
reinforcement for ?errors? in conditional discriminations, multiple schedules, and simple 
concurrent schedules.  They began by clarifying some of the model?s most fundamental 
assumptions.  First, that the concurrent discriminated operant is the fundamental analytic 
unit.  Second, that discriminative stimuli and reinforcers function similarly (i.e., they both 
effect behavior to the extent that their respective contingencies with their respective 
23 
responses are discriminable).  Third, that two processes occur in determining steady-state 
behavior (in its current form, the model does not account for acquisition, transition, or 
extinction).  The first process is one by which their discriminability parameters interact 
with environmental conditions to determine the effective allocation of reinforcers.  The 
second process is one by which behavior allocation strictly matches the effective 
reinforcer distributions. 
 They went on to describe fully the model as it applies to a 2x2 conditional 
discrimination analogous to the standard signal detection arrangement (i.e., a multiple 
concurrent VI Ext concurrent Ext VI schedule) emphasizing the interrelationships of d
sb
 
and d
br
 (Davison & Nevin, 1999, pp. 447-452).  Of particular interest here was how the 
model formally integrated the concept of stimulus generalization as responsible for the 
effective allocation of reinforcement effects following Nevin (1981).  They demonstrated 
the flexibility of the model in how it could be adapted to account for performance in 2x2 
conditional discrimination procedures with reinforcers for ?errors? and in complex 
conditional discriminations consisting of multiple stimuli and multiple responses. 
 Davison?s approach to model building is to let model changes be driven by data 
and then to test each new version against existing data (Davison, 1991).  Any model 
meant to replace an existing model must not neglect the data that led to the development 
of previous models.  Consequently, Davison and Nevin (1999) illustrated the goodness of 
fit of their model to 2x2 conditional discriminations, value transfer, reinforcement for 
errors, matching to sample and its variants (identity v. symbolic matching, delayed 
matching and delayed reinforcement, and second-order discrimination of mixed delays), 
complex stimulus discrimination, multiple stimuli and multiple correct responses, 
multiple schedules, and concurrent schedules.  In each case, they concluded that it 
described the data well. 
 Of particular interest to the present discussion is the model?s prediction regarding 
conventional two-response concurrent schedules.  Davison and Nevin (1999) made the 
case that in such an arrangement there is no conditional discrimination, just simple 
discrimination between alternatives.  Accordingly, there is no S
1
-S
2
 difference and 
therefore no need for two equations.  The corresponding equation is, 
 
?
?
?
?
?
?
?
?
?
?
?
?
+
+
=
br
br
d
R
R
d
R
R
c
B
B
1
2
2
1
2
1
.        (18) 
They described how this formulation successfully accounts for the data from studies that 
manipulated ?extraneous? reinforcement, overall reinforcement rates, extreme ratios of 
reinforcement, and concurrent VI Ext schedules.  However, they acknowledged that the 
model is not able to account for the effects of other choice-controlling variables such as 
reinforcer magnitude, delay, and quality, which are known to contribute to determination 
of behavior allocation in concurrent schedules.  The theoretical problem is that when one 
of these dimensions is differentially arranged for two or more choices, the reinforcer 
?value? (Baum & Rachlin, 1969) is changed concurrently with its discriminability.  They 
offered two possibilities, but concluded, ?a substantial research effort will be required to 
identify independent functions for the discriminability and value of the consequences of 
choice? (p. 472).  Nevertheless, a prediction of their specific model, and of CDT 
generally, is that qualitatively different reinforcers differentially presented in a two 
24 
25 
choice arrangement should add to the response-consequence contingency discriminability 
of the responses.  This prediction arises from work on the differential outcomes effect. 
The Differential Outcomes Effect 
 Trapold (1970) is credited with the first known study on what has come to be 
called the differential outcomes effect (DOE).  He was investigating the inferred role of 
the s
g
 component of Spence?s (1956) r
g
-s
g
 mechanism.  He reasoned that expectancies 
formed throughout the course of establishing the S-R association during instrumental 
conditioning could function as discriminative stimuli in much the same way as 
exteroceptive stimuli.  He proposed that if qualitatively different reinforcers were 
presented in a discrete trial conditional discrimination task, different expectations arising 
from the different reinforcers would each have their own differing stimulus properties.  
These stimulus properties should add to the stimulus complex and should therefore result 
in faster learning than if there were no differences between reinforcers (and thus 
discriminative stimuli).  He exposed rats to a discrimination problem that required a 
response to one lever in the presence of a clicking sound and a response to another lever 
in the presence of a tone.  He found an increased rate of acquisition and greater accuracy 
when correct responses to the clicking sound produced food and correct responses to the 
tone produced a sucrose solution than when both responses in the presence of either 
stimulus produced the same reinforcer. 
 The DOE is a robust phenomenon.  Goeters, Blakely, & Poling (1992) reviewed 
and summarized the DOE literature to date and identified 38 studies designed specifically 
to test for it.  They described how it had been demonstrated across a wide range of 
subjects including pigeons, rats, dogs, and humans, with a variety of consequences 
26 
including food versus water, with different delays to reinforcement, and with both within- 
and between-subject experimental designs.  However, all studies included in their review 
used discrete trials methods, typically some variation of a matching to sample procedure.  
In fact, no DOE studies since have been found to use a free-operant procedure.  
Furthermore, they identified only 7 studies that had been done with human subjects, all of 
which were classified as ?mentally retarded? or autistic, and two of which were 
?methodologically weak? (Goeters et al., 1992. p. 398) clinical reports with only one 
subject.  Furthermore, while Goeters et al. criticized the various studies? theoretical 
analyses because they continued to rely on expectancies, their proposed analysis is not 
much more convincing.  Their reliance on private events, interoceptive stimuli, and 
proprioceptive stimuli seems equally unamenable to direct investigation. 
 An alternative theoretical analysis was offered by Wixted (1989) and Alling, 
Nickel, and Poling (1991).  They suggested that sample-specific responding could 
enhance discrimination simply by increasing the discriminability of the sample stimuli 
(i.e., increase d
sb
).  This idea was quickly refuted by Urcuioli (1991) who clearly 
demonstrated retarded acquisition when particular outcomes always followed the same 
sample stimuli and unreliably followed the comparison stimuli, and facilitated acquisition 
when the same outcomes always followed the same sample and comparison stimuli.  He 
concluded, 
These results clearly demonstrate that differential outcomes do not affect 
conditional discrimination learning merely by enhancing the discriminability or 
distinctiveness of the sample with which they are associated.  Rather, they 
apparently give rise to another discriminative cue (viz., an outcome expectancy), 
27 
which can either enhance or interfere with performance, depending on its 
predictive validity.  (p. 29). 
It is unclear how confusable the outcomes may have been, but one outcome was food 
(delivered in the feeder) and the other was the feeder light being illuminated.  If nothing 
else, the spatial proximity of the two outcomes could have contributed to contingency 
discriminability (d
br
) and could thus have functioned as the other discriminative cue 
referred to by Urcuioli (1991).  It could be possible that an analysis of differential 
outcomes in the context of CDT could lead ?to predictions that cannot readily be 
distinguished from those of the elaborate conceptual machinery of? (Nevin, 1981, p. 14) 
expectations as discriminative stimuli. 
 The utility of the GMR in testing the DOE.  Baum?s (1974) GMR has been shown 
to be a generally reliable predictor of nonhuman operant behavior (deVilliers, 1977 but 
see Davison & McCarthy, 1988), has been shown in many cases to be suitable for 
describing human operant behavior (Pierce & Epling, 1983; but see Kollins, Newland, & 
Critchfield, 1997), and has been tested and expanded to consider more of the variables 
responsible for control of behavior (see Davison & McCarthy, 1988; Davison & Nevin, 
1999).  As such, it may be considered a useful tool with which to address some 
unanswered questions.  A concurrent schedules arrangement allows qualitatively different 
consequences to compete directly for control of behavior and the GMR?s bias and 
sensitivity parameters (log c and a, respectively) provide a means of quantitatively 
describing and comparing the behavioral response to those different outcomes.  Magoon 
and Critchfield (2005) took just this approach to investigate the relative effects of 
positive and negative reinforcement on human behavior.  They were interested in whether 
28 
a systematic bias would emerge if the two contingency types competed for behavior, but 
found unanticipated results.  To understand the relevance of their findings to CDT, it will 
be informative first to understand previous efforts to compare positive reinforcement to 
negative reinforcement within a generalized matching paradigm. 
The Matching Relation and Negative Reinforcement 
 Research with nonhumans.  Catania (1966) was the first to write a comprehensive 
review of research on concurrent schedules.  In that review, he discussed the research 
involving concurrent schedules of positive reinforcement and concurrent schedules of 
negative reinforcement.  There was little at the time and none of it had been evaluated in 
terms of Equation 1.  The primary concern of those previous studies was with dependent 
variables such as rate constancy and response independence (Catania, 1966).  Another 
reason why Equation 1 was not used prior to Catania?s writing was methodological in 
nature.  The programming of schedules of negative reinforcement up to that point was 
based on Sidman?s (1953) shock delay procedure where shocks are presented at regular, 
experimenter-defined intervals and each response delays the next shock presentation for a 
period also specified by the experimenter.  This procedure does not allow response rates 
to vary with changes in various dimensions of reinforcement (e.g., rate or magnitude) 
because of the temporal regularities imbedded in the programming (deVilliers, 1972). 
 deVilliers (1972) was the first to respond to Hineline?s (1970) suggestion that 
aversive conditioning procedures (i.e., negative reinforcement and punishment) should be 
studied in ways analogous to those used to study positive reinforcement.  He viewed 
Herrnstein?s (1970) revised equation as the vehicle that would allow such comparisons to 
be made.  However, in order to do that, he needed to develop a procedure for 
29 
programming schedules of negative reinforcement that would circumvent the problems 
associated with the Sidman?s (1953) method.  Sidman (1966) was the first to propose 
using fixed-cycle schedules to study negative reinforcement.  These types of schedules 
are different from Sidman?s (1953) schedules in that high rates of responding do not 
produce ever-increasing delays to shock.  In fixed-cycle procedures, the first response 
made in an interval deletes the next shock and subsequent responses have no further 
effect until a new cycle begins.  deVilliers (1972) modified the procedure to eliminate the 
predictability associated with fixed intervals by varying the intervals according to 
Fleshler and Hoffman?s (1962) progression.  The resulting variable cycle (VC) schedules 
of negative reinforcement share many of the same properties of VI schedules of positive 
reinforcement (Baron, 1991). 
 With his new procedure in hand, deVilliers (1972) was ready to examine the 
properties of negative reinforcement in much the same way that positive reinforcement 
had been researched.  In his first experiment, he arranged single and multiple schedules 
of shock maintained negative reinforcement for rats bar pressing and found contrast in 
the multiple schedule components similar to what Bloomfield (1967) found with positive 
reinforcement.  He then derived the free parameters in Herrnstein?s (1970) equation for 
multiple schedules from the data using both received shock rate and shock-frequency 
reduction as the reinforcers.  To test the validity of Herrnstein?s equations, he then used 
the obtained parameters and the obtained reinforcement rates from the single schedule 
components to solve for Herrnstein?s equation for single schedule performance again 
using both received shock rate and shock frequency reduction as the reinforcers.  The 
goal was to determine which conception of reinforcement was most appropriate for 
30 
studying negative reinforcement.  He found that Herrnstein?s single response equation 
predicted responding better when shock frequency reduction was used as the reinforcer 
maintaining responding. 
 Although this finding was important to the one- vs. two- factor theory-of-
avoidance debate (e.g., Anger, 1963; Baum, 2001; Dinsmoor, 2001; Herrnstein, 1969; 
Herrnstein & Hineline, 1966; Mowrer 1947; Rescorla & Solomon, 1967; Schoenfeld, 
1950; Sidman, 1962), the more important observation for present purposes is that ?the 
relationship between response rate and negative reinforcement in random-interval [read 
as VC] avoidance schedules is accurately described by the formulation of the law of 
effect developed by Herrnstein for positive reinforcement? (deVilliers, 1972, p. 506).  
This was the first attempt to examine negative reinforcement using similar procedures as 
those used to study positive reinforcement. 
 Although deVilliers (1972) validated the use of Herrnstein?s equations to study 
negative reinforcement in the same way as positive reinforcement, it did little to compare 
the two contingencies.  deVilliers (1974) ran a parametric study using the same 
procedures as he used before (deVilliers, 1972).  In his first experiment, he exposed rats 
to an array of single VC schedules of negative reinforcement.  He then fit the data to 
Herrnstein?s (1970) equation for single schedule performance and found that, when 
shock-frequency reduction was used as the reinforcer, it described the performance 
accurately.  Furthermore, he described his results as comparing favorably to those 
obtained by Catania and Reynolds (1968) for pigeons responding on VI schedules of food 
reinforcement.  In his second experiment, he used multiple VC schedules of negative 
reinforcement and varied the duration of the components.  He suggested that the 
31 
component duration in which the relative response rates were maximal would be the 
point at which interaction between schedules was maximal.  If Herrnstein?s interaction 
parameter is at maximum (i.e., equal to 1), that is the point where matching would be 
expected.  He found that maximal relative response rates were obtained with brief 
component durations (40 s) and that it was at that point where matching was obtained 
using Herrnstein?s (1970) equation for multiple schedules.  These and other features of 
the data were compared to results obtained with positive reinforcement and the general 
conclusion was that, if shock-frequency reduction is taken as the reinforcer for negative 
reinforcement, both can be integrated into the same conceptual framework.  These were 
not direct comparisons, however.  They were comparisons made across laboratories, 
subjects, reinforcers, and procedures.  Other means of comparison needed to be made. 
 Baum and Rachlin (1969) investigated the possibility that relative rates of 
reinforcement matched relative time rather than relative response rates on concurrent 
schedules.  To do so, they arranged an apparatus designed to record time spent in each of 
two simultaneously presented schedules while requiring nonspecific responses in those 
schedules.  Food reinforcement was presented at variable times while the pigeon was in 
each component.  They found that the pigeons matched the relative time spent in each 
schedule to the relative reinforcement obtained from each schedule. 
 Baum (1973) replicated Baum and Rachlin?s (1969) procedures exactly except 
using timeout from shock as the reinforcer instead of food delivery.  The physical 
appearance of the apparatus and the subjects used were the same as those used by Baum 
and Rachlin (1969).  By holding as much as possible constant across experiments except 
for the type of reinforcer, some of the difficulties found with deVilliers interpretations 
32 
were avoided.  The data were graphed both independently and in combination with the 
data from Baum and Rachlin?s (1969) study using positive reinforcement.  Graphed 
independently, the relative time spent in each schedule matched the relative number of 
timeouts from shock.  When viewed together the data from both studies showed some 
marked similarities.  First, the changeover patterns were similar although the range of 
changeovers was significantly more for negative reinforcement than it was for positive 
reinforcement.  Second, across studies, the bias and sensitivity parameters were 
comparable for some subjects and averaged data were very similar.  The general 
implications of the results are that (a) the reduction of shock plays the same role in 
negative reinforcement as does the rate of food presentation in positive reinforcement and 
(b) that the matching relation can serve as the vehicle by which direct comparisons can be 
made between the two contingency types. 
 Logue and deVilliers (1978) investigated whether behavior and time allocation 
maintained by simultaneously concurrent (as opposed to multiple or concurrent 
changeover-key procedures) schedules of negative reinforcement could also be described 
by Baum?s (1974) equation.  They arranged a standard operant chamber with two levers 
and exposed rats to various combinations of VC schedules of negative reinforcement 
using the same programming tactic as had been used by deVilliers (1972, 1974).  After a 
careful and extensive shaping procedure, they found that the data best fit the matching 
equation when relative time allocation ratios were graphed as a function of the relative 
ratios of avoided shocks.  The data were also described well by the relative ratios of 
responses.  In addition, using responses and avoided shocks, the parameters from Baum?s 
33 
(1974) GMR equation were comparable to those found in concurrent schedules of 
positive reinforcement. 
 Nonhuman behavior maintained by single and multiple VC schedules of negative 
reinforcement had been shown to be described by Herrnstein?s (1970) equations 
(deVilliers, 1972, 1974), time allocation maintained by concurrent VC schedules of 
negative reinforcement had been shown to be described by what was to become Baum?s 
(1974) GMR equation (Baum, 1973), and behavior and time allocation maintained by 
concurrent VC schedules of negative reinforcement had been shown to be described by 
Baum?s (1974) GMR equation (Logue & deVilliers, 1978).  All of these studies 
paralleled the findings from methodologically similar studies with positive reinforcement.  
When the outcomes of these studies are considered together, the matching relation seems 
to provide an appropriate framework from which to evaluate the relative effects of 
positive and negative reinforcement.  Up to this point however, positive and negative 
reinforcement had only been compared via similar procedures.  The most appropriate 
way to evaluate the relative effects of positive and negative reinforcement would be to pit 
them against one another directly in a concurrent arrangement and see how the data 
conform to the GMR. 
 Logue and deVilliers (1981) arranged equal concurrent VI schedules of milk 
reinforcement for rats.  Once responding was established and stabilized, they introduced a 
third independent VC schedule of shock avoidance on one lever at a time.  A modified 
version of the GMR was used to evaluate the relationship between reinforcement and 
response rates.  This version assumed that the reinforcing effects of milk and shock 
avoidance would be additive.  In such a case, the ratio of response rates would be 
34 
expected to match the ratio of reinforcement rates when either the numerator or the 
denominator of the reinforcement ratio consisted of number of milk reinforcers delivered 
plus the number of shocks avoided and the other component of the ratio consisted of only 
the number of milk reinforcers delivered.  One other parameter was included in this 
formulation of the GMR.  A scaling constant had to be included to account for possible 
differences in the reinforcing effects of milk and avoidance of shock.  The estimation of 
the scaling constant will be discussed below. 
 When schedules of shock avoidance were overlaid on the schedules of milk 
reinforcement both responses and time spent responding increased on that schedule while 
the number of food reinforcers received did not vary.  Unfortunately, probably due to 
poor counterbalancing procedures, baselines were extremely variable both within and 
across subjects complicating the analysis.  Consequently, their dependent measures were 
not direct response and time measures, but were the percentage difference between the 
response and time measures of a shock condition and its preceding baseline condition.  It 
is unclear how this data manipulation could have affected other data analyses.  An even 
more troubling aspect of their data analysis is method by which they calculated and 
concluded the scaling constant.  The authors fit nine constants ranging from .1 to 100 to 
the data with their equation and ostensibly used the constant that resulted in the highest 
correlation coefficients for time and responses.  They concluded that the constant that fit 
the data the best was 1.0 (r = .81, .71, .84, .86, respectively) meaning that one avoided 
shock was equal to one milk reinforcer, however they reported seemingly better 
correlations with a scaling constant of 100 (r = .82, .75, .85, .84, respectively).  Why they 
chose to conclude that 1.0 was the better scaling constant is not clear.  Furthermore, that 
35 
the correlations were so similar for scaling constants differing by two orders of 
magnitude calls into question the validity of the scaling procedure itself.  Nevertheless, 
after fitting their data to their modified GMR equation using a scaling constant of 1.0, the 
authors concluded that their version of the GMR used in the experiment proved 
successful in describing response strength involving both food and shock avoidance as 
reinforcers. 
 Although this experiment was the most direct comparison of positive and negative 
reinforcement up to the time, it has limited relevance because of the issues involved with 
deriving the scaling constant (see also Farley & Fantino, 1978).  Properly evaluating the 
relative effects of positive and negative reinforcement (or any other qualitatively different 
consequences) in an operant context would require using quantitatively equal consequent 
stimuli programmed on identical schedules differing only by contingency type.  This 
could be accomplished, of course, only with consequences that can be readily compared 
on a unit-by-unit basis.  Human experimental procedures offer a distinct advantage in this 
regard because they typically employ conditioned reinforcers such as money as the basis 
for operant consequences (Pilgrim, 1998).  Money gains and money losses are measured, 
quite literally, in the same currency, and thus are readily compared on a unit-by-unit 
basis. 
 Research with humans.  Research on concurrent schedules of positive versus 
negative reinforcement with human subjects in the context of any version of the matching 
relation is sparse.  Only three studies were found that took this approach.  Ruddle, 
Bradshaw, and Szabadi (1981) devised an apparatus composed of two panels with 
colored lights.  One panel was the main panel on which were three rows of five lights, a 
36 
counter below the rows of lights, an additional green light to the left of the counter, a red 
light to the right of the counter, and a response button below the counter facing the 
subject that could be depressed by a force of 6 N (600 g).  The second panel was smaller 
and had only three lights and a response button that could be depressed by a force of 2 N 
(200 g).  The top row of lights on the main panel was orange, the middle row was blue, 
and the bottom row was white.  On the smaller panel, the left light was orange, the 
middle one was blue, and the right one was white. 
 Three subjects participated in a series of thirty 70 min sessions.  Each session 
consisted of 10 min exposures to one of five different schedules with 5 min of rest 
between each exposure.  The experiment was divided into three phases, ten sessions to 
each phase.  The first phase involved negative reinforcement only, the second involved 
positive reinforcement only, and the third involved both.  Negative reinforcement was 
programmed using VC schedules (deVilliers, 1972, 1974) and positive reinforcement was 
programmed using VI schedules.  Points exchangeable for money were used as 
reinforcers (1 point = 1 pence) and were accumulated within sessions and across days.  
Thus, whatever value remained on the counter at the end of the daily sessions was added 
to cumulative daily earnings and a lump sum was paid at the conclusion of the study. 
 In the first phase of the experiment, the counter was programmed to begin at 200 
at the start of each daily session.  Subjects were given instructions indicating that when a 
white light was on they could occasionally lose points.  A point loss would be signaled by 
the brief illumination of the red light and a decrease of the counter by one.  Subjects were 
given nonspecific instructions about the response button.  Each of the white lights was 
correlated with a different schedule of VC negative reinforcement.  Except for the first 
37 
(training) session where the schedules were presented (and signaled) in descending order 
from the most dense (far left light) to the least dense (far right light), the various VC 
schedules were presented in a quasi-random sequence.  Within sessions, each of five 
schedules was signaled by one of the five lights without replacement.  Across sessions, 
no schedule could be associated with the same light it had been during the previous 
session. 
 In the second phase of the experiment, the counter was programmed to begin at 
zero at the start of each daily session.  Subjects were given a new set of instructions 
indicating that when an orange light was on they could occasionally earn points by 
pressing the button on the main panel (the small panel had not been introduced yet).  An 
earned point would be signaled by the brief illumination of the green light and an 
increase of the counter by one.  The same procedure for presenting the schedules and 
their associated stimuli was used as was used in the previous phase. 
 In the third phase of the experiment, it is not stated specifically whether there 
were any preprogrammed supplemental earnings to parallel the conditions in phase one or 
if the counter began at zero as in phase two, but their subject instructions make it appear 
as if there was not.  This phase introduced the smaller panel for the first time.  Subjects 
were given instructions indicating that only the white lights would be operating on the 
main panel.  However, pressing the button on the small panel would turn off the white 
lights on the main panel and turn on the orange light on the smaller panel.  In effect, the 
button on the small panel functioned as a changeover key (Findley, 1958) and the button 
on the main panel was the response button associated with both the white and the orange 
lights.  The same procedures for presenting the VC schedules of negative reinforcement 
38 
were used in this phase as were used in phase one with the addition of the concurrently 
available schedule of VI positive reinforcement signaled by the orange light.  No COD 
was employed. 
 The data for the single schedule phases (i.e., phases 1 and 2) were analyzed using 
Herrnstein?s (1970) equation for single schedules.  The equation accounted for 69%, 
95%, and 82% of the variance for each of the subjects under negative reinforcement 
conditions and 93%, 98%, and 59% of the variance under positive reinforcement 
conditions, respectively.  The primary question, however, concerned how the concurrent 
performance data would fit Baum?s (1974) GMR.  When the logarithms of the ratio of 
responses (responses to negative/responses to positive) were plotted as a function of the 
logarithms of ratio of reinforcers (point losses avoided/points earned) marked 
undermatching was found for all subjects.  In one case, the slope of the regression line 
did not deviate significantly from zero.  No bias was observed in any case.  Time 
allocation data were consistent with response rate data. 
 Ruddle, Bradshaw, Szabadi, & Foster (1982) replicated Ruddle, et al. (1981) with 
the goals of extending the findings and exploring the possibility that a lack of a COD in 
their previous experiment was the reason for the marked undermatching.  The procedures 
were the same as Ruddle et al. (1981) except that the single schedules of positive and 
negative reinforcement were run merely as preliminary training sessions and were run for 
only one session each.  The primary independent variable for this experiment was length 
of COD.  Three subjects were run under conditions where there was a 5 s COD, two of 
those three subjects were rerun through all conditions using a 2 s COD, and one of the 
remaining subjects was rerun through all conditions without any COD. 
39 
 With a 5 s COD, undermatching was found for one of the three subjects.  The 
slopes of the regression lines for the other subjects did not significantly deviate from one.  
One of the three subjects showed a slight bias towards positive reinforcement while the 
other two subjects exhibited no bias.  The time allocation data were not different from the 
response rate data.  With a 2 s COD, the slopes of both subject?s matching functions 
decreased.  One of the subject?s data showed marked undermatching with a bias toward 
negative reinforcement.  The other subject?s data did not show either a bias or a slope 
different from one.  Again, the time allocation data were not different from the response 
rate data.  The response rate data from the only subject run during the no COD conditions 
again showed a decrease in the slope, but it was not significantly different from one and 
showed no bias.  There was also no bias demonstrated when considering time allocation 
data, but there was a slight tendency toward undermatching. 
 These results suggest that positive and negative reinforcement contingencies are 
functionally symmetrical in the context of the matching relationship and that the 
avoidance of point loss exerts an equal effect on behavior as point gain (i.e., there was no 
orderly bias).  However, there is reason to be concerned with some aspects of the 
methods employed by Ruddle et al. (1981) and Ruddle et al. (1982).  First, the schedules 
used for the positive and negative reinforcement conditions were not identical.  VC 
schedules of negative reinforcement are programmed such that the first response in an 
interval cancels the delivery of the next programmed shock (or point loss) and subsequent 
responses have no effect until a new interval begins (deVilliers, 1972, 1974).  In contrast, 
VI schedules of positive reinforcement are programmed such that responses within each 
interval have no effect until the end of an interval when a reinforcer is made available.  
40 
Only then, once an interval has timed out, does a response result in the delivery of a 
reinforcer.  Although these schedules may bear notable similarities (Baron, 1991), it 
remains unclear if this difference affects response patterns differently. 
 A second concern with Ruddle et al.?s (1981) and Ruddle et al.?s (1982) methods 
is that they did not incorporate the use of a baseline against which to measure relative 
differences between consequences.  Under their procedures, such a comparison would be 
between concurrent schedules of VI positive versus VI positive reinforcement and 
concurrent schedules of VC negative versus VI positive reinforcement.  Ruddle et al.?s 
results might only show that performance on concurrent schedules of VC negative versus 
VI positive reinforcement can be adequately described by the GMR similarly to 
concurrent schedules of VC negative versus VC negative reinforcement and to concurrent 
schedules of VI positive versus VI positive reinforcement.  Their results cannot 
necessarily be interpreted to mean that the different consequences exert a similar effect 
on behavior without some sort of within-subject or between-groups comparison. 
 A concern specific to Ruddle et al.?s (1982) methods is their use of a COD.  A 
COD used with concurrent schedules of positive versus positive reinforcement is an 
interval, initiated by a switch between response options, during which no responses are 
effective and thus no positive reinforcers are earned.  Note that a COD is programmed 
either to pause schedule timers or to make responses ineffective at producing the 
consequence for a specified length of time.  Both of these methods create unique 
difficulties with concurrent schedules of negative versus positive reinforcement.  If 
schedule timers are paused during the COD, then a positive reinforcer cannot be 
delivered for responding on the manipulandum associated with the positive reinforcement 
41 
schedule and a loss cannot occur for not responding on the manipulandum associated 
with the schedule of negative reinforcement.  In this case, changing over from positive to 
negative reinforcement would functionally create a safety period, and could therefore 
promote changing over from positive to negative reinforcement.  The same COD 
discourages changing over to positive reinforcement (Brownstein & Pliskoff, 1968; 
Catania, 1966; deVilliers, 1977; Herrnstein, 1961; and Shull & Pliskoff, 1967).  Thus, 
this type of COD would be expected to promote ?preference? for negative reinforcement.  
If the COD renders responses temporarily ineffective, then the possibility arises for 
responding on the negative reinforcement side to be punished adventitiously, thereby 
promoting a ?preference? for the positive reinforcement contingency. 
 A fourth problem with Ruddle et al.?s (1981) and Ruddle et al.?s (1982) methods 
arises from the unique situation that resulted from their programming independent 
schedules using a changeover-key (Findley, 1958) arrangement with VC schedules of 
negative reinforcement.  In phase 3, while a subject was working on the schedule of 
positive reinforcement the light associated with the schedule of negative reinforcement 
was turned off indicating the inability to affect that schedule.  Since the schedules were 
programmed independently, the schedule of negative reinforcement continued to time 
and points could still have been lost with no clear indication as to whether the loss was 
due to a response associated with the light on the small panel, was response independent, 
or was due to the timing of the schedule of negative reinforcement.  That is, the subject 
could not have been able to discriminate the source of the point loss.  Using 
nonindependent schedules could have avoided this problem because no point loss would 
ever have been experienced while the subject worked on the positive reinforcement 
42 
schedule, but would have resulted in its own problem.  If schedules had been 
programmed nonindepenently, points could not have been lost on the schedule of 
negative reinforcement while a subject worked on the schedule of positive reinforcement 
and points could not have set up on the schedule of positive reinforcement while a subject 
worked on the schedule of negative reinforcement.  Under such conditions, it would be 
likely that exclusive preference for the schedule of positive reinforcement would occur 
since, with this response pattern, points would only be gained and never lost. 
 A final criticism of the Ruddle et al. (1981) and Ruddle et al. (1982) methods is 
their inconsistent use of the points counter.  It is unclear what effect having a visible 
counter may have on performance especially if it is programmed differently across phases 
of the experiment.  In Ruddle et al.?s (1981) phase one (single schedules of negative 
reinforcement), the counter started at 200, and, if the subject did not respond at all, 432 
points would be lost per daily session resulting in a balance of -232.  In phase two (single 
schedules of positive reinforcement), the counter started at zero and, with perfect 
responding by the subject (i.e., no losses), 126 points would be earned per daily session 
resulting in a balance of 126.  Assuming the counter started at zero in phase three (each 
phase one schedule of negative reinforcement concurrently available with a single phase 
two schedule of positive reinforcement), if all reinforcers were earned on both schedules, 
the final daily balance would be 59 (no losses, 59 gained).  If all losses were avoided and 
no positive reinforcers were earned, the final daily balance would be zero (no losses, no 
gains).  If all positive reinforcers were earned and no losses were avoided, the final daily 
balance would be -373 (432 lost, 59 gained).  If no reinforcers were earned from either 
schedule, the final daily balance would be -432 (432 lost, no gains).  Thus, the range of 
43 
daily session earnings was different across phases (phase one:  -232 ? 200; phase two:  0 
? 126; phase three:  -432 ? 59) and the counter started at different values across phases.  
These differences across phases are threats to the internal validity of the study to the 
extent that these stimulus differences might influence behavior (e.g., differential 
establishing operations, Michael, 1982, 1993, 2000). 
 Magoon and Critchfield (2005) devised a procedure following Madden and 
Perone (1999) to overcome the deficiencies found with Ruddle et al.?s (1981) and Ruddle 
et al.?s (1982) methods.  Subjects faced a computer monitor displaying a software 
program that divided the screen into two equal left and right halves.  Within each half 
was a target box that slowly moved in random directions within its half of the screen.  
The subject?s task was to use an attached computer mouse to position the curser over one 
or the other of the two target boxes and press the mouse button.  Reinforcers (points 
exchangeable for money) could be lost or earned according to the programming of the 
active schedule. 
 As a solution to the asymmetry of schedule structure found in the Ruddle studies, 
both schedules of negative and positive reinforcement were programmed following 
deVilliers (1972, 1974) VC structure.  In both cases, the first response in an interval 
influenced the end-of-interval consequence and subsequent responses within the interval 
had no programmed effect.  With negative reinforcement, the first response in an interval 
cancelled the scheduled point loss at the end of the interval with no signal and further 
responses in the interval had no effect.  If no response occurred during the interval, point 
loss was signaled at the end of the interval by a flashing stimulus indicating the amount 
of money lost.  With positive reinforcement, the first response in an interval earned the 
44 
positive reinforcer scheduled for that interval signaled by a flashing stimulus indicating 
the amount of money earned and further responses in that interval had no effect.  If no 
response occurred during the interval, there was no signal at the end of the interval and 
the next interval began timing. 
 Magoon and Critchfield (2005) also used a baseline matching function consisting 
of concurrent schedules of VC positive versus VC positive reinforcement to compare 
against the experimental matching function consisting of concurrent schedules of VC 
negative versus VC positive reinforcement.  An identical range of relative reinforcement 
ratios was used across each phase (i.e., matching function) to ensure symmetry of 
frequency of reinforcement.  The use of a baseline allowed for relative comparisons to be 
made between phases rather than to the presumed standard bias (log c = 0) and slope (a = 
1) values of Baum?s (1974) GMR.  This way, Baum?s GMR parameters could be used as 
metrics of comparison between phases rather than against assumed ideals. 
 To overcome the COD difficulties posed by Ruddle et al.?s (1982) procedure, 
Magoon and Critchfield (2005) employed a compromise changeover method that 
combined the more traditional elements of concurrent schedule arrangements with a 
?Findley-type? changeover response (COR).  The apparatus itself more closely 
approximated those used in typical concurrent schedule studies of nonhumans because 
both response options were visible and operational simultaneously (i.e., both target boxes 
were constantly visible and their schedules operated continuously).  This is in contrast to 
Ruddle et al?s apparatus that more closely approximated Findley?s (1958) procedure (i.e., 
one response option, one changeover key, and different stimuli signaling different 
schedules).  In addition to the physical differences in apparatus, Magoon and Critchfield 
45 
(2005) used a COR button that was located between the two screen sides and was labeled 
?change.?  Five responses on the button executed a changeover.  This is functionally 
equivalent to a COD because it takes time to execute the COR (Baum, 1982).  Schedule 
timers did not pause and responses remained effective on the active target box except that 
a target-box response prior to the completion of the five changeover responses reset the 
changeover response requirement.  The only time schedule timers paused was during the 
flashing signals indicating point loss or point gain.  This arrangement allowed point loss 
to occur during a changeover, but the subject was responding on the changeover button 
not on the target box associated with the schedule of negative reinforcement thereby 
preventing adventitious punishment of that operant.  Furthermore, since schedules never 
stopped timing during a changeover, no safety periods existed that could promote 
changing over to negative reinforcement. 
 An important point regarding independence of schedules in the context of 
negative reinforcement is that the schedules must be highly discriminable from one 
another.  To the degree that schedules are indiscriminable, they could be considered one 
larger, more complex operant (i.e., subjects would not be able to discriminate the source 
of point loss).  The spatial separation of the target boxes and the COR went some way to 
distinguish the operants in Magoon and Critchfield?s study, but discriminability was 
presumably increased by some additional stimuli.  At the beginning of a session, both 
sides of the screen were white rectangles.  The first response on either side of the screen 
changed the white rectangle on the other side black, presented the words ?Mouse On? 
below the white half of the screen, and presented the words ?Mouse Off? below the black 
half of the screen.  Both target boxes remained visible and active, but only the schedule 
46 
with the white background and the words ?Mouse On? associated with it could be 
influenced by a subject?s responses.  The completion of a COR changed the white 
background to black, the black background to white, the words ?Mouse On? under the 
previously active side to ?Mouse Off,? and the words ?Mouse Off? under the previously 
inactive side to ?Mouse On.?  To differentiate the operants further, colors were randomly 
chosen from a pool of 16 and used as colors for the target boxes.  The colors within 
condition (i.e., each relative reinforcement ratio) were always different from each other 
and efforts were made ensure equal use of all colors across conditions.  Finally, when 
points were lost on a schedule of negative reinforcement, the target box associated with 
that schedule flashed red and indicated the amount of money lost, and when points were 
gained on a positive reinforcement schedule, the target box associated with that schedule 
flashed the amount of money gained.  The spatial separation of the target boxes, the 
COR, the added stimuli, the differentially colored target boxes, and the explicit signals 
indicating which target box was the source of which consequence presumably maximized 
discriminability, and thus independence, between schedules. 
 Since it was unclear what affect the visible points counter might have on 
responding, Magoon and Critchfield (2005) did not use a visible counter during any part 
of the study.  Instead, a message was presented on the screen at the end of each session 
informing the subject how much money had been earned in that session.  Presession 
supplements were used for all negative reinforcement conditions and were set so that if 
no responding occurred, earnings for that schedule would equal zero (i.e., a session could 
never end at a negative value). 
47 
 Three subjects were exposed to the following VC schedules (relative 
reinforcement ratios in parentheses) for both concurrent schedules of VC positive versus 
VC positive reinforcement baselines and concurrent schedules of VC negative versus VC 
positive reinforcement experimental conditions with appropriate counterbalancing:  
VC20:VC20 (1:1), VC15:VC30 (2:1), VC13:VC50 (4:1), VC12:VC72 (6:1), and 
VC11:VC100 (9:1).  One subject withdrew from the study prematurely, leaving behind a 
data set incorporating fewer reinforcement ratio comparisons than that of the other two, 
but adequate to support planned analyses.  No subject showed a significant bias for either 
condition (compared against the log c = 0 ideal of the GMR) and, more importantly, VC 
positive versus VC positive reinforcement matching function bias values were not 
different from VC negative versus VC positive reinforcement matching function bias 
values.  This means that, in the context of these procedures, there is no systematic bias 
for either type of reinforcement.  However, there was an orderly and pronounced, 
sensitivity (i.e., slope) difference between phases.  In every case, the VC negative versus 
VC positive reinforcement matching function was steeper than the VC positive versus 
VC positive reinforcement matching function.  While these results indicate that neither 
reinforcement contingency worked better, was stronger, was more effective, generated 
more behavior, et cetera, they also indicate that positive and negative reinforcement are 
in some way qualitatively different.  If valid, this outcome would correspond with the 
CDT prediction of a free-operant DOE when two qualitatively different outcomes 
compete for behavior. 
 Summary.  Considering the evidence presented above, there is good reason to 
propose that positive and negative reinforcement appear to be equally amenable to 
48 
investigation through the procedural and analytical conventions associated with 
concurrent schedules.  This outcome is demonstrated most clearly when the two types of 
consequences can be compared on some scale of measurement independent of their 
effects on behavior, as is the case when humans work under schedules of generalized 
conditioned reinforcement such as money.  However, as evidenced by the matching 
function slope differences found by Magoon and Critchfield (2005), positive and negative 
reinforcement are not phenomenologically identical.  The two types of contingencies 
yield different kinds of response-contingent stimulus changes, so they differ perceptually.  
That these two kinds of reinforcement are perceptually dissimilar makes them useful in 
more thoroughly testing the predictions of CDT. 
Rationale for Current Studies 
 Magoon and Critchfield (2005) replication.  Magoon and Critchfield?s (2005) 
results demonstrated no bias differences but systematic sensitivity differences when 
performance under schedules of concurrent VC positive versus VC positive 
reinforcement was compared with performance under schedules of concurrent VC 
negative versus VC positive reinforcement within subject.  It was noted earlier that 
reasons for sensitivity differences are unclear.  Davison and Nevin?s (1999) model of 
CDT suggests that the slope differences could be due to d
sb
 or to d
br
 differences.  
Although they suggest that d
sb
 is not a factor in a simultaneously available two-response 
concurrent schedules arrangement, and care was taken to ensure that the two responses 
were as discriminable from one another as possible (note all of the stimuli used to 
indicate a separation of the target boxes), it remains possible that the differential use of 
target box colors could have somehow been differentially correlated with phase thus 
49 
incorporating a nonunit value of d
sb
.  It is questionable whether d
sb
 can ever be made 
infinitely large, but it is possible to hold it constant across conditions by using the same 
target box color for both response options regardless of the difference in reinforcement 
contingency.  Accordingly, any difference between conditions would be a function only 
of response-consequence contingency differences (i.e., d
br
). 
 Following the procedures of Ruddle et al. (1981) and Ruddle et al. (1982), 
Magoon and Critchfield (2005) programmed presession supplemental earnings in 
negative reinforcement phases (although no visible counter was used).  The primary 
rationale for this was to avoid sessions where subjects would earn very little or no money 
or would lose money.  One of the difficulties with studies of the matching relation with 
human subjects is the amount of time per session and the number of session required to 
complete the necessary conditions.  If a great many of these resulted in low or negative 
earnings, subject retention could become difficult.  Supplements were employed to avoid 
this eventuality.  However, using supplements for negative reinforcement creates an 
asymmetry with positive reinforcement.  As noted above, the supplements were 
programmed such that, in any given session, earnings could not go below zero.  That is, 
just like in positive reinforcement conditions, if the subject emitted no responses during a 
session the end-of-session message would indicate earnings of zero.  The problem with 
this is that, although the number of reinforcers is equal to the equivalent reinforcement 
ratio in concurrent schedules of positive reinforcement, the negative reinforcers are 
functionally ?double-valued.?  Not only does earning a negative reinforcer avoid the loss, 
but in terms of the final amount earned for the session, it also amounts to a gain equal to 
the gain of a positive reinforcer.  This is most evident when comparing final session totals 
50 
for comparable relative reinforcement rates for negative and positive reinforcement:  
session earnings were roughly equal.  Since subject retention was the reason for the use 
of supplements, a solution to the problem would be to make a portion of their hourly 
earnings contingent on attendance rather than strictly on performance and begin every 
session with the counter set at zero.  End-of-session totals would differ across 
reinforcement ratios, but all reinforcers would be quantitatively of equal magnitude. 
 Magoon and Critchfield (2005) ran only three subjects.  While the findings were 
consistent and orderly across all three, the finding needs intersubject replication (Sidman, 
1960) to advance generality of findings.  Consequently, a first experiment would be a 
systematic replication of Magoon and Critchfield (2005) using identically colored target 
boxes and no supplemental earnings.  Successful replication of previous findings with 
these procedural differences would provide support for the reliability and validity of the 
slope changing effects found when negative reinforcement competes with positive 
reinforcement in a concurrent schedules arrangement and would indicate that the slopes 
differences were a function of only response-consequence contingency discriminability 
as predicted by Equation 18. 
 Investigation of sensitivity differences.  Baum?s (1974) GMR offers a metric for 
comparing behavioral sensitivity between matching functions, but it does not 
unambiguously imply whether any operations (and if so, what operations) should affect 
the sensitivity parameter (a).  CDT generally, and Davison and Nevin?s (1999) model 
specifically, offers some insight.  They predict that a differential outcome will increase 
the response-consequence contingency discriminability (d
sb
) between alternatives.  Given 
that positive and negative reinforcement are both processes that increase (or maintain) 
51 
ongoing operant behavior and the proposed procedures presumably hold d
sb
 constant and 
use quantitatively equal outcomes, it is not unreasonable to suggest that sensitivity 
differences between concurrent schedules of VC positive versus VC positive 
reinforcement and concurrent schedules of VC negative versus VC positive 
reinforcement is somehow simply a function of their differential outcomes. 
 The outcomes of positive and negative reinforcement differ in two ways.  First, 
positive reinforcement involves gains and negative reinforcement involves losses.  The 
important differential outcome between positive and negative reinforcement could simply 
be that behavior is more sensitive to losses than it is to gains.  Second, there is a structural 
feedback asymmetry between positive and negative reinforcement.  Consider a session 
where 10 reinforcers could be earned and the subject successfully earned 7 of them.  If 
they were earned via positive reinforcement, the subject would be presented 7 feedback 
stimuli over the course of the entire session (one for each reinforcer earned).  If they were 
earned via negative reinforcement, the subject would be presented 3 feedback stimuli 
over the course of the entire session (one for each reinforcer missed).  The important 
differential outcome between positive and negative reinforcement could be this feedback 
asymmetry. 
 By testing the necessity and sufficiency of both ?loss vs. gain? and ?feedback 
asymmetry? by manipulating them across experiments and comparing each manipulation 
to an appropriate baseline condition within subject, the functional and fundamental 
difference between positive and negative reinforcement could be isolated.  If one of these 
variables proves necessary and sufficient and the other does not, valuable information 
regarding the difference between positive and negative reinforcement would be gained, 
52 
but a significant challenge would be presented both to CDT generally and to Davison and 
Nevin?s (1999) model specifically (i.e., because a case would be presented where 
outcomes differed but there were no sensitivity differences).  If neither ?loss vs. gain? nor 
?feedback asymmetry? proves both necessary and sufficient to increase sensitivity and all 
that is required is any difference between outcomes, little would be added to knowledge 
regarding positive reinforcement vis-?-vis negative reinforcement, but CDT generally and 
Davison and Nevin?s model specifically would receive further support. 
53 
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62 
Footnote 
 
1
 The term ?negative reinforcement? is typically defined as the increase or 
maintenance of responding by either the removal or avoidance of some stimulus.  By this 
definition, the term can refer to two procedures; one wherein on ongoing stimulus is 
terminated contingent on the response (escape), and a second wherein a stimulus that has 
previously been presented in the absence of responding is avoided contingent on the 
response (avoidance).  The more general term ?negative reinforcement? will be used 
throughout the paper to refer to the specific case of avoidance rather than escape. 
63 
Figure Caption 
Figure 1.  The four possible outcomes from a signal detection trial.  S
1
 is the presentation 
of the signal-plus-noise stimulus and S
2
 is the noise-only stimulus.  B
1
 is a ?signal 
present? response and B
2
 is a ?signal absent? response.  Hits (R
11
) and Correct Rejections 
(R
22
) are typically followed by reinforcement and Misses (R
12
) and False Alarms (R
21
) 
are typically followed by punishment or extinction. 
Figure 1 
Response 
B
1 
B
2 
HIT 
R
11
C. R. 
R
22
F. A. 
R
21
MISS 
R
12
S
1 
Stimulus 
S
2 
64 
65 
CHAPTER 2 
RESPONSE-CONSEQUENCE CONTINGENCY DISCRIMINABILITY WHEN 
POSITIVE AND NEGATIVE REINFORCEMENT COMPETE 
IN CONCURRENT SCHEDULES 
 Most operant research can be characterized as belonging to one of two broad, and 
typically mutually exclusive, categories:  consequence control and stimulus control.  
Studies of consequence control tend to hold antecedent stimuli constant and vary one or 
more different consequence dimensions (e.g., frequency, magnitude, type, delay, etc.).  
Studies of stimulus control tend to hold maximally different consequence conditions 
constant (e.g., continuous reinforcement versus extinction) and vary antecedent stimuli.  
The formulation of a unified theory capable of accounting for the research results from 
both domains would be a landmark achievement. 
 The generalized matching relation (GMR) (Baum, 1974) is a quantitative 
expression of a general theory of choice that has proven successful in characterizing the 
results from a variety of studies of consequence control.  Its generality has been 
demonstrated across species, procedures, and behaviors and has been extended to 
describe the effects of a range of independent variables (see Davison & McCarthy, 1988, 
for a review).  In its most general form for a two-ply concurrent schedules arrangement, 
the equation 
 c
X
X
a
B
B
x
logloglog
2
1
2
1
+
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
      (1) 
describes the relationship between the distribution of responses (B) and the distribution of 
the different dimensions of reinforcement (X) (e.g., frequency, magnitude, type, delay) 
across the two measured response options (1 and 2).  Rarely is a perfect one to one 
relationship (i.e., strict matching, Herrnstein, 1961) observed, and the parameters a
x
 and 
log c describe deviations from this ideal.  The a
x
 parameter is a measure of behavioral 
sensitivity to changing distributions of the independent variable (X) (Baum, 1979) and 
has been described as measuring ?the degree of control that those variables exert over 
preference? (Landon, Davison, & Elliffe, 2003).  The log c parameter is a measure of 
response bias and reflects a constant preference for responding to one option over the 
other regardless of the ratio(s) of the independent variable(s) (Baum, 1974). 
 Most concurrent schedules research has focused on varying the relative frequency 
of reinforcement.  Consequently, the most familiar form of Equation 1 is 
 c
R
R
a
B
B
r
logloglog
2
1
2
1
+
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
      (2) 
where B
1
 and B
2
 represent the number of responses to each option, R
1
 and R
2
 represent 
the number of reinforcements obtained from responding to each option, a
r
 measures 
behavioral sensitivity to changing ratios of reinforcement frequency, and log c measures 
constant response bias.  Data obtained from concurrent schedules research typically are 
evaluated by plotting logarithms of response ratios as a function of the logarithms of 
reinforcement ratios, and then employing least-squares linear regression to obtain 
estimates of a
r
 and log c.  Behavioral sensitivity is reflected as the estimate of a
r
, which is 
66 
67 
the slope of the regression line.  Strict matching is revealed by a slope of one, but the 
distribution of empirical slope values across studies tends to center around .8 (Baum, 
1979; Kollins, Newland, & Critchfield, 1997; Robinson, 1992; Wearden & Burgess, 
1982).  Constant response bias is reflected as a nonzero estimate of log c and a shift of 
the regression line up or down on the ordinate, depending on for which option there is 
bias. 
 Operant research on stimulus control has not provided a comparably effective 
quantitative model.  Davison (1991) argued that this is why stimulus control research has 
declined in popularity in recent decades.  However, at about the same time the matching 
relation (Herrnstein, 1961) was being developed, classical signal detection theory (SDT) 
(Green & Swets, 1966) produced a relatively successful quantitative model that was 
designed to separate stimulus effects from other effects (e.g., consequences).  In a typical 
signal detection task, a signal (i.e., stimulus) is either presented with noise (i.e., some 
other stimuli) or the noise is presented without the signal in discrete trials.  This allows 
four possible outcomes on each trial.  When the signal-with-noise is presented, the 
subject can report (verbally with humans, some other operant response with nonhumans) 
the signal?s presence (i.e., a hit) or its absence (i.e., a miss).  When the noise-without-
signal is presented, the subject can also report the signal?s presence (i.e., a false alarm) or 
its absence (i.e., a correct rejection).  Hits and correct rejections are followed by 
reinforcement and misses and false alarms are followed by extinction or punishment.  
Plotting the probability of hits as a function of the probability of false alarms reveals 
orderly relationships (see Green & Swets, 1966, for elaboration). 
68 
 ?The most striking achievement of the theory is that if signal strength is constant, 
[the measure of sensory sensitivity to the difference between stimuli] remains the same 
within variations of any given experiment?More importantly, it remains constant across 
different classes of experiment? (Nevin, 1969, p. 477).  However, SDT provided 
elaborate conceptual machinery to explain biasing effects (e.g., effects from 
consequences) that Nevin (1981) thought might better be explained by incorporating the 
matching relation.  His work began an effort to develop an integrated quantitative model 
of behavioral detection according to what was later to become contingency 
discriminability theory (CDT) (Alsop, 1991; Davison & Jenkins, 1985; Davison & Nevin, 
1999; Davison & Tustin, 1978; Nevin, 1981, 2005). 
 To summarize CDT it is first necessary to recount the features of an operant 
choice situation in which two or more responses share a common stimulus context.  In 
such a situation, responses are mutually exclusive, meaning that they cannot be 
performed simultaneously, and therefore time and effort devoted to one response 
precludes the occurrence of others.  Aside from this competition, however, concurrent 
responses have traditionally been viewed as essentially independent, in the sense that 
each is maintained by a different reinforcement contingency (Baum 1974; Herrnstein, 
1970; Pierce & Epling, 1983; Redmon & Lockwood, 1986).  Thus, reinforcer R
1
 
strengthens response B
1
 but not response B
2
, and reinforcer R
2
 strengthens response B
2
 
but not response B
1
. 
 CDT challenges this assumption of independence, instead viewing the response-
consequence contingency as similar to the stimulus-to-be-reported in a signal detection 
task.  SDT views a stimulus report as controlled partly by the stimulus and partly by the 
69 
noise.  The response on a given trial is influenced both by the similarity of the stimuli and 
by the reporter's imperfect perceptual/attentive abilities to discriminate among them.  
Similarly, CDT views a given response as controlled partly by the consequence that is 
contingent upon it and partly by the ?noise? of other simultaneously available response-
consequence contingencies.  The relative strength of a response is influenced both by its 
contingent consequence and by other response-consequence contingencies to the extent 
that the organism's imperfect "response-consequence contingency detection" abilities 
allow it to discriminate among them. 
 According to Davison & Nevin (1999), reinforcement contingencies are 
"confusable" to the extent that some factor diminishes the ?distinctiveness of the relation 
between behavior and reinforcement for one discriminated operant relative to another? 
(Davison & Nevin, 1999, p. 445).  In the absence of confusability, behavior allocation 
will exactly match relative reinforcement frequency, yielding a GMR slope of 1.  
Theoretically, all dimensions of reinforcement (e.g., frequency, magnitude, type, delay) 
contribute to confusability, so if they are all identical across competing responses, the 
responses will be undifferentiated and will occur at identical rates.  In the typical operant 
choice experiment, reinforcement frequency is varied across competing behaviors while 
all other dimensions are held constant (i.e., are completely confusable).  From the 
perspective of CDT then, it is not surprising that the modal outcome of these experiments 
is pronounced undermatching, or slope < 1. 
 It is axiomatic to CDT that anything that increases response-consequence 
discriminability should increase response differentiation in operant choice.  Although 
CDT has proven to have great heuristic value ? it has suggested new research questions 
70 
and allowed the integration of a number of seemingly disparate findings (Davison & 
Nevin, 1999) ? this central precept has been inadequately tested.  For example, CDT 
clearly predicts that the slope of the GMR should be steeper when two concurrent 
responses are maintained by qualitatively different reinforcers than when they are 
maintained by qualitatively identical reinforcers.  Although several experiments have 
employed the former, most have lacked the latter as a control function (e.g., Farley & 
Fantino, 1978; Hollard & Davison, 1971; Logue & deVilliers, 1981; Miller, 1976; 
Ruddle, Bradshaw, Szabadi, & Foster, 1982). 
 Apparently, the increased behavioral sensitivity that is predicted by CDT when 
concurrently available reinforcers are qualitatively different has been tested in only three 
experiments, one with possums as subjects (Bron, Foster, Sumpter, & Temple, 2003) and 
two with humans as subjects (Critchfield & Lane, 2005; Magoon & Critchfield, 2005).  
Bron et al. (2003) assessed the GMR three times within subject.  In "baseline" phases, 
both responses led to a 3-s presentation of a magazine containing barley.  In the two 
"experimental" phases, the barley in one magazine had been soaked in a salt-water 
solution (either 4% or 6%).  Analyses focusing on response allocation showed a steeper-
than-baseline slope for 2 of 4 subjects who completed the 4% phase, and for 4 of 5 
subjects who completed the 6% phase.  It should be noted that where slope increases 
were observed, the differences ranged from .01 to .11.  These differences are small 
enough to warrant concern over their functional importance.  Additionally, so little is 
known about operant behavior in possums and the procedures used to study it, that these 
findings support CDT provisionally at best. 
71 
 Magoon and Critchfield (2005) assessed the GMR twice within subject for three 
subjects.  In ?baseline? phases, both responses were maintained through positive 
reinforcement.  In ?experimental? phases, one response was maintained through positive 
reinforcement and the other was maintained through negative reinforcement.
1
  Slopes 
were steeper in the latter case for all three subjects.  Critchfield and Lane (2005) 
replicated the effect with an additional three subjects with only minor procedural 
modifications. 
 Before the results from Magoon and Critchfield (2005) and Critchfield and Lane 
(2005) can be interpreted as supporting CDT, two procedural ambiguities must be 
resolved.  First, responses consisted of mouse clicks directed at either of two moving 
target boxes on a computer screen, and in each experimental condition, the target boxes 
were different colors that varied unsystematically from condition to condition.  
According to CDT, in addition to the response-consequence contingency discriminability 
described above, the distinctiveness of the stimulus-response contingencies and of the 
responses themselves contributes to functional reinforcer allocation and thus to steady-
state responding.  It is possible, therefore, that varying the target box color pairs across 
experimental conditions could have been responsible for the slope increasing effects 
observed rather than the response-consequence contingency differences. 
 Second, in the procedure employed by Magoon and Critchfield (2005), subject 
earnings were supplemented at the beginning of each session, so that money losses 
encountered through negative reinforcement would not result in end-of-session totals 
below zero.  This practice, initiated in an attempt to keep subjects from withdrawing from 
the experiment when earnings were low, may have created a different economic context 
72 
when negative reinforcement was programmed than when it was not.  This, too, could 
have contributed to the slope increasing effects observed rather than the response-
consequence contingency differences.  It is interesting to note that when Critchfield and 
Lane (2005) omitted the money supplements, slope effects were less pronounced than in 
the Magoon and Critchfield (2005) experiment. 
 The purpose of the present investigation was to replicate and extend the effects 
reported by Magoon and Critchfield (2005) and Critchfield and Lane (2005).  Experiment 
1 employed the same procedures as those two experiments except that (a) the targets used 
to define responses were identically colored within and across experimental conditions, 
and (b) no money supplements were used.  Following replication of the slope effect, 
Experiments 2 and 3 were an attempt to determine what particular feature(s) of negative 
reinforcement makes it qualitatively different from positive reinforcement as expressed 
by the slope increasing effect predicted by CDT.  Experiment 4 was a control experiment 
that compared the slopes of two matching functions with the same within-phase 
consequences, but with different between-phase consequences. 
GENERAL METHOD 
Subjects 
 Participants.  Subjects volunteered in response to notices posted on a recruitment 
board and were selected for participation based only on scheduling convenience.  
Fourteen individuals were accepted into the investigation and two dropped out 
prematurely without giving reasons. 
 Money earnings and payment.  Subjects were paid $2.00 per hour of participation, 
in cash, immediately following each visit to the laboratory.  Additional monies were 
73 
earned within experimental sessions.  Reinforcement contingencies were programmed to 
result in aggregate earnings of approximately $4.00 per hour.  Thus, combining 
attendance pay and session earnings, subjects earned about $6.00 per hour of 
participation.  Payment of session earnings was delivered following the conclusion of 
each individual's participation. 
Setting and Apparatus 
 Experimental sessions were conducted in a 3m x 3m room with stereo speakers 
affixed to the ceiling.  Two large study carrels, each with a chair, a color computer 
monitor, a computer mouse, and a small fan, served as subject workspaces.  The carrels 
were separated by curtain dividers which kept subjects from observing one another if 
more than one subject was running at a time.  Each subject had the choice of having the 
fan on and listening to soft instrumental music from the speakers, having the fan on and 
listening to their own music from the speakers, or listening to their own personal audio 
playback device with headphones (e.g., an MP3 player).  IBM
?
-compatible computers in 
an adjacent room controlled experimental events and collected the data according to a 
custom program created using QuickBasic
?
. 
Procedure 
 Subjects visited the laboratory four or five days per week for 2 hours per day.  
Experimental sessions lasted 8 min and were separated by short breaks of about 1 to 5 
min during which the experimenter recorded the data and initiated the next session. 
 Instructions.  Appendix A describes the intake and training procedures and the 
instructions used for each experiment. 
74 
 Experimental task.  The concurrent-schedules procedure was nearly identical to 
that of Magoon and Critchfield (2005), with slight modifications for each experiment.  
Sessions began with the display of the message ?Click here to begin? centered on the 
screen and directly above a rectangular box with the word ?Ready? inside of it.  An 
arrow-shaped cursor indicated the virtual position of the mouse at all times during the 
session.  Positioning the cursor on the box and pressing the left mouse button cleared the 
prompts and produced two white rectangles, or work areas, each approximately 13 cm 
wide by 17 cm tall arranged one on each side of the screen both against a background the 
color of which varied with experimental condition (see Tables 1-4).  Within each of the 
two work areas was a small (approximately 1.6 square cm) red target box.  Throughout 
each session, the target boxes moved in random directions about 1.25 cm per s.  Pressing 
the left mouse button with the cursor positioned on either of the two target boxes 
constituted the two measured responses.  Pressing the left mouse button while the cursor 
was positioned elsewhere was ineffective (unless it was a changeover response, see 
below) and was not counted.  The side on which a subject?s first response occurred 
remained white and the message, ?Mouse On,? appeared just below it.  The other work 
area turned black and the message, ?Mouse Off,? appeared below it.  Both target boxes 
remained visible and reinforcement schedules associated with each one continued to 
operate.  Responses on the ?Mouse On? side were recorded and influenced the schedule 
of reinforcement programmed for that side, while responses on the ?Mouse Off? side 
were not recorded and had no programmed effect.  Located between the two work areas 
was a 2.5 cm square changeover (CO) area labeled with the word ?Change.?  Positioning 
the cursor on the CO area and pressing the left mouse button five consecutive times 
75 
reversed the status of the two work areas.  A response on the active target prior to 
completing five consecutive changeover responses reset the CO counter to zero.  Session 
and reinforcement schedule timers continued to operate during CO responding.  At the 
end of each session, the screen cleared and a message was presented indicating that the 
session was over and displaying the earnings for that session. 
 Schedules.  Responding on the moving target boxes influenced money gains or 
losses (depending on the schedule in effect) according to independent, concurrent 
variable-cycle (VC) schedules using constant-probability distributions of intervals 
(Fleshler & Hoffman, 1962).  VC schedules of reinforcement (deVilliers, 1972) are 
programmed to deliver one consequence per interval contingent on the first response in 
that interval.  Subsequent responses in the interval are counted but have no further 
influence on the programmed schedule.  If no response is made in a given interval, the 
programmed consequence does not occur. 
 Under all conditions, the programmed overall rate of reinforcement was 360 
reinforcers per hour of session time aggregated across the two work areas.  Within 
experimental phases, 2:1 and 5:1 relative ratios of reinforcement were programmed via 
concurrent VC15:VC30 and VC12:VC60 schedules of reinforcement, respectively.  
Across conditions, attempts were made to avoid consistent relationships between the 
work area (i.e., left vs. right), reinforcement frequency (i.e., rich vs. lean schedule), and 
reinforcement type (e.g., ?standard? positive vs. ?standard? negative).  Tables 1-4 show 
the specific conditions experienced by each subject in each experiment and the sequence 
in which they were completed. 
76 
 Consequences.  Sometimes schedules were programmed such that responses 
resulted in an accrual of money and failing to respond resulted in a lost opportunity to 
accrue money.  Sometimes schedules were programmed such that money was deducted 
for failing to respond and responses resulted in canceling the deduction of money.  The 
manner in which these consequent events were signaled varied across experiments and 
will be described separately for each. 
 The magnitude of each accrual and deduction was established separately for each 
experiment so that earnings per hour remained relatively constant for all subjects across 
all experiments.
2
  The magnitude of consequent events is indicated separately for each 
experiment. 
 Cumulative earnings within a session were not displayed on the subject's screen, 
although the experimenter kept a running total of these earnings.  Subjects were free to 
ask how much they had earned up to a point at any time either before or after, but not 
during, a daily visit.  Subjects rarely asked. 
 Stability criteria.  A condition was terminated when the following criteria were 
met: (a) for both response-allocation and time-allocation proportions, over 4 consecutive 
sessions, the difference in means between the first and second pair of sessions differed by 
no more than 10% of the 4-session mean; and (b) visual analysis revealed no systematic 
trend in the data. 
Data Analysis 
 The present investigation was concerned primarily with understanding the 
conditions affecting increased behavioral sensitivity.  Commensurate with this emphasis, 
the focus of the data analysis was on the slopes of the linear functions (and their within-
77 
subject, between-phase differences) created from using least-squares linear regression to 
fit Equation 2 to individual data (Baum, 1974, 1979).  The intercepts of these functions (a 
measure of bias) are not central to the research question, but will be described for each 
experiment out of convention. 
Experiment 1 
 Magoon and Critchfield (2005) examined human matching under concurrent VC 
schedules of positive versus positive reinforcement (P:P) and negative versus positive 
reinforcement (N:P).  For all subjects, matching slopes were steeper, and therefore 
responding was more sensitive to relative reinforcement frequency differences, under N:P 
reinforcement (i.e., N:P a-values > P:P a-values). 
 The slope differences observed by Magoon and Critchfield (2005) appeared to 
support the prediction of CDT, that, when responses are simultaneously and concurrently 
available, sensitivity to reinforcement should be increased when their respective 
consequences are qualitatively dissimilar relative to when they are qualitatively identical.  
The purpose of the present experiment was to replicate the Magoon and Critchfield 
(2005) study, correcting for two procedural ambiguities described previously.  
Specifically, to keep the stimulus context of the concurrent responses as similar as 
possible, the moving target boxes were always a single color (red), and to keep the 
economy of P:P and N:P phases as similar as possible, the post-session money 
supplements used by Magoon and Critchfield (2005) were omitted. 
Method 
 Subjects were three college students.  In conditions of one phase, VC schedules of 
?standard? positive reinforcement were programmed for both work areas (P:P).  In 
78 
conditions of the other phase, VC schedules of ?standard? negative reinforcement were 
programmed for one work area and VC schedules of ?standard? positive reinforcement 
were programmed for the other (N:P).  Consequence magnitudes were 4?.  Table 1 shows 
experimental arrangements and the sequence of conditions completed by each subject for 
Experiment 1. 
 In VC schedules of ?standard? positive reinforcement, the first response in an 
interval immediately caused a money gain to be signaled by the disappearance of the 
target box associated with that schedule and flashing black text stating, ?+4? (5 text 
flashes at 0.25 s per flash with 0.25 s between flashes, consequence magnitude = 4?).  
During this display, the cursor disappeared, responses were ineffective, and all timers 
were suspended.  Following the conclusion of the money-gain message, further target 
responses were counted but did not influence the schedule for the remainder of the 
interval.  If no response was made during an interval, the money gain programmed for 
that interval was cancelled at the end of the interval without stimulus change. 
 In VC schedules of ?standard? negative reinforcement, the first response in an 
interval immediately cancelled the programmed money deduction for that interval 
without stimulus change.  Further target responses were counted but did not influence the 
schedule for the remainder of the interval.  If no response was made during an interval, a 
money deduction was signaled at the end of the interval by a flashing alternation of the 
target box associated with that schedule and black text stating, ?-4? (5 text flashes and 5 
red target flashes at 0.25 s per flash each, consequence magnitude = 4?).  During this 
display, the cursor disappeared, responses were ineffective, and all timers were 
suspended. 
79 
Results 
 Figure 1 shows for each subject (a) plots of the logarithms of the relative response 
ratios (left panels) and relative time allocation ratios (right panels) as functions of the 
logarithms of the relative obtained reinforcement ratios using averaged data from the last 
four (stable) sessions of each condition (see Appendix B for raw data values) and (b) 
lines of best fit, as determined by Equation 2, to the data of each phase.  Closed circles 
and heavy lines represent the data for the P:P conditions, and closed triangles and light 
lines represent the data for the N:P conditions. 
 In Figure 1, the data in the P:P phases plot the logarithms of the ratios of left 
responses (or time) to right responses (or time) (L/R) against the logarithms of the ratios 
of obtained left reinforcers to obtained right reinforcers (L/R).  However, plotting 
left/right ratios for the data in the N:P phases, in principle, could distort any differential 
effects of ?standard? negative reinforcement because the location of ?standard? negative 
reinforcement (L v. R) varied unsystematically with relative reinforcement ratios (rich v. 
lean) across conditions within phase.  Specifically, plotting the data in the N:P phases by 
left/right ratios might alter the shape (i.e., slope) or, more likely, the location (i.e., 
intercept) of the matching functions to reflect more heavily the effects of location than 
reinforcement type (see Magoon and Critchfield, 2005, for elaboration).  Consequently, 
the N:P functions in Figure 1 show the logarithms of the ratios of ?standard? negative 
reinforcement responses (or time) to ?standard? positive reinforcement responses (or 
time) (N/P) against the corresponding logarithms of the ratios of obtained ?standard? 
negative reinforcement reinforcers to obtained ?standard? positive reinforcement 
reinforcers (N/P). 
80 
 Table 5 lists the regression equations (from Equation 2) and r
2
 values for 
individual data, separately for response allocation and time allocation, for both P:P and 
N:P phases.  The proportions of variance accounted for ranged from acceptable (e.g., 
SO104 P:P time r
2
 = .865) to excellent (e.g., TM102 P:P responses r
2
 = .998), with 
generally better fits for N:P phases (.950 ? r
2
 ? .987, M = .971) than for P:P phases (.865 
? r
2
 ? .998, M = .919).  Parameter estimates are addressed below. 
Slopes (Sensitivity) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 1 shows that, in all cases, the N:P slopes are steeper than the P:P slopes, 
although the differences for TB101 for responses and time are small. 
 Descriptive analysis.  The fifth column of Table 5 lists the difference between the 
N:P phase a (slope) coefficient and the P:P phase a coefficient for each subject (a
(N:P)
 ? 
a
(P:P)
).  A positive a-difference indicates a steeper a for the N:P phase than for the P:P 
phase, and a negative a-difference indicates a shallower a for the N:P phase than for the 
P:P phase.  As with visual inspection, a-difference outcomes were consistent across 
subjects.  They were all positive (.264 ? a
(N:P)
 ? a
(P:P)
 ? .722, M = .490), indicating that, 
for each subject, the N:P slope was greater than its P:P counterpart.  This effect generally 
was more pronounced for response-based analyses (.296 ? a
(N:P)
 ? a
(P:P)
 ? .722, M = .550) 
than for time-based analyses (.264 ? a
(N:P)
 ? a
(P:P)
 ? .596, M = .430).  All but one of the 
N:P slopes (SO104?s slope for time) and none of the P:P slopes were greater than 1. 
 Normative analysis.  The goal of the present investigation was to determine 
whether manipulation of one or more elements of different reinforcer types would create 
a change in slope of the function derived from fitting Equation 2 to the data from two 
81 
experimental phases completed by the same individual.  Making this determination would 
be facilitated by knowing the test-retest reliability of the slope parameter of Equation 2.  
In descriptive terms, a slope effect could be defined as a change in the slope estimate that 
exceeds the typical range of within-subject variance.  Unappreciated at the time this 
investigation was initiated, however, was the fact that, despite the publication of several 
reviews of the many dozens of experiments employing Equation 2 (e.g., Baum, 1979; 
Kollins, et al., 1997; Robinson, 1992; Wearden & Burgess, 1982), the test-retest 
reliability of this model's fitted parameters apparently has not been assessed 
systematically.  Only a few published studies have assessed the matching relation twice 
for the same subjects under identical conditions (e.g., McLean & Blampied, 2001; 
Takahashi & Iwamoto, 1986; Todorov, Oliveira Castro, Hanna, Bittencourt de Sa, & 
Barreto, 1983), and too few of these cases exist to support any actuarial conclusions.  
This surprising weakness in the literature creates problems for the present investigation. 
 In lieu of authoritative information on the stability of matching functions over 
time for individual subjects, what can be determined from the published literature is the 
amount of between-subject variance that occurs in matching slopes.  Robinson (1992) 
reviewed all nonhuman studies in which Equation 2 was employed, and found that these 
estimates were approximately normally distributed.  Robinson?s (1992) data set is large 
enough (N = 125 individual response slopes) that it is possible to derive an estimate of 
the typical range of intersubject slope differences. 
 Robinson's (1992) Figure 1 (p. 439, top left panel) serves as the basis for such an 
estimate.  By assuming a normal distribution, using the median as the measure of central 
tendency, and counting ? the number of cases to either side of the median that together 
82 
constitute 95% of the total number of cases (i.e., 2 standard deviations to each side), the 
?normal? range of slope values can be estimated at .427 ? 1.202.  Robinson cited the 
mean of the distribution as .81, therefore the range of slope values two standard 
deviations below the mean is estimated at .383 (.81 ? .427 = .383) and the range of slope 
values two standard deviations above the mean is estimated at .392 (1.202 ? .81 = .392).  
The average, then, of what could be considered two standard deviations is .388 (.392 + 
.383/2 = .3875).  Thus, for the ?normative analysis? in the present investigation, a 
difference between slopes of ? .388 for response-based analyses was considered out of 
the ?normal? range of variation and used as a makeshift significance criterion.  No 
evaluations of slope differences for time-based analyses will be made using criteria from 
Robinson (1992) because, for most concurrent-schedules procedures, response allocation 
and time allocation are strongly correlated (for a review, see Robinson, 1992; for an 
example, see Critchfield, Paletz, MacAleese, & Newland, 2003). 
 Two subjects had slope differences larger than .388 (TM102 difference = .722, 
SO104 difference = .632) and one did not (TB101 difference = .296). 
 Inferential statistical analysis.  In addition to the three previous analyses, slope 
effects were evaluated for each individual using multiple regression/correlation analysis 
(MRC) (Cohen, Cohen, West, & Aiken, 2003).  This type of analysis regresses the 
dependent variable (for matching analyses, response allocation and/or time allocation) on 
two or more independent variables (in the present investigation, reinforcement frequency 
and reinforcer type) simultaneously, according to two different models, and then 
evaluates the individual coefficients via t-tests and the changes in the proportion of 
variance accounted for between the two models via F-tests.  One model employs one 
83 
parameter for each independent variable (in the present investigation, B
1
 for relative 
reinforcement frequency and B
2
 for reinforcement type) to evaluate the main effect of 
each and a constant (B
0
) to evaluate an overall mean difference between conditions apart 
from the main effects (i.e., partialed bias).  The second model is the same as the first 
model except that it incorporates a fourth parameter (B
12
) as a measure of any possible 
interaction effects between independent variables (in the present investigation, 
reinforcement frequency x reinforcement type).  The interaction parameter is the measure 
of the difference between the slopes of the individual regression lines, but considered 
separately (i.e., partialed) from the main effects of each independent variable and the 
overall mean difference. 
 The measure of fit for the regression of each model is R
2
 ? the proportion of the 
dependent variable?s variance shared with the optimally weighted independent variables.  
For present purposes, the crucial issue is whether the interaction parameter of the second 
model (a) is statistically significantly different from zero, and (b) accounts for a 
statistically significant increase in R
2
 over and above that found by the first model.  Both 
tests yield identical p values so only the results of the latter test will be reported. 
 Table 6 summarizes the results of the MRC analysis.  All R
2
 values were 
acceptable (e.g., TM102 M.E. responses R
2
 = .872) to excellent (e.g., TM102 Full time R
2
 
= .989). 
 In Table 6, the ?R
2
 Change? value is the change in variance accounted for by the 
addition of the B
12
 interaction parameter and the p value is the probability of getting a 
difference of that size if there is no actual difference in variance.  By this test, two of the 
three subjects showed a statistically significant slope increase for the responses-based 
84 
analysis (TM102 and SO104) and one showed a statistically significant slope increase for 
the time-based analysis (TM102) (although it should be noted that SO104?s time-based 
test approached statistical significance, p = .063).  This test indicated that the perceived 
slope differences between N:P and P:P functions in Figure 1 were ?real? ? in the sense 
conveyed by inferential statistics ? for only two of the subjects for responses and for one 
subject for time.  However, if SO104?s p value for the time-based analysis is considered 
in the context of the conclusions of the visual and descriptive analyses, it would not be 
unreasonable to conclude that the perceived slope difference for SO104?s time-based 
analysis is functionally important. 
Intercepts (Bias) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 1 shows no systematic bias for either type of reinforcement.  The graphs show 
no pronounced intercept difference between functions for TB101 and TM102, and a 
higher intercept for N:P than for P:P for SO104. 
 Descriptive analysis.  The last column of Table 5 lists the difference between the 
N:P phase log c (intercept) coefficient and the P:P phase log c coefficient for each subject 
(c
(N:P)
 ? c
(P:P)
).  A positive log c-difference indicates a higher log c for the N:P phase than 
for the P:P phase, and a negative log c-difference indicates a lower log c for the N:P 
phase than for the P:P phase.  As with visual inspection, log c-difference outcomes were 
inconsistent across subjects.  Two subjects had positive log c-differences for both 
response-based and time-based analyses (TB101 responses = .158, time = .136; SO104 
responses = .588, time = .461) while the third had negative log c-differences (TM102 
responses = -.140, time = -.171).  Two subjects had larger log c-differences for response-
85 
based analyses than for time-based analyses (TB101 and SO104) while the third had a 
larger log c-difference for the time-based analysis than for the response-based analysis 
(TM102).  Two subjects had log c-differences close to zero for both response-based and 
time-based analyses (TB101 and TM102) while the third had much larger log c-
differences (SO104). 
 Normative analysis.  The normative approach employed to evaluate slope effects 
for response-based analyses was not applied to bias estimates. 
 Inferential statistical analysis.  The intercept of any MRC regression model 
represents the estimated measure of the dependent variable for the reference group apart 
from the effects of each independent variable and their interactions (i.e., reference group 
bias).  In the context of the present investigation, the intercept represents the logarithm of 
the relative ratio of responding when there is equal reinforcement obtained from each of 
the two measured concurrent response options (because X/X = 1 and log 1 = 0).  MRC 
analysis provides two relevant statistical tests of intercepts. 
 The first test of intercepts evaluates whether the intercept of the regression 
function from each phase (e.g., N:P and P:P) is significantly different from zero (two-
tailed test).  In the present case, this is done by building two full models: one using the 
data from the P:P phase (L/R ratios as described in the Experiment 1 Results section) as 
the reference group and one using the data from the N:P phase (N/P ratios) as the 
reference group.  The intercept parameter (B
0
) of each model represents the response bias 
resulting from reinforcement type (N:P data) or side (P:P data) and the t-test of that 
parameter evaluates whether that intercept is significantly different from zero.  A 
significant positive t-value indicates that the intercept is statistically significantly larger 
86 
than zero (i.e., there is a bias toward whatever is represented in the numerator of that 
phase).  A significant negative t-value indicates that the intercept is statistically 
significantly smaller than zero (i.e., there is a bias away from whatever is represented in 
the numerator of that phase). 
 For the t-tests of the intercepts against the nil hypothesis, none of the P:P 
regressions for either response-based analyses or time-based analyses was significantly 
different from zero (i.e., there was no side bias), one of the N:P regressions for response-
based analyses was significantly different from zero (SO104, t = 5.112, bias toward 
?standard? negative reinforcement, p = .007), and two of the N:P regressions for time-
based analyses were significantly different from zero (TM102, t = -3.423, bias away from 
?standard? negative reinforcement, p = .027; SO 104, t = 5.197, bias toward ?standard? 
negative reinforcement, p = .007). 
 The second test of intercepts evaluates if there is a significant difference between 
the intercepts of the two phases (two-tailed test).  A full model with either phase as the 
reference group provides the relevant t-test.  The data from either phase are acceptable as 
the reference group because the effect is judged by the coefficient for the main effect of 
reinforcement type (B
2
).  The absolute value of that parameter, and thus the p value, is 
the same regardless of which phase is used as the reference group; only the sign differs. 
 For the t-tests of the intercepts against each other, the data from the conditions of 
the P:P phase were used as the reference group.  This means that a significant positive t-
value indicates that the intercept of the N:P phase is statistically significantly larger than 
the intercept of the P:P phase (i.e., there is a bias toward ?standard? negative over 
?standard? positive reinforcement) and a significant negative t-value indicates that the 
87 
intercept of the N:P phase is statistically significantly smaller than the intercept of the P:P 
phase (i.e., there is a bias toward ?standard? positive over ?standard? negative 
reinforcement).  These t-tests of the intercepts resulted in one subject showing a 
significant difference between the two phases for response-based analyses (SO104, t = 
4.109, bias toward ?standard? negative over ?standard? positive reinforcement, p = .015), 
and two subjects showing a significant difference between the two phases for time-based 
analyses (TM102, t = -2.985, bias toward ?standard? positive over ?standard? negative 
reinforcement, p = .041; SO104, t = 4.194, bias toward ?standard? negative over 
?standard? positive reinforcement, p = .014). 
Experiment 1 Results Summary 
 Visual and descriptive analyses showed a difference in slopes for all three 
subjects for both response-based and time-based analyses.  The normative and MRC 
analyses showed a difference in slopes for two of three subjects for the response-based 
analysis.  The MRC analysis showed a difference in slopes for only one subject for the 
time-based analysis (though it would not be unreasonable, in the context of all analyses, 
to conclude that SO104?s time-based slopes were different, meaning that two subjects 
rather than one showed the difference).  No systematic bias effects were observed under 
any analysis. 
Discussion 
 Visual and descriptive analyses of slopes showed increased behavioral sensitivity 
to concurrently available ?standard? negative versus ?standard? positive reinforcement 
over that of concurrently available ?standard? positive versus ?standard? positive 
reinforcement for all subjects for both response-based and time-based analyses.  This 
88 
finding replicates the results of Magoon and Critchfield (2005) and Critchfield and Lane 
(2005). 
 According to the normative and MRC analyses, a slope effect was observed for 
two of three subjects for the response-based analysis (TM102 and SO104) and for only 
one subject for the time-based analysis (TM102).  The failure of the other subject's slope 
effect to meet the criterion of the normative approach or statistical significance might be 
attributed to measurement error, individual differences, or some other factor.  It would 
have been desirable to add more subjects to the experiment to clarify such possibilities, 
but resource constraints precluded this.  Ultimately, the normative and MRC analyses of 
the present experiment highlight two things.  First, not all modes of analysis will always 
agree.  Second, in comparing empirical functions within subject in free-operant 
experiments, the question of how different is "really" different poses some challenges.  
This matter will be taken up in the General Discussion. 
 Visual and descriptive analyses supported two conclusions regarding slope.  First, 
in three experiments using nearly identical procedures (the present one; Critchfield & 
Lane, 2005; Magoon & Critchfield, 2005), N:P slopes have been steeper than P:P slopes 
for 9 of 9 subjects.  Assuming that no two matching slopes will be precisely identical, the 
probability of this aggregate outcome occurring by chance is 0.5
9
 = .00195, or about 1 
chance in 500.  Second, the present results are similar to those of Magoon and Critchfield 
(2005) despite changes in stimulus features designed to control for possible differential 
conditional stimulus control and despite no use of monetary supplements for ?standard? 
negative reinforcement conditions.  This outcome suggests that the suspected procedural 
ambiguities in Magoon and Critchfield (2005) did not play an integral part in their 
89 
results, bolstering the conclusion that the slope effects reflect response-consequence 
discriminability only. 
Experiment 2 
 The most important finding from Experiment 1 was that the procedural changes 
from Magoon and Critchfield (2005) did not preclude the slope differences between 
phases.  The slope differences were found despite the use of identical target box colors 
and no use of monetary supplements.  This outcome suggests that between phase 
differences are not likely the result of systematic differences in stimulus-response 
contingency discriminability, but are likely due to differences in response-consequence 
contingency discriminability.  The question now becomes what particular feature(s) of 
?standard? negative reinforcement make(s) it qualitatively different from ?standard? 
positive reinforcement as expressed by the slope increasing effect observed in 
Experiment 1. 
 The two most salient differences between ?standard? positive and ?standard? 
negative reinforcement, as programmed in Experiment 1, are differences of gains versus 
losses and feedback differences.  For differences of gains versus losses, in the context of 
the present investigation, ?standard? positive reinforcement involves gaining money for 
response patterns that meet schedule requirements (e.g., responding at a high rate) and 
not gaining money for response patterns that fail to meet schedule requirements (e.g., no 
responding).  Money can never be lost.  ?Standard? negative reinforcement involves 
losing money for response patterns that fail to meet schedule requirements and avoiding 
losing money for response patterns that meet schedule requirements.  Money can never 
be gained.  For feedback differences, ?standard? positive reinforcement results in a 
90 
stimulus change only when a reinforcer is ?earned? (i.e., a gain is signaled), but 
?standard? negative reinforcement results in a stimulus change only when a reinforcer is 
?missed? (i.e., a loss is signaled).  Consequently, more feedback occurs under ?standard? 
positive reinforcement than it does under ?standard? negative reinforcement when more 
than 50% of the programmed number of reinforcers are earned from each type of 
reinforcement, but more feedback occurs under ?standard? negative reinforcement than it 
does under ?standard? positive reinforcement when less than 50% of the programmed 
number of reinforcers are earned from each type of reinforcement.  Experiments 2 and 3 
were designed to test the necessity and sufficiency of these two variables in producing the 
slope differences found in Experiment 1, Magoon and Critchfield (2005), and Critchfield 
and Lane (2005). 
 Experiment 2 was designed to test the sufficiency of feedback differences and the 
necessity of gains versus losses to produce the slope differences found between the N:P 
and P:P phases of Experiment 1, Magoon and Critchfield (2005), and Critchfield and 
Lane (2005).  This was done by restructuring the consequences to keep the feedback 
distinction but to eliminate the gain/loss distinction.  Gains were programmed for all 
contingencies of all conditions in both phases.  However, the feedback structure in the 
conditions of the ?experimental? phase was designed to mimic the feedback structure of 
?standard? negative reinforcement.  This type of contingency is referred to here as 
?inverse? positive (IP) reinforcement. 
Method 
 Subjects were three college students.  In conditions of one phase, VC schedules of 
?standard? positive reinforcement were programmed for both work areas (P:P).  In 
91 
conditions of the other phase, VC schedules of ?inverse? positive reinforcement were 
programmed for one work area and VC schedules of ?standard? positive reinforcement 
were programmed for the other (IP:P).  Consequence magnitudes were 2?.  Table 2 
shows experimental arrangements and the sequence of conditions completed by each 
subject for Experiment 2. 
 VC schedules of standard ?standard? positive reinforcement were programmed as 
described in Experiment 1. 
 In VC schedules of ?inverse? positive reinforcement, the first response in an 
interval immediately caused an unsignaled money gain.  Further target responses were 
counted but did not influence the schedule for the remainder of the interval.  If no 
response was made during an interval, the loss of an opportunity to earn money was 
signaled at the end of the interval by a flashing alternation of the target box associated 
with that schedule and black text stating, ?No +2? (5 text flashes and 5 red target flashes 
at 0.25 s per flash each, consequence magnitude = 2?).  During this display, the cursor 
disappeared, responses were ineffective, and all timers were suspended. 
Results 
 Figure 2 plots the data for Experiment 2 (see Appendix B for raw data values) 
according to the conventions of Experiment 1, but with the response and reinforcement 
rates from the ?inverse? positive reinforcement contingencies calculated in the 
numerators of the response (and time allocation) and reinforcement ratios for the 
?experimental? phase data.  Also as in Experiment 1, least-squares regression lines, as 
determined by Equation 2, were fit to the data of each phase.  Closed circles and heavy 
92 
lines represent the data for the P:P conditions, and closed diamonds and light lines 
represent the data for the IP:P conditions. 
 Table 7 lists the regression equations (from Equation 2) and r
2
 values for 
individual data, separately for response allocation and time allocation, for both P:P and 
IP:P phases.  The proportions of variance accounted for ranged from acceptable (e.g., 
GE105 P:P time r
2
 = .864) to excellent (e.g., GE105 IP:P time r
2
 = .996), with similar fits 
for both phases (P:P = .864 ? r
2
 ? .987, M = .956; IP:P = .915 ? r
2
 ? .996, M =.959).  
Parameter estimates are addressed below. 
Slopes (Sensitivity) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 2 shows that, in all cases, the IP:P slopes are steeper than the P:P slopes. 
 Descriptive analysis.  The fifth column of Table 7 lists the difference between the 
IP:P phase a (slope) coefficient and the P:P phase a coefficient for each subject (a
(IP:P)
 ? 
a
(P:P)
).  A positive a-difference indicates a steeper a for the IP:P phase than for the P:P 
phase, and a negative a-difference indicates a shallower a for the IP:P phase than for the 
P:P phase.  As with visual inspection, a-difference outcomes were consistent across 
subjects.  They were all positive (.572 ? a
(IP:P)
 ? a
(P:P) 
? .931, M = .749), indicating that, 
for each subject, the IP:P slope was greater than its P:P counterpart.  This effect generally 
was more pronounced for response-based analyses (.761 ? a
(IP:P)
 ? a
(P:P) 
? .931, M = .871) 
than for time-based analyses (.572 ? a
(IP:P)
 ? a
(P:P) 
? .729, M = .628).  All but two of the 
IP:P slopes (GE105 and GR108?s slopes for time) and none of the P:P slopes were 
greater than 1. 
93 
 Normative analysis.  According to the normative criterion derived from 
Robinson's (1992) review of the matching literature, a difference of slopes ? .388 is a 
meaningful difference.  All slope differences in Experiment 2 were larger than .388. 
 Inferential statistical analysis.  Table 8 summarizes the results of the MRC 
analysis.  Not all R
2
 values met the tacit standard of acceptability found in the literature 
(i.e., R
2
 ? .80).  GR108?s main effects only regression models for the response- and time-
based analyses accounted for just 76.2% and 79.3% of the variance, respectively.  
However, GR108?s full regression models, including the interaction term, accounted for 
92.5% of the variance for the response-based analysis and for 94.3% of the variance for 
the time-based analysis.  This large increase in variance accounted for between models 
under both analyses indicates a strong interaction effect.  The remaining regression fits 
were acceptable (e.g., MJ106 M.E. time R
2
 = .828) to excellent (e.g., GE105 Full time R
2
 
= .995). 
 In Table 8, the ?R
2
 Change? value is the change in variance accounted for by the 
addition of the B
12
 interaction parameter and the p value is the probability of getting a 
difference of that size if there is no actual difference in variance.  By this test, all three 
subjects showed a statistically significant slope increase for both the responses-based and 
time-based analyses. 
Intercepts (Bias) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 2 shows a systematic bias for ?inverse? positive reinforcement.  Since the IP:P 
phase data are plotted with ?inverse? positive reinforcement data in the numerators of 
both the response ratios and the reinforcement ratios, the higher point at which the 
94 
regression lines for those phases cross the ordinates indicates higher rates of responding 
to contingencies of ?inverse? positive reinforcement than to ?standard? positive 
reinforcement regardless of the relative reinforcement rate between concurrent schedules. 
 Descriptive analysis.  The last column of Table 7 lists the difference between the 
IP:P phase log c (intercept) coefficient and the P:P phase log c coefficient for each 
subject (c
(IP:P)
 ? c
(P:P)
).  A positive log c-difference indicates a higher log c for the IP:P 
phase than for the P:P phase, and a negative log c-difference indicates a lower log c for 
the IP:P phase than for the P:P phase.  As with visual inspection, log c-difference 
outcomes were consistent across subjects.  All three subjects had positive log c-
differences for both response-based analyses and time-based analyses (.181 ? c
(IP:P)
 ? 
c
(P:P)
 ? .614) with generally larger log c-differences for response-based analyses (.255 ? 
c
(IP:P)
 ? c
(P:P)
 ? .614, M =.409) than for time-based analyses (.181 ? c
(IP:P)
 ? c
(P:P)
 ? .425, M 
=.277). 
 Inferential statistical analysis.  For the t-tests of the intercepts against the nil 
hypothesis, none of the P:P regressions for either response-based analyses or time-based 
analyses was significantly different from zero (i.e., there was no side bias), two of the 
IP:P regressions for response-based analyses were significantly different from zero 
(GE105, t = 19.065, bias toward ?inverse? positive reinforcement, p = .000; MJ106, t = 
3.211, bias toward ?inverse? positive reinforcement, p = .033), and one of the IP:P 
regressions for time-based analyses was significantly different from zero (GE105, t = 
23.087, bias toward ?inverse? positive reinforcement, p = .000) (although it should be 
noted that GR108?s time-based test approached statistical significance in the direction 
indicating a bias toward ?inverse? positive reinforcement, p = .052). 
95 
 For the t-tests of the intercepts against each other, the data from the conditions of 
the P:P phase were used as the reference group.  This means that a significant positive t-
value indicates that the intercept of the IP:P phase is statistically significantly larger than 
the intercept of the P:P phase (i.e., there is a bias toward ?inverse? positive over 
?standard? positive reinforcement) and a significant negative t-value indicates that the 
intercept of the IP:P phase is statistically significantly smaller than the intercept of the 
P:P phase (i.e., there is a bias toward ?standard? positive over ?inverse? positive 
reinforcement).  These t-tests of the intercepts resulted in one subject showing a 
significant difference between the two phases for both the response-based and time-based 
analyses (GE105 response-based t = 13.287, bias toward ?inverse? positive over 
?standard? positive reinforcement, p = .000; time-based t = 16.071, bias toward ?inverse? 
positive over ?standard? positive reinforcement, p = .000) (although it should be noted 
that MJ106?s response-based test approached statistical significance, p = .061).  The 
results of these tests indicate that the perceived intercept differences between the IP:P and 
P:P functions in Figure 2 are ?real? ? in the sense conveyed by inferential statistics ? for 
only one subject.  However, if MJ106?s p value for the response-based analysis is 
considered in the context of the conclusions of the visual and descriptive analyses, it 
would not be unreasonable to conclude that the perceived intercept difference for 
MJ106?s response-based analysis is functionally important. 
Experiment 2 Results Summary 
 Visual, descriptive, normative, and MRC analyses all showed a difference in 
slopes for all three subjects for both response-based and time-based analyses.  Although 
not every analysis verified the perceived bias toward ?inverse? positive reinforcement 
96 
over ?standard? positive reinforcement in every case, the evidence converged on the 
conclusion that there was a systematic bias for the ?inverse? positive reinforcement 
contingency. 
Discussion 
 Visual and descriptive analyses of slopes showed increased behavioral sensitivity 
to concurrently available ?inverse? positive versus ?standard? positive reinforcement 
over that of concurrently available ?standard? positive versus ?standard? positive 
reinforcement for all subjects for both response-based and time-based analyses.  All 
differences between phase slopes exceeded the normative criterion of .388 and all within-
subject slope differences were statistically significant.  Overall, slope effects were 
qualitatively similar to those found in Experiment 1, by Magoon and Critchfield (2005), 
and by Critchfield and Lane (2005), although the magnitudes of the shifts may be larger 
than seen previously.  These findings suggest that a gain-loss difference is not necessary, 
but feedback asymmetry is sufficient to heighten response-consequence contingency 
discriminability.  The procedures of this experiment do not address whether feedback 
asymmetry is necessary and gains versus losses are sufficient to produce the increased 
sensitivity to reinforcement frequency.  Experiment 3 will address these issues. 
 Visual and descriptive analyses of bias showed all ?inverse? positive 
reinforcement intercepts to be higher than their comparable ?standard? positive 
reinforcement intercepts indicating a systematic bias toward ?inverse? positive 
reinforcement.  This effect appears comparable to that found when concurrent schedules 
with different magnitude reinforcers are used (e.g., Critchfield & Merrill, 2005; McLean 
& Blampied, 2001), but has not been reported before in procedures using equal 
97 
magnitude reinforcers.  As the primary focus of the present investigation is on the 
variables that may influence sensitivity to reinforcement, not bias, no speculation 
regarding the variables responsible for the intercept shifts in Experiment 2 will be offered 
here.  However, the phenomenon seems robust enough to warrant further study. 
 The failure of two subjects? differences between intercepts to meet statistical 
significance, and thus to corroborate entirely the conclusions from visual and descriptive 
analyses, once again highlights the fact that not all modes of analysis will always agree 
with each other and that comparing empirical functions within subject in free-operant 
experiments poses some difficult challenges. 
Experiment 3 
 The results of Experiment 2 illustrated the sufficiency of feedback asymmetry to 
produce an increased behavioral sensitivity to relative reinforcement.  To show that a 
variable is sufficient to produce an effect, however, does not make it necessary to 
produce the effect.  Furthermore, just because gains versus losses were shown not to be 
necessary to produce the effect in Experiment 2, does not rule out their possible 
sufficiency (as predicted by CDT).  Experiment 3 was designed to test the necessity of 
feedback asymmetry and the sufficiency of gains versus losses to produce increased 
behavioral sensitivity to relative reinforcement.  This was accomplished by holding 
feedback asymmetry constant across phases while manipulating gains versus losses in 
one of the phases.  The only way to hold feedback constant in a manner that was not 
more akin to ?standard? negative or ?standard? positive reinforcement was to provide 
feedback (i.e., present a stimulus) for all possible outcomes of each schedule cycle, 
98 
regardless of phase.  This type of contingency is referred to here as ?total feedback? 
reinforcement. 
Method 
 Subjects were three college students.  In conditions of one phase, VC schedules of 
?total feedback? positive reinforcement were programmed for both work areas (TP:TP).  
In conditions of the other phase, VC schedules of ?total feedback? negative 
reinforcement were programmed for one work area, and VC schedules of ?total 
feedback? positive reinforcement were programmed for the other (TN:TP).  Consequence 
magnitudes were 4?.  Table 3 shows experimental arrangements and the sequence of 
conditions completed by each subject for Experiment 3. 
 In VC schedules of ?total feedback? positive reinforcement, the first response in 
an interval immediately caused a money gain to be signaled by the disappearance of the 
target box associated with that schedule and flashing black text stating, ?+4? (5 text 
flashes at 0.25 s per flash with 0.25 s between flashes, consequence magnitude = 4?).  
Following the conclusion of the money-gain message, further target responses were 
counted but did not influence the schedule for the remainder of the interval.  If no 
response was made during an interval, the loss of an opportunity to earn money was 
signaled at the end of the interval by a flashing alternation of the target box associated 
with that schedule and black text stating, ?No +4? (5 text flashes and 5 red target flashes 
at 0.25 s per flash each, consequence magnitude = 4?).  During both types of feedback 
messages, the cursor disappeared, responses were ineffective, and all timers were 
suspended. 
99 
 In VC schedules of ?total feedback? negative reinforcement, the first response in 
an interval immediately caused the cancellation of a programmed money deduction to be 
signaled by the disappearance of the target box associated with that schedule and flashing 
black text stating, ?No -4? (5 text flashes and 5 red target flashes at 0.25 s per flash each, 
consequence magnitude = 4?).  Following the conclusion of the cancellation message, 
further target responses were counted but did not influence the schedule for the remainder 
of the interval.  If no response was made during an interval, a money deduction was 
signaled at the end of the interval by a flashing alternation of the target box associated 
that schedule and black text stating, ?-4? (5 text flashes and 5 red target flashes at 0.25 s 
per flash each, consequence magnitude = 4?).  During both types of feedback messages, 
the cursor disappeared, responses were ineffective, and all timers were suspended. 
Results 
 Figure 3 plots the data for Experiment 3 (see Appendix B for raw data values) 
according to the conventions of Experiments 1 and 2, but with the response and 
reinforcement rates from the ?total feedback? negative reinforcement contingencies 
calculated in the numerators of the response (and time allocation) and reinforcement 
ratios for the ?experimental? phase data.  Also as in Experiments 1 and 2, least-squares 
regression lines, as determined by Equation 2, were fit to the data of each phase.  Open 
circles and heavy lines represent the data for the TP:TP conditions, and closed squares 
and light lines represent the data for the TN:TP conditions. 
 Table 9 lists the regression equations (from Equation 2) and r
2
 values for 
individual data, separately for response allocation and time allocation, for both TP:TP 
and TN:TP phases.  The proportions of variance accounted for ranged from good (e.g., 
100 
JE109 TP:TP time r
2
 = .914) to excellent (e.g., SL110 TP:TP time r
2
 = .998), with similar 
fits for both phases (TP:TP = .914 ? r
2
 ? .998, M = .953; TN:TP = .916 ? r
2
 ? .992, M = 
.959).  Parameter estimates are addressed below. 
Slopes (Sensitivity) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 3 shows that, in all cases, the TN:TP slopes are steeper than the TP:TP slopes, 
although the differences for SL110 for responses and time are small. 
 Descriptive analysis.  The fifth column of Table 9 lists the difference between the 
TN:TP phase a (slope) coefficient and the TP:TP phase a coefficient for each subject 
(a
(TN:TP)
 ? a
(TP:TP)
).  A positive a-difference indicates a steeper a for the TN:TP phase than 
for the TP:TP phase, and a negative a-difference indicates a shallower a for the TN:TP 
phase than for the TP:TP phase.  As with visual inspection, a-difference outcomes were 
consistent across subjects.  They were all positive (.263 ? a
(TN:TP)
 ? a
(TP:TP) 
? .734, M = 
.545), indicating that, for each subject, the TN:TP slope was greater than its TP:TP 
counterpart.  This effect generally was more pronounced for response-based analyses 
(.433 ? a
(TN:TP)
 ? a
(TP:TP) 
? .734, M = .607) than for time-based analyses (.263 ? a
(TN:TP)
 ? 
a
(TP:TP) 
? .631, M = .482).  All but one of the TN:TP slopes (JE109?s slope for time) and 
only one of the TP:TP slopes (SL110?s slope for time) were greater than 1. 
 Normative analysis.  According to the normative criterion derived from 
Robinson's (1992) review of the matching literature, a difference of slopes ? .388 is a 
meaningful difference.  All slope differences in Experiment 3 were larger than .388. 
101 
 Inferential statistical analysis.  Table 10 summarizes the results of the MRC 
analysis.  All R
2
 values were acceptable (e.g., JE109 M.E. responses R
2
 = .859) to 
excellent (e.g., JE109 Full responses R
2
 = .982). 
 In Table 10, the ?R
2
 Change? value is the change in variance accounted for by the 
addition of the B
12
 interaction parameter and the p value is the probability of getting a 
difference of that size if there is no actual difference in variance.  By this test, only one of 
the three subjects showed a statistically significant slope increase for the responses-based 
analysis (JE109) and two showed a statistically significant slope increase for the time-
based analysis (JE109 and NN111) (although it should be noted that NN111?s response-
based test approached statistical significance, p = .061).  This test indicated that the 
perceived slope differences between TN:TP and TP:TP functions in Figure 3 were ?real? 
? in the sense conveyed by inferential statistics ? for only one subject for responses and 
for two subjects for time.  However, if NN111?s p value for the response-based analysis 
is considered in the context of the conclusions of the visual and descriptive analyses, it 
would not be unreasonable to conclude that the perceived slope difference for NN111?s 
response-based analysis is functionally important. 
Intercepts (Bias) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 3 shows no systematic bias for either type of reinforcement.  The graphs show 
no pronounced intercept difference between functions for any subject and all intercepts 
are close to zero. 
 Descriptive analysis.  The last column of Table 9 lists the difference between the 
TN:TP phase log c (intercept) coefficient and the TP:TP phase log c coefficient for each 
102 
subject (c
(TN:TP)
 ? c
(TP:TP)
).  A positive log c-difference indicates a higher log c for the 
TN:TP phase than for the TP:TP phase, and a negative log c-difference indicates a lower 
log c for the TN:TP phase than for the TP:TP phase.  As with visual inspection, log c-
difference outcomes were inconsistent across subjects.  Two subjects had positive log c-
differences for response-based analyses (JE109 = .151; NN111 = .005) while the third 
had a negative log c-difference (SL110 = -.136).  Two subjects had negative log c-
differences for time-based analyses (SL110 = -.098; NN111 = -.037) while the third had a 
positive log c-difference (JE109 = -.151).  Two subjects had larger log c-differences for 
response-based analyses than for time-based analyses (JE109 and SL110) while the third 
had a larger log c-difference for time-based than for response-based analyses (NN111).  
All subjects had log c-differences close to zero (-.136 ? c
(TN:TP)
 ? c
(TP:TP)
 ? .151). 
 Inferential statistical analysis.  For the t-tests of the intercepts against the nil 
hypothesis, none of the TP:TP regressions for either response-based analyses or time-
based analyses was significantly different from zero (i.e., there was no side bias) and 
none of the TN:TP regressions for either response-based analyses or time-based analyses 
was significantly different from zero (i.e., there was no bias toward either type of 
reinforcement). 
 For the tests of the intercepts against each other, the data from the conditions of 
the TP:TP phase were used as the reference group.  This means that a significant positive 
t-value indicates that the intercept of the TN:TP phase is statistically significantly larger 
than the intercept of the TP:TP phase (i.e., there is a bias toward ?total feedback? 
negative over ?total feedback? positive reinforcement) and a significant negative t-value 
indicates that the intercept of the TN:TP phase is statistically significantly smaller than 
103 
the intercept of the TP:TP phase (i.e., there is a bias toward? total feedback? positive 
over ?total feedback? negative reinforcement).  These t-tests of the intercepts resulted in 
no subjects showing a significant difference between the two phases for either the 
response-based or the time-based analyses. 
Experiment 3 Results Summary 
 Visual and descriptive analyses showed a difference in slopes for all three 
subjects for both response-based and time-based analyses.  The normative analysis also 
showed a difference for all three subjects for the response-based analysis.  However, 
MRC analysis showed a difference in slopes for only one of three subjects for the 
response-based analysis and for only two subjects for the time-based analysis (though it 
would not be unreasonable, in the context of all analyses, to conclude that NN111?s 
response-based slopes were different, meaning that two subjects rather than one showed 
the difference).  No systematic bias effects were observed under any analysis. 
Discussion 
 Visual and descriptive analyses of slopes showed increased behavioral sensitivity 
to concurrently available ?total feedback? negative versus ?total feedback? positive 
reinforcement over that of concurrently available ?total feedback? positive versus ?total 
feedback? positive reinforcement for all subjects for both response-based and time-based 
analyses.  As in Experiment 2, all differences between phase slopes exceeded the 
normative criterion of .388 corroborating the findings of visual and descriptive analyses.  
In the context of the conclusions from these analyses, and considering that NN111?s 
MRC statistical test of slope differences for the response-based analysis approached 
significance, the evidence converges on the conclusion that at least two of the three 
104 
subjects demonstrated the slope difference predicted by CDT.  Thus, overall slope effects 
of Experiment 3 were similar to those of Experiments 1 and 2, Magoon and Critchfield 
(2005), and Critchfield and Lane (2005).  The primary conclusions supported by this 
outcome is that neither the gain-loss difference nor feedback asymmetry is necessary, but 
both are sufficient, to heighten response-consequence contingency discriminability.  This 
conclusion supports the prediction of CDT that any difference between consequences will 
increase response-consequence contingency discriminability, but does not add any new 
information regarding the qualitative difference between positive and negative 
reinforcement. 
 Small and inconsistent intercept differences indicate no systematic shifts (i.e., 
bias) toward either type of reinforcement.  This finding mirrors the results of Experiment 
1, Magoon and Critchfield (2005), and Critchfield and Lane (2005).  That the consistent 
and orderly bias found in Experiment 2 was not reproduced in the current experiment 
further emphasizes the uniqueness of that phenomenon to that experiment. 
Experiment 4 
 When considering the convergent evidence of all methods of analysis, at least 2 of 
3 subjects demonstrated the slope differences between phases in Experiment 1, 3 of 3 
demonstrated the slope differences in Experiment 2, and at least 2 of 3 demonstrated the 
slope differences in Experiment 3.  The overall conclusion based on this analysis is that 
neither the gain-loss difference nor feedback asymmetry is necessary, but both are 
sufficient, to heighten response-consequence contingency discriminability.  This outcome 
is predicted by the CDT interpretation of the differential outcomes effect (Trapold, 1970).  
At its most fundamental level, the prediction is that any difference between consequences 
105 
that compete for behavior in a concurrent arrangement will heighten the discriminability 
of the response-consequence contingencies of the competing responses.  The conceptual 
relationship of this prediction to the outcomes of Experiments 1-3 is that the slopes 
generally were steeper for ?experimental? functions simply because the consequences of 
the concurrent responses were different.  There is, however, an alternative possibility.  
The steeper slopes in Experiments 1-3 somehow might have resulted from the mere 
presence of one of the analogues of negative reinforcement (i.e., ?standard? negative, 
?inverse? positive, ?total feedback? negative).  To support the former interpretation of the 
results from Experiments 1-3, a manipulation was required that was able to produce no 
difference in slopes between phases despite the presence of one of the negative 
reinforcement analogues in only one of the phases. 
 Experiments 1-3 compared a phase consisting of concurrent different types of 
reinforcement (X:Y) to a phase consisting of concurrent identical types of reinforcement 
(X:X).  To support the interpretation that the steeper slopes found in the former phases in 
those experiments were due simply to the different types of consequences of those 
concurrent responses, two phases consisting of concurrently arranged identical types of 
reinforcement were compared to each other, but with the identical types within phase 
differing across phases (X:X to Y:Y).  The best arrangement to meet this criterion was to 
compare phases that used consequences that were as alike as possible, but where, in one 
phase, the consequences were one of the negative reinforcement analogues.  If the 
consequences within phase are identical to each other, CDT predicts that the matching 
functions should have similar within-subject slopes. 
106 
Method 
 Subjects were three college students.  In conditions of one phase, VC schedules of 
?total feedback? positive reinforcement schedules were programmed for both work areas 
(TP:TP).  In conditions of the other phase, VC schedules of ?total feedback? negative 
reinforcement were programmed for both work areas (TN:TN).  Consequence 
magnitudes were 7.5?.  Table 4 shows experimental arrangements and the sequence of 
conditions completed by each subject for Experiment 4. 
Results 
 Figure 4 plots the data for Experiment 4 (see Appendix B for raw data values) as 
in Experiments 1-3, except, because both phases consisted of concurrently available 
identical types of reinforcement within phase, no special considerations had to be made 
when plotting the data.  Both response (and time allocation) and reinforcement ratios 
were calculated with left responses in the numerators.  Also as in Experiments 1-3, least-
squares regression lines, as determined by Equation 2, were fit to the data of each phase.  
Open circles and heavy lines represent the data for the TP:TP conditions, and open 
squares and light lines represent the data for the TN:TN conditions. 
 Table 11 lists the regression equations (from Equation 2) and r
2
 values for 
individual data, separately for response allocation and time allocation, for both TP:TP 
and TN:TN phases.  The proportions of variance accounted for ranged from good (e.g., 
SS114 TN:TN time r
2
 = .939) to excellent (e.g., JL113 TP:TP responses r
2
 = .998), with 
similar fits for both phases (TP:TP = .966 ? r
2
 ? .998, M = .983; TN:TN = .939 ? r
2
 ? 
.989, M =.971).  Parameter estimates are addressed below. 
107 
Slopes (Sensitivity) 
 Visual analysis.  Visual inspection of response-based graphs in Figure 4 shows a 
difference in slopes between the TN:TN and TP:TP matching functions for one subject.  
SS114?s TN:TN response-based slope is steeper than the TP:TP response-based slope, 
but the time-based slopes are not different.  There is no difference between slopes for 
either of the other subjects for either the response-based or the time-based analyses. 
 Descriptive analysis.  The fifth column of Table 11 lists the difference between 
the TN:TN phase a (slope) coefficient and the TP:TP phase a coefficient for each subject 
(a
(TN:TN)
 ? a
(TP:TP)
).  A positive a-difference indicates a steeper a for the TN:TN phase 
than for the TP:TP phase, and a negative a-difference indicates a shallower a for the 
TN:TN phase than for the TP:TP phase.  As with visual inspection, a-difference 
outcomes were inconsistent across subjects.  Two subjects had positive a-differences for 
response-based analyses (JL113 = .206; SS114 =.376) while the third had a negative a-
difference (MJ112 = -.067).  Two subjects had positive a-differences for time-based 
analyses (JL113 =.116; SS114 = .119) while the third had a negative a-difference (MJ112 
= -.049).  All subjects had larger a-differences for responses than for time.  Two subjects 
had a-differences close to zero for response-based analyses (MJ112 and JL113) while the 
third had a much larger a-difference (SS114).  All subjects had a-differences close to 
zero for time-based analyses.  Three of six TP:TP slopes (MJ112?s and JL113?slopes for 
responses and MJ112?s slope for time) and all but one of the TN:TN slopes (SS114?s 
slope for time) were greater than 1. 
108 
 Normative analysis.  According to the normative criterion derived from 
Robinson's (1992) review of the matching literature, a difference of slopes ? .388 is a 
meaningful difference.  No slope differences in Experiment 4 were larger than .388. 
 Inferential statistical analysis.  Table 12 summarizes the results of the MRC 
analysis.  All R
2
 values were good (e.g., SS114 M.E. responses R
2
 = .926) to excellent 
(e.g., JL113 Full time R
2
 = .993). 
 In Table 12, the ?R
2
 Change? value is the change in variance accounted for by the 
addition of the B
12
 interaction parameter and the p value is the probability of getting a 
difference of that size if there is no actual difference in variance.  By this test, none of the 
subjects showed a statistically significant slope difference for either the responses-based 
or the time-based analyses. 
Intercepts (Bias) 
 Visual analysis.  Visual inspection of both response-based and time-based graphs 
in Figure 4 shows no systematic bias for either type of reinforcement.  The graphs show 
no pronounced intercept difference between functions for any subject and all intercepts 
are close to zero. 
 Descriptive analysis.  The last column of Table 11 lists the difference between the 
TN:TN phase log c (intercept) coefficient and the TP:TP phase log c coefficient for each 
subject (c
(TN:TN)
 ? c
(TP:TP)
).  A positive log c-difference indicates a higher log c for the 
TN:TN phase than for the TP:TP phase, and a negative log c-difference indicates a lower 
log c for the TN:TN phase than for the TP:TP phase.  As with visual inspection, log c-
difference outcomes were inconsistent across subjects.  Two subjects had negative log c-
differences for response-based analyses (JL113 = -.272; SS114 = -.024) while the third 
109 
had a positive log c-difference (MJ112 = .149).  Two subjects had negative log c-
differences for time-based analyses (JL113 = -.193; SS114 = -.041) while the third had a 
positive log c-difference (MJ112 = .128).  Two subjects had larger log c-differences for 
response-based analyses than for time-based analyses (MJ112 and JL113) while the third 
had a larger log c-difference for the time-based analysis than for the response-based 
analysis (SS114).  All subjects had log c-differences close to zero (-.272 ? c
(TN:TN)
 ? 
c
(TP:TP)
 ? .149). 
 Inferential statistical analysis.  For the t-tests of the intercepts against the nil 
hypothesis, one subject showed statistically significant biases, though they were to 
opposite sides for the different phases.  JL113 showed a statistically significant left side 
bias for both response-based and time-based analyses for the regressions of the data from 
the TP:TP phase (response t = 2.785, p = .050; time t = 2.940, p = .042) and a statistically 
significant right side bias for both response-based and time-based analyses for the 
regressions of the data from the TN:TN phase (response t = -2.792, p = .049; time t = -
2.910, p = .044). 
 For the tests of the intercepts against each other, the data from the conditions of 
the TP:TP phase were used as the reference group.  This means that a significant positive 
t-value indicates that the intercept of the TN:TN phase is statistically significantly larger 
than the intercept of the TP:TP phase (i.e., there is a larger left side bias for concurrent 
?total feedback? negative reinforcement than there is for concurrent ?total feedback? 
positive reinforcement) and a significant negative t-value indicates that the intercept of 
the TN:TN phase is statistically significantly smaller than the intercept of the TP:TP 
phase (i.e., there is a larger left side bias for concurrent ?total feedback? positive 
110 
reinforcement than there is for concurrent ?total feedback? negative reinforcement).  
These t-tests of the intercepts of Experiment 4 resulted in one subject showing a 
statistically significant difference between the two phases.  JL113 showed a significantly 
larger left side bias for the regression of the data from the TP:TP phase over the 
regression of the data from the TN:TN phase for both response-based and time-based 
analyses (response t = -3.944, p = .017; time t = -4.137, p = .014). 
Experiment 4 Results Summary 
 Evidence from visual, normative, and MRC analyses all converge on the results 
that there were no systematic slope or intercept differences for any subject for either the 
response-based or the time-based analyses.  Descriptive analysis was the only analysis 
that resulted in slopes and intercepts differences for all three subjects for both response-
based and time-based analyses, however, the differences were unsystematic. 
Discussion 
 Visual, normative, and MRC analyses all converged on the conclusion that there 
were no slope or intercept differences for any subject.  In contrast, descriptive analysis 
resulted in slope and intercept differences for all three subjects for both response-based 
and time-based analyses, though not in any systematic way.  A contradiction such as this 
is not surprising whenever success is measured as the absence of an effect.  That is 
because simple comparisons of regression coefficients from two different functions will 
almost always result in the conclusion that they are different.  It is highly unlikely that 
within subject matching functions would ever result in exactly the same coefficients, 
even if exactly the same consequences were used for both phases.  Given that the 
differences found from the descriptive analysis were unsystematic, those results may be 
111 
interpreted as corresponding to the results from the visual, normative, and MRC analyses 
which may, in total, converge on and support the tentative conclusion from Experiment 3 
that neither the gain-loss difference nor feedback asymmetry is necessary, but both are 
sufficient, to heighten response-consequence contingency discriminability.  This 
conclusion supports the general prediction made by CDT that any difference between 
consequences will heighten the response-consequence contingency discriminability of 
concurrent responses making behavior more sensitive to changing relative rates of 
reinforcement. 
GENERAL DISCUSSION 
Results Summary 
 A prediction of CDT (Alsop, 1991; Davison & Jenkins, 1985; Davison & Nevin, 
1999; Davison & Tustin, 1978; Nevin, 1981, 2005) is that any qualitative difference 
between consequences of concurrent responses will increase response-consequence 
contingency discriminability between those responses and, as a result, will increase 
behavioral sensitivity to individual response-consequence contingencies.  That steeper 
least-squares regression slopes were found in the present investigation when responding 
was maintained by concurrently available different consequences than when it was 
maintained by concurrently available identical consequences supports this prediction.  
Figure 5 illustrates this by showing the slopes (top panel) and between-phase slope 
differences (bottom panel) for each subject in the four experiments. 
 The top panel of Figure 5 shows slope values for the data from each phase for 
each subject.  Dark bars represent the slopes of ?baseline? phases and light bars represent 
the slopes of ?experimental? phases.  In Experiments 1-3, ?baseline? phases arranged 
112 
identical consequences for each component of the concurrent schedules and 
?experimental? phases arranged different consequences for each component.  Experiment 
4 arranged identical consequences within both phases but different consequences across 
phases.  It can be seen in the top panel of Figure 5 that all ?experimental? phase slopes 
were greater than 1 whereas only three ?baseline? phase slopes were.  Of those three, two 
were in Experiment 4 where both phases used identical consequences within phase.  This 
panel also shows that slopes were consistently higher when phases arranged concurrent 
different consequences than when they arranged concurrent identical consequences 
(Experiments 1-3) and were not consistently different when both phases arranged 
identical consequences (Experiment 4).  The lower panel of Figure 5 further highlights 
this outcome. 
 In the lower panel of Figure 5, bars represent slope differences between 
regression functions ("experimental" phase slope minus ?baseline? phase slope).  In all 
cases where phases that arranged concurrent different consequences were compared to 
phases that arranged concurrent identical consequences (Experiments 1-3), the 
?experimental? phase slope values were larger, as reflected by the positive slope 
differences.  When identical consequences were used within phase for both phases 
(Experiment 4), one slope had a negative slope difference and the other two had positive 
slope differences.  The horizontal line in the lower panel of Figure 5 identifies the 
normative slope-change criterion determined from Robinson?s (1992) data.  All but one 
of the subjects in Experiments 1-3 met this criterion.  None of the subjects in Experiment 
4 did. 
113 
 In addition to the response-consequence contingency discriminability prediction 
discussed above, CDT predicts increased behavioral sensitivity (i.e., slope increases) if 
the stimuli signaling the availability of concurrent responses are distinct (i.e., stimulus-
response contingency discriminability).  Magoon and Critchfield (2005) and Critchfield 
and Lane (2005) found slope differences like those of the present investigation using 
nearly identical procedures but using unsystematically different target-box colors across 
conditions.  Consequently, those experiments could not reasonably determine whether 
their results were due to stimulus-response contingency discriminability, response-
consequence contingency discriminability, or an interaction/combination of the two.  The 
present procedures used identical target-box colors in every condition; therefore, within 
the context of CDT, all slope differences are interpreted as being solely the product of 
differential response-consequence contingency discriminability between phases. 
 Another difference between Magoon and Critchfield?s (2005) procedures and 
those of the present investigation was that their experiment employed money 
supplements for sessions involving negative reinforcement.  Replication of the slope 
differences in the present investigation without such supplements indicated that they have 
no differential functional effect on behavior.  It was noted earlier that Critchfield and 
Lane (2005) found much smaller slope differences than Magoon and Critchfield without 
using supplements.  That was not the case in the present investigation.  The magnitude of 
slope differences in the present investigation more closely approximated those found by 
Magoon and Critchfield than those found by Critchfield and Lane. 
114 
Implications for Quantitative Model Development of CDT 
 Various quantitative expressions of CDT have been proposed (Alsop, 1991; 
Davison & Jenkins, 1985; Davison & Nevin, 1999; Davison & Tustin, 1978; Nevin, 
1981, 2005), the relative merits of which are still being debated.  While the conceptual 
foundations of CDT are widely accepted by the proponents of all existing models, it 
seems premature to commit to any particular one.  However, the present investigation 
might provide both a strategy to address the debate generally and results to inform model 
development efforts specifically. 
 As described previously, CDT predicts that a difference between concurrently 
available consequences along any dimension (e.g., reinforcement frequency, magnitude, 
type, delay) will heighten response-consequence contingency discriminability and 
thereby increase behavioral sensitivity to individual consequences.  However, neither 
CDT nor any quantitative expressions of it specify the manner in which these other 
dimensions interact with behavior or each other to affect behavioral outcomes.  For 
example, Davison and Nevin (1999) invoked two parameters, d
sb
 and d
br
, to quantify 
CDT?s stimulus-response and response-consequence contingency discriminability 
propositions, respectively.  However, they did not specify how choice-controlling 
variables such as reinforcement frequency, magnitude, type, and delay may (or may not) 
interact to contribute to d
br
.  They acknowledged that ?[i]f [their] model is to be extended 
to choice-controlling variables other than frequency of reinforcement, a substantial 
research effort will be required to identify independent functions for the discriminability 
and value of the consequences of choice? (Davison & Nevin, 1999, p. 472).  The 
implication was that it is at least in principle possible to specify how these variables 
115 
interact to contribute to d
br
.  The methods of the present investigation provide a possible 
strategy by which to approach the problem. 
 Equation 1 provides two measures that characterize deviations from strict 
matching (Herrnstein, 1961).  Log c describes constant response bias (Baum, 1974) and 
a
x
 describes the degree of effect a given variable (X) has on response allocation (Baum, 
1979; Landon et al., 2003).  These parameters could be the metrics by which to compare 
the interactions (or lack thereof) of different choice-controlling variables and their 
influence on behavior.  Some research on magnitude of reinforcement has already taken 
this approach and serves here to illustrate the general strategy. 
 Landon et al. (2003) arranged a concurrent schedule switching-key procedure in 
which pigeons' key-pecking responses were reinforced.  Relative frequency of 
reinforcement and overall absolute magnitude of reinforcement were held equal and 
constant across conditions but relative magnitude was varied.  They found that pigeon?s 
pecking behavior undermatched (i.e., a < 1) relative reinforcer magnitude ratios and did 
so to a greater degree than found in a different study of the same birds when relative 
reinforcer frequency ratios were varied (i.e., magnitude a < frequency a) (see Landon, et 
al., 2003, Table 2 for the relevant comparison).  Two of their conclusions were that 
behavior is less sensitive to reinforcer magnitude than it is to reinforcer frequency and 
that the effects of these two variables are independent. 
 McLean & Blampied (2001) arranged a two-key concurrent schedules procedure 
in which pigeons? key-pecking responses were reinforced.  Relative frequency of 
reinforcement was varied across identical ranges for two phases, one in which the 
concurrently available reinforcers were of identical magnitude, and one in which the 
116 
concurrently available reinforcers were of different magnitude.  In the phase with 
different magnitudes of reinforcement, there was a pronounced bias for the larger 
magnitude reinforcers (i.e., log c ? 0 towards larger magnitude reinforcer) while there 
was no systematic bias in the other phase (i.e., log c = 0).  There were no systematic slope 
(i.e., a) differences between the two phases.  While McLean and Blampied?s results 
corresponded well with Landon et al.?s (2003) conclusion that reinforcement frequency 
and magnitude effect behavior independently, their results did not agree with Landon et 
al.?s conclusion that behavior is less sensitive to reinforcer magnitude than it is to 
reinforcer frequency. 
 Critchfield & Merrill (2005) extended McLean and Blampied?s work to human 
subjects using procedures modeled closely after those of the present investigation.  One 
of their phases arranged concurrently available schedules of positive reinforcement with 
equal magnitude reinforcers and the other arranged concurrently available schedules of 
positive reinforcement with different magnitudes of reinforcement.  Their results 
mirrored those of McLean and Blampied (2001) in that the phase with the different 
magnitudes of reinforcement showed a clear bias toward the larger magnitude reinforcers, 
the other phase showed no bias, and there were no slope differences between phases. 
 The three studies just discussed illustrate how within subject comparisons of 
matching functions can be used to analyze the separate effects of frequency and 
magnitude of reinforcement on behavior.  The results of all three studies converge on the 
conclusion that magnitude of reinforcement exerts an independent effect from that of 
reinforcement frequency.  Landon et al. (2003) came to this conclusion because nonzero 
slopes resulted when only relative magnitude of reinforcement was varied.  McLean and 
117 
Blampied (2001) and Critchfield and Merrill (2005) came to the same conclusion when 
there were intercept but not slope differences between phases when the range of relative 
reinforcement frequency was held constant across phases but magnitude was the same 
within one phase and different within the other.  In all three cases, the parameters derived 
from Equation 1 were the metrics by which effects were evaluated. 
 The present investigation adopted this same general strategy to assess independent 
and interactive effects between frequency and type of reinforcement.  The difference 
between outcomes of Experiments 1-3 and Experiment 4 suggests independence of 
reinforcer-frequency effects and reinforcer-type effects that is similar to the independence 
found between reinforcer-frequency effects and reinforcer-magnitude effects just 
described.  However, these results cannot rule out the possible necessity of an interaction 
between frequency and type-difference to produce the increased slopes found in 
Experiments 1-3.  To test further for frequency and type independence would require an 
arrangement where frequency was constant and unchanged in all conditions but type was 
manipulated across conditions. 
 Consider an experiment where the ?baseline? phases consisted of concurrently 
available schedules of positive reinforcement with the relative reinforcement frequency 
ratio fixed at 1:1 for all conditions and the relative reinforcement magnitude ratios varied 
across a range of values (as in Landon et al., 2003), and where the ?experimental? phases 
consisted of identical schedules as the ?baseline? phases except that reinforcer type (e.g., 
positive vs. negative) would be different for the two concurrent responses.  The findings 
of Landon et al. (2003) predict a nonzero slope for the ?baseline? function based strictly 
on the effects of varied relative reinforcer magnitudes.  Any increase in slope in the 
118 
?experimental? phase would further support the independence of reinforcer frequency 
and type.  However, even given this outcome from such an experiment, it would be 
premature to assume that the effects resulting from positive and negative reinforcement 
manipulation would apply to all instances of concurrently available different types of 
reinforcement.  Further research would require experiments with similar methods using 
other qualitatively different outcomes such as money versus college course extra credit 
with college students as subjects, or qualitatively different types of food with nonhumans 
as subjects.  Extending this general research strategy to other response-consequence 
choice-controlling variables and their various combinations could provide the means by 
which they might be entered into a more fully integrated quantitative expression of CDT.  
However, before such a research program could proceed, an effort needs to be made to 
identify a standard means by which to evaluate GMR parameter differences. 
Evaluating GMR Parameter Differences 
 If a serious effort is to be made toward investigating the possible interactions 
among choice-controlling variables using procedures that compare matching functions, 
an equally serious effort will have to be made toward developing a standard, objective 
method of determining whether matching parameters (e.g., slopes) derived from the same 
individual in two experimental phases differ significantly from each other.  A search of 
the literature in the experimental analysis of behavior revealed few instances in which 
fitted parameters of a single quantitative model were compared.  Rather, a common 
strategy has been to evaluate the variance accounted for by a given model (e.g., Baum, 
1979; Davison & Nevin, 1999), or to compare variance accounted for by two different 
models (e.g., Alsop, 1991; Davison, 1991; Davison & Jenkins, 1985; Davison & Tustin, 
119 
1978).  When experimental designs have permitted the determination of fitted parameters 
for two or more functions, using the same model and subject, no consistency is apparent 
across investigations in the method of comparing parameter estimates.  Some 
investigators have relied only on nontechnical means such as visual inspection of graphed 
data or of fitted parameter estimates (e.g., Bron, et al., 2003; Madden & Perone, 1999; 
McLean & Blampied, 2001; White, Pipe, & McLean, 1984), while others have included 
applying inferential statistics toward this end (e.g., Landon, et al., 2003; McCarthy & 
Davison, 1980; McCarthy, Davison, & Jenkins, 1982). 
 The conclusions of the present investigation, both within and across experiments, 
were based on convergent evidence from all methods of analysis (i.e., exploratory data 
analysis).  However, the results of individual analyses illustrate that different means of 
comparing parameter estimates can promote different conclusions.  This is highlighted by 
referring to Table 13, which summarizes the results of each analysis of slopes for each 
experiment of the present investigation.  Each cell of Table 13 shows the proportion of 
subjects who showed a slope increase for ?experimental? phases over that of ?baseline? 
phases.  Individually, the visual and normative analyses support the overall conclusions 
stated above (though visual analysis may not and may be more akin to descriptive 
analysis if JL113?s slopes are considered different), but the descriptive and MRC 
analyses each support a different conclusion.  Descriptive analysis per se promotes no 
conclusion because all but one subject showed a slope increase regardless of independent 
variable manipulation.  MRC analysis per se promotes the conclusion that feedback 
differences are both necessary and sufficient and gains versus losses are neither necessary 
nor sufficient to increase behavioral sensitivity because all three subjects showed a slope 
120 
increase in Experiment 2 and only one showed a slope increase in Experiment 3.  While 
this conclusion would provide interesting information regarding positive and negative 
reinforcement, it would fail to support CDT. 
 Each method of analysis has its own limitations.  Visual inspection may admit a 
degree of subjectivity (DeProspero & Cohen, 1979; Fisch, 1998) because as effects 
become less clear, human observers become less reliable in judging them (DeProspero & 
Cohen, 1979, Jones, Weinrott, & Vaught, 1978; Parsonson & Baer, 1978, 1986, 1992).  
Descriptive analysis, which in the present investigation means ordinal-scale comparisons 
of parameter estimates of Equation 2, will always result in the conclusion that slopes are 
different because it does not take into account the magnitude of the difference ? a 
difference of .01 is the same as a difference of 1.0 ? and inherent behavioral variability 
virtually guarantees some difference.  The normative criterion derived from Robinson 
(1992) is based on intersubject variance, which is not functionally identical to 
intrasubject variance because intersubject variance incorporates not only the variance 
attributable to the independent variable, but also inherent behavioral error variance and 
the effects of other study-specific factors that might have had a possible systematic 
bearing on slopes (e.g., changeover delay duration). 
 MRC analysis, while a valid statistical tool for assessing slope differences 
between least-squares linear regressions, is limited by the procedures of the present 
investigation.  Specifically, the research tradition underlying the current procedures 
requires extended observation of each individual in each experimental condition (i.e., 
many sessions) so that error variance arising from transitory variables (e.g., acquisition) 
may be minimized and so that the data show what is typical for each individual under 
121 
each condition (Sidman, 1960).  This approach tends to yield strong experimental control 
but at a high cost, particularly when using humans as subjects, as experiments become 
lengthy (making subject retention difficult) and expensive (when money is used as 
reinforcement, an obvious economic constraint is put on the researcher).  For practical 
reasons, then, experimental analyses within this research tradition tend to yield relatively 
few data points per subject and few data points per subject means that the power of any 
within-subject inferential-statistical test is likely to be extremely low (Cohen, 1988). 
 Statistical power is broadly defined as the probability that a statistical test will 
detect an effect when an effect is actually present.  The limitation of potentially low 
statistical power was not an issue in the present investigation when MCR resulted in 
statistical significance; in fact, reaching significance with a likely low power test supports 
the conclusion of an extremely strong effect.  The issue is only relevant when statistical 
significance was not reached or ?approached? significance (e.g., Experiment 1:  SO104?s 
?R
2
 Change? for time-based analysis, p = .063; Experiment 4:  NN111?s ?R
2
 Change? for 
response-based analysis, p = .061).  In those cases, it is unknown whether an effect was 
not significant because of inadequate effect size or because of inadequate sample size.  
This is particularly relevant in Experiment 4 where no effects were statistically 
significant and the absence of an effect was considered a ?success?.  It would have been 
useful to know the power of the tests with the sample sizes used in the present 
investigation, but power tables provided by Cohen (1988) for MRC analyses provide 
values only for cases with a minimum of 20 degrees of freedom.  In the present 
experimental design, the available degrees of freedom were 5 for Main Effects models 
and 4 for Full models. 
122 
 Several strategies to address concerns over statistical power in within subject, 
parametric investigations are worth considering.  One strategy could be to run more 
conditions per empirical function, but as just discussed, subject retention and cost are 
formidable problems. 
 A second strategy worth exploring would be to develop procedures that could 
generate asymptotic responding after less extensive contingency exposure.  It should be 
noted, however, that with existing procedures, humans typically achieve asymptotic 
response levels much quicker than do nonhumans.  For example, stability was achieved 
in the present investigation within 5 to 23 eight-minute sessions (M = 10.64), or about 40 
to 184 minutes of contingency exposure (see Appendix B), and in the McLean and 
Blampied (2001) study (pigeons) within 20 to 76 forty-minute sessions, or about 800 to 
3040 minutes of contingency exposure.  It is worth questioning, therefore, how much 
more efficient the experimental procedures can become. 
 A third strategy worth considering would be to abandon the individual as the 
primary unit of analysis, and adopt the traditional approach of seeking effects in the 
aggregated data of many individuals.  However, if roughly the same procedures of the 
present investigation were replicated with more subjects, the subject retention issue might 
be avoided, but the cost of running an experiment would increase exponentially.  To 
make a groups-design approach more practically tenable, experimental conditions could 
be abbreviated (e.g., put a strict limit on number of sessions per condition regardless of 
performance), or each matching function data point could be obtained from a different 
group, but these approaches would compromise the research tradition?s historical 
123 
emphasis on asymptotic performance and strong within-subject experimental control, 
respectively. 
 However they might be obtained, empirical functions incorporating a sufficient 
number of experimental conditions to meet minimum criteria for power analysis could be 
analyzed via MRC analysis, the statistical power of those tests could then be determined 
empirically for each individual (Cohen, 1988), and the power analysis could serve as an 
index of the confidence to be placed in the statistical test.  One can imagine an approach, 
for instance, in which only subjects achieving sufficient statistical power would be 
considered in the analysis.  Other subjects would be reported but not included in the 
analysis based on weak experimental control. 
 An alternative to the methods of GMR parameter comparison used in the present 
investigation and to any of the individual analyses per se would be to obtain normative 
data on the intrasubject parameter variance.  Needed are studies that include within 
subject matching function replications across many subjects and many species.  Given the 
historical emphasis in the experimental analysis of behavior on replication as a primary 
tool in increasing experimental control (Sidman, 1960), this would seem the preferred 
course of action. 
A Methodological Concern of the Present Investigation 
 The methods employed in the present investigation appear to provide a promising 
set of tools with the potential to advance a broad research agenda.  However, before they 
can be viewed as a model by which to proceed, a specific procedural issue needs to be 
addressed.  Humans are useful as subjects because they allow the use of verbal stimuli, 
but they are troublesome as subjects for the same reason. 
124 
 While instructional stimuli are valuable tools that promote acquisition in the 
absence of explicit shaping (Pilgrim, 1998), they and other verbal stimuli (e.g., ?+?, ???, 
and the word ?No? in the present investigation) can be problematic because they 
necessarily rely on subjects? pre-experimental histories.  Because these histories may 
vary across subjects in unknown ways, such stimuli introduce a possible source of 
intersubject variability.  For example, Lane and Cherek (1999) reported that non-
reinforced trials, or lost opportunities to earn reinforcement (e.g., ?No +4?), might serve 
as ?aversive? stimuli and exert substantial differential control over behavior.  The present 
investigation conceptualized a stimulus signaling a loss (i.e., ??4?) as essentially 
equivalent to a stimulus signaling a lost opportunity to earn (i.e., ?No +4).  If Lane and 
Cherek are correct, there is no way of knowing whether this conceptualization is 
accurate.  As a matter of conjecture, an inequality between the ?aversiveness? of these 
stimuli may have been responsible for the bias observed in Experiment 2.  As a matter of 
further conjecture, the bias may not have been observed in Experiments 3 and 4, where 
the ?No +4? stimulus was also used, because of the overall richer feedback context.  It 
would be worth exploring procedures in which experimental repertoires are strictly 
shaped, and in which nonsense stimuli are established as conditioned consequences, as 
per procedures used with nonhumans.  The latter task would be especially difficult to 
accomplish, however, because the required conditioning would necessarily involve some 
stimuli with which subjects have had some previous experience.  Nevertheless, the 
overall goal would be to establish procedures eliminating as many verbal stimuli as 
possible. 
125 
 Another approach to assessing the potentially troublesome role of verbal stimuli 
of the present procedures would be to find a means of testing the interspecies generality 
of the effects.  The nonhuman conditioned reinforcement procedure developed by 
Jackson and Hackenberg (1996) provide such a means.  In that procedure, a row of lights 
is presented above the response keys and individual lights in the row are illuminated as 
requirements of the schedule of reinforcement in effect are met.  After a set time, number 
of obtained conditioned reinforcers, or responses, a period of exchange is introduced 
where responses on a different key allow access to food for a brief time and extinguish 
one of the lights.  It seems reasonable that one row of lights could be arranged for each of 
two response keys associated with one schedule of a two-ply concurrent schedule.  One 
schedule could program ?light extinguishings? according to one variable-cycle schedule 
and the other schedule could program ?light illuminations? according a different variable-
cycle schedule.  Responses on the key associated with the former could cancel scheduled 
?light extinguishings? and responses on the key associated with the latter could present 
?light illuminations.?  After appropriate shaping, pigeons could then be exposed to the 
same series of conditions as in the present investigation.  Replication of the present 
investigation?s results would suggest an insignificant role for verbal stimuli in 
contributing to those results.  Naturally, a similar procedure could be arranged for a 
variety of species and could be arranged to examine other choice-controlling variables 
(e.g., different colored lights associated with different magnitudes of reinforcement). 
Conclusion 
 The present investigation supported CDT?s qualitative prediction that 
concurrently available different reinforcer types enhance behavioral sensitivity to 
126 
changing reinforcement rates.  CDT is a promising unified theory of both stimulus and 
consequence control and determining its validity is an important mission.  Perhaps just as 
important, however, the present investigation illustrated a general strategy for mapping 
interactions among choice-controlling consequence variables.  It also raised critical 
questions about how the results of studies conducted according to this strategy are to be 
evaluated.  Given that theories come and go, the present investigation's most valuable 
contribution may pertain to these methodological issues. 
127 
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134 
Footnotes 
 
1
 The term ?negative reinforcement? is typically defined as the increase or 
maintenance of responding by either the removal or avoidance of some stimulus.  By this 
definition, the term can refer to two procedures; one wherein on ongoing stimulus is 
terminated contingent on the response (escape), and a second wherein a stimulus that has 
previously been presented in the absence of responding is avoided contingent on the 
response (avoidance).  The more general term ?negative reinforcement? will be used 
throughout the paper to refer to the specific case of avoidance rather than escape. 
 
2
 The strategy of holding overall earnings as constant as possible across 
experiments was taken for two reasons.  First, differential earnings rates might have 
differentially affected outcomes in some unforeseen way.  Second, laboratory lore 
informs us that if earning rates are too low, subject retention becomes difficult, and if 
they are too high, experimental control becomes challenging. 
135 
Table 1 
Experimental Conditions ? Experiment 1 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
TB101 1 P : P 5 : 1 12 : 60 0, 0, 63 
  2 P : P 1 : 2 30 : 15 0, 63, 0 
  3 N : P 5 : 1 12 : 60 63, 0, 63 
  4 P : N 1 : 2 30 : 15 63, 63, 0 
  5 P : P 1 : 5 60 : 12 0, 63, 63 
  6 P : N 5 : 1 12 : 60 63, 20, 63 
  7 N : P 1 : 2 30 : 15 63, 63, 20 
  8 P : P 2 : 1 15 : 30 20, 20, 63 
TM102 1 P : P 1 : 5 60 : 12 0, 0, 63 
  2 P : P 2 : 1 15 : 30 0, 63, 0 
  3 N : P 2 : 1 15 : 30 63, 0, 63 
  4 N : P 1 : 5 60 : 12 63, 63, 0 
  5 P : P 5 : 1 12 : 60 0, 63, 63 
  6 P : N 2 : 1 15 : 30 63, 20, 63 
  7 P : N 1 : 5 60 : 12 63, 63, 20 
  8 P : P 1 : 2 30 : 15 20, 20, 63 
(Table Continues) 
136 
Table 1 (con?t) 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
SO104 1 P : P 1 : 5 60 : 12 0, 0, 63 
  2 P : P 2 : 1 15 : 30 0, 63, 0 
  3 N : P 2 : 1 15 : 30 63, 0, 63 
  4 N : P 1 : 5 60 : 12 63, 63, 0 
  5 P : P 5 : 1 12 : 60 0, 63, 63 
  6 P : N 2 : 1 15 : 30 63, 20, 63 
  7 P : N 1 : 5 60 : 12 63, 63, 20 
  8 P : P 1 : 2 30 : 15 20, 20, 63 
a
Background colors are represented as ?RGB? numbers with each number reflecting the 
saturation of red, green, and blue hues respectively.  Each number could be varied from a 
minimum of zero to a maximum of 63.  Thus, for example, ?0, 0, 63? has no red or green 
hue and the maximum blue hue resulting in ?pure? blue. 
137 
Table 2 
Experimental Conditions ? Experiment 2 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
GE105 1 P : P 5 : 1 12 : 60 0, 0, 63 
  2 IP : P 5 : 1 12 : 60 0, 63, 0 
  3 P : IP 1 : 2 30 : 15 63, 0, 63 
  4 P : P 2 : 1 15 : 30 63, 63, 0 
  5 IP : P 1 : 2 30 : 15 0, 63, 63 
  6 P : P 1 : 5 60 : 12 63, 20, 63 
  7 P : IP 5 : 1 12 : 60 63, 63, 20 
  8 P : P 1 : 2 30 : 15 20, 20, 63 
MJ106 1 P : IP 2 : 1 15 : 30 0, 0, 63 
  2 P : P 1 : 5 60 : 12 0, 63, 0 
  3 IP : P 2 : 1 15 : 30 63, 0, 63 
  4 P : P 5 : 1 12 : 60 63, 63, 0 
  5 P : P 1 : 2 30 : 15 0, 63, 63 
  6 P : IP 1 : 5 60 : 12 63, 20, 63 
  7 IP : P 1 : 5 60 : 12 63, 63, 20 
  8 P : P 2 : 1 15 : 30 20, 20, 63 
(Table Continues) 
138 
Table 2 (con?t) 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
GR108 1 P : P 1 : 2 30 : 15 0, 0, 63 
  2 P : IP 5 : 1 12 : 60 0, 63, 0 
  3 IP : P 1 : 2 30 : 15 63, 0, 63 
  4 P : P 2 : 1 15 : 30 63, 63, 0 
  5 P : P 5 : 1 12 : 60 0, 63, 63 
  6 P : IP 1 : 2 30 : 15 63, 20, 63 
  7 IP : P 5 : 1 12 : 60 63, 63, 20 
  8 P : P 1 : 5 60 : 12 20, 20, 63 
a
Background colors are represented as ?RGB? numbers with each number reflecting the 
saturation of red, green, and blue hues respectively.  Each number could be varied from a 
minimum of zero to a maximum of 63.  Thus, for example, ?0, 0, 63? has no red or green 
hue and the maximum blue hue resulting in ?pure? blue. 
139 
Table 3 
Experimental Conditions ? Experiment 3 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
JE109 1 TP : TP 5 : 1 12 : 60 0, 0, 63 
  2 TN : TP 5 : 1 12 : 60 0, 63, 0 
  3 TP : TN 1 : 2 30 : 15 63, 0, 63 
  4 TP : TP 2 : 1 15 : 30 63, 63, 0 
  5 TN : TP 1 : 2 30 : 15 0, 63, 63 
  6 TP : TP 1 : 5 60 : 12 63, 20, 63 
  7 TP : TN 5 : 1 12 : 60 63, 63, 20 
  8 TP : TP 1 : 2 30 : 15 20, 20, 63 
SL110 1 TP : TN 2 : 1 15 : 30 0, 0, 63 
  2 TP : TP 1 : 5 60 : 12 0, 63, 0 
  3 TN : TP 2 : 1 15 : 30 63, 0, 63 
  4 TP : TP 5 : 1 12 : 60 63, 63, 0 
  5 TP : TP 1 : 2 30 : 15 0, 63, 63 
  6 TP : TN 1 : 5 60 : 12 63, 20, 63 
  7 TN : TP 1 : 5 60 : 12 63, 63, 20 
  8 TP : TP 2 : 1 15 : 30 20, 20, 63 
(Table Continues) 
140 
Table 3 (con?t) 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
NN111 1 TP : TP 1 : 2 30 : 15 0, 0, 63 
  2 TP : TN 5 : 1 12 : 60 0, 63, 0 
  3 TN : TP 1 : 2 30 : 15 63, 0, 63 
  4 TP : TP 2 : 1 15 : 30 63, 63, 0 
  5 TP : TP 5 : 1 12 : 60 0, 63, 63 
  6 TP : TN 1 : 2 30 : 15 63, 20, 63 
  7 TN : TP 5 : 1 12 : 60 63, 63, 20 
  8 TP : TP 1 : 5 60 : 12 20, 20, 63 
a
Background colors are represented as ?RGB? numbers with each number reflecting the 
saturation of red, green, and blue hues respectively.  Each number could be varied from a 
minimum of zero to a maximum of 63.  Thus, for example, ?0, 0, 63? has no red or green 
hue and the maximum blue hue resulting in ?pure? blue. 
141 
Table 4 
Experimental Conditions ? Experiment 4 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
MJ112 1 TP : TP 5 : 1 12 : 60 0, 0, 63 
  2 TN : TN 1 : 2 30 : 15 0, 63, 0 
  3 TP : TP 1 : 2 30 : 15 63, 0, 63 
  4 TN : TN 5 : 1 12 : 60 63, 63, 0 
  5 TP : TP 2 : 1 15 : 30 0, 63, 63 
  6 TP : TP 1 : 5 60 : 12 63, 20, 63 
  7 TN : TN 2 : 1 15 : 30 63, 63, 20 
  8 TN : TN 1 : 5 60 : 12 20, 20, 63 
JL113 1 TP : TP 1 : 2 30 : 15 0, 0, 63 
  2 TN : TN 5 : 1 12 : 60 0, 63, 0 
  3 TN : TN 2 : 1 15 : 30 63, 0, 63 
  4 TP : TP 1 : 5 60 : 12 63, 63, 0 
  5 TP : TP 5 : 1 12 : 60 0, 63, 63 
  6 TN : TN 1 : 2 30 : 15 63, 20, 63 
  7 TP : TP 2 : 1 15 : 30 63, 63, 20 
  8 TN : TN 1 : 5 60 : 12 20, 20, 63 
(Table Continues) 
142 
Table 4 (con?t) 
 
 
  Schedules (L : R)  
Subject Condition Type Ratio Mean Intervals (s) Background Color
a 
 
SS114 1 TP : TP 1 : 5 60 : 12 0, 0, 63 
  2 TP : TP 2 : 1 15 : 30 0, 63, 0 
  3 TN : TN 5 : 1 12 : 60 63, 0, 63 
  4 TP : TP 1 : 2 30 : 15 63, 63, 0 
  5 TN : TN 1 : 2 30 : 15 0, 63, 63 
  6 TN : TN 1 : 5 60 : 12 63, 20, 63 
  7 TP : TP 5 : 1 12 : 60 63, 63, 20 
  8 TN : TN 2 : 1 15 : 30 20, 20, 63 
a
Background colors are represented as ?RGB? numbers with each number reflecting the 
saturation of red, green, and blue hues respectively.  Each number could be varied from a 
minimum of zero to a maximum of 63.  Thus, for example, ?0, 0, 63? has no red or green 
hue and the maximum blue hue resulting in ?pure? blue. 
143 
Table 5 
Experiment 1 Independent Regressions 
 
 
Subject Condition Equation r
2
 a
(N:P)
 - a
(P:P)
 c
(N:P)
 - c
(P:P)
 
Responses 
 TB101 P:P y = 0.806x ? .116 .892 .296   .158 
  N:P y = 1.102x + .042 .950 
TM102 P:P y = 0.547x + .043 .998 .722 -.140 
  N:P y = 1.269x ? .097 .979 
 SO104 P:P y = 0.600x ? .058 .870 .632   .588 
  N:P y = 1.232x + .530 .974 
 
Time 
 TB101 P:P y = 0.737x ? .111 .893 .264   .136 
  N:P y = 1.001x + .025 .960 
TM102 P:P y = 0.478x + .031 .996 .596 -.171 
  N:P y = 1.074x ? .140 .987 
 SO104 P:P y = 0.464x ? .047 .865 .429   .461 
  N:P y = 0.893x + .414 .973 
144 
Table 6 
Experiment 1 MRC Regressions 
 
 
Subject Model Equation R
2
 R
2
 Change p 
 
Responses 
 TB101 M.E. y = 0.971x
1
 + 0.140x
2
 ? 0.107 .912 
  Full y = 0.806x
1
 + 0.157x
2
 + 0.295x
12
 ? 0.116 .933 .021 .330 
TM102 M.E. y = 0.969x
1
 ? 0.167x
2
 + 0.035 .872 
  Full y = 0.547x
1
 ? 0.140x
2
 + 0.722x
12
 + 0.043 .982 .110 .007 
 SO104 M.E. y = 0.986x
1
 + 0.638x
2
 ? 0.050 .911 
  Full y = 0.600x
1
 + 0.587x
2
 + 0.633x
12
 ? 0.058 .971 .060 .044 
 
Time 
 TB101 M.E. y = 0.884x
1
 + 0.121x
2
 ? 0.103 .920 
  Full y = 0.737x
1
 + 0.136x
2
 + 0.264x
12
 ? 0.111 .940 .020 .313 
TM102 M.E. y = 0.826x
1
 ? 0.194x
2
 + 0.025 .887 
  Full y = 0.478x
1
 ? 0.172x
2
 + 0.595x
12
 + 0.031 .989 .102 .003 
 SO104 M.E. y = 0.727x
1
 + 0.495x
2
 ? 0.041 .919 
  Full y = 0.464x
1
 + 0.460x
2
 + 0.429x
12
 ? 0.047 .969 .050 .063 
145 
Table 7 
Experiment 2 Independent Regressions 
 
 
Subject Condition Equation r
2
 a
(IP:P)
 - a
(P:P)
 c
(IP:P)
 - c
(P:P)
 
Responses 
 GE105  P:P y = 0.228x + .020 .947 .920 .614 
  IP:P y = 1.148x + .634 .990 
 MJ106  P:P y = 0.442x ? .044 .973 .931 .357 
  IP:P y = 1.373x + .313 .963 
 GR108  P:P y = 0.312x + .006 .987 .761 .255 
  IP:P y = 1.073x + .261 .915 
 
Time 
 GE105  P:P y = 0.156x + .014 .864 .582 .425 
  IP:P y = 0.738x + .439 .996 
 MJ106  P:P y = 0.376x ? .037 .981 .729 .226 
  IP:P y = 1.105x + .189 .952 
 GR108  P:P y = 0.278x + .003 .986 .572 .181 
  IP:P y = 0.850x + .184 .936 
146 
Table 8 
Experiment 2 MRC Regressions 
 
 
Subject Model Equation R
2
 R
2
 Change p 
 
Responses 
 GE105 M.E. y = 0.757x
1
 + 0.667x
2
 + 0.023 .848 
  Full y = 0.228x
1
 + 0.614x
2
 + 0.920x
12
 + 0.020 .994 .146 .001 
 MJ106 M.E. y = 1.050x
1
 + 0.345x
2
 ? 0.023 .832 
  Full y = 0.442x
1
 + 0.357x
2
 + 0.931x
12
 ? 0.044 .966 .134 .016 
 GR108 M.E. y = 0.766x
1
 + 0.276x
2
 ? 0.006 .762 
  Full y = 0.312x
1
 + 0.254x
2
 + 0.761x
12
 + 0.006 .925 .163 .042 
 
Time 
 GE105 M.E. y = 0.491x
1
 + 0.458x
2
 + 0.016 .862 
  Full y = 0.156x
1
 + 0.425x
2
 + 0.582x
12
 + 0.014 .995 .133 .000 
 MJ106 M.E. y = 0.852x
1
 + 0.217x
2
 ? 0.020 .828 
  Full y = 0.376x
1
 + 0.226x
2
 + 0.729x
12
 ? 0.037 .956 .129 .026 
 GR108 M.E. y = 0.620x
1
 + 0.197x
2
 ? 0.006 .793 
  Full y = 0.278x
1
 + 0.181x
2
 + 0.571x
12
 + 0.003 .943 .150 .032 
147 
Table 9 
Experiment 3 Independent Regressions 
 
 
Subject Condition Equation r
2
 a
(TN:TP)
 - a
(TP:TP)
 c
(TN:TP)
 - c
(TP:TP)
 
Responses 
 JE109 TP:TP y = 0.484x ? .077 .932 .655   .151 
  TN:TP y = 1.139x + .074 .989 
 SL110 TP:TP y = 1.081x + .015 .996 .433 -.136 
  TN:TP y = 1.514x ? .121 .916 
 NN111 TP:TP y = 0.839x + .106 .937 .734   .005 
  TN:TP y = 1.573x + .111 .960 
 
Time 
 JE109 TP:TP y = 0.416x ? .064 .914 .552   .104 
  TN:TP y = 0.968x + .040 .992 
 SL110 TP:TP y = 0.903x + .014 .998 .263 -.098 
  TN:TP y = 1.166x ? .084 .918 
 NN111 TP:TP y = 0.794x + .099 .939 .631 -.037 
  TN:TP y = 1.425x + .062 .980 
148 
Table 10 
Experiment 3 MRC Regressions 
 
 
Subject Model Equation R
2
 R
2
 Change p 
 
Responses 
 JE109 M.E. y = 0.843x
1
 + 0.153x
2
 ? 0.069 .859 
  Full y = 0.484x
1
 + 0.151x
2
 + 0.655x
12
 ? 0.077 .982 .123 .006 
 SL110 M.E. y = 1.299x
1
 ? 0.144x
2
 + 0.011 .917 
  Full y = 1.081x
1
 ? 0.136x
2
 + 0.433x
12
 + 0.015 .942 .025 .260 
 NN111 M.E. y = 1.254x
1
 + 0.005x
2
 + 0.114 .881 
  Full y = 0.839x
1
 + 0.006x
2
 + 0.734x
12
 + 0.106 .956 .074 .061 
 
Time 
 JE109 M.E. y = 0.719x
1
 + 0.105x
2
 ? 0.057 .860 
  Full y = 0.416x
1
 + 0.104x
2
 + 0.552x
12
 ? 0.064 .981 .122 .007 
 SL110 M.E. y = 1.036x
1
 ? 0.102x
2
 + 0.011 .932 
  Full y = 0.903x
1
 ? 0.097x
2
 + 0.263x
12
 + 0.014 .947 .015 .351 
 NN111 M.E. y = 1.151x
1
 ? 0.038x
2
 + 0.106 .905 
  Full y = 0.794x
1
 ? 0.037x
2
 + 0.631x
12
 + 0.099 .972 .067 .036 
149 
Table 11 
Experiment 4 Independent Regressions 
 
 
Subject Condition Equation r
2
 a
(TN:TN)
 - a
(TP:TP)
 c
(TN:TN)
 - c
(TP:TP)
 
Responses 
 MJ112 TP:TP y = 1.383x ? .055 .966 -.067   .149 
  TN:TN y = 1.316x + .094 .985 
 JL113 TP:TP y = 1.093x + .136 .998   .206 -.272 
  TN:TN y = 1.299x ? .136 .984 
 SS114 TP:TP y = 0.822x + .069 .988   .376 -.024 
  TN:TN y = 1.198x + .045 .945 
 
Time 
 MJ112 TP:TP y = 1.287x ? .047 .969 -.049   .128 
  TN:TN y = 1.238x + .081 .985 
 JL113 TP:TP y = 0.929x + .097 .998   .116 -.193 
  TN:TN y = 1.045x ? .096 .989 
 SS114 TP:TP y = 0.665x + .042 .979   .119 -.041 
  TN:TN y = 0.784x + .001 .939 
150 
Table 12 
Experiment 4 MRC Regressions 
 
 
Subject Model Equation R
2
 R
2
 Change p 
 
Responses 
 MJ112 M.E. y = 1.352x
1
 + 0.147x
2
 ? 0.054 .974 
  Full y = 1.383x
1
 + 0.148x
2
 ? 0.067x
12
 ? 0.055 .975 .001 .776 
 JL113 M.E. y = 1.192x
1
 ? 0.270x
2
 + 0.134 .983 
  Full y = 1.093x
1
 ? 0.272x
2
 + 0.207x
12
 + 0.136 .990 .007 .164 
 SS114 M.E. y = 1.012x
1
 ? 0.021x
2
 + 0.067 .926 
  Full y = 0.822x
1
 ? 0.023x
2
 + 0.376x
12
 + 0.069 .958 .032 .154 
 
Time 
 MJ112 M.E. y = 1.263x
1
 + 0.127x
2
 ? 0.047 .976 
  Full y = 1.287x
1
 + 0.128x
2
 ? 0.049x
12
 ? 0.047 .976 .000 .816 
 JL113 M.E. y = 0.985x
1
 ? 0.192x
2
 + 0.096 .990 
  Full y = 0.929x
1
 ? 0.193x
2
 + 0.115x
12
 + 0.097 .993 .003 .234 
 SS114 M.E. y = 0.725x
1
 ? 0.040x
2
 + 0.042 .949 
  Full y = 0.665x
1
 ? 0.041x
2
 + 0.119x
12
 + 0.042 .955 .006 .492 
151 
Table 13 
Proportion of Subjects Showing a Steeper Slope for ?Experimental? Phases than for 
?Baseline? Phases in Each Experiment by Response-Based Analyses 
 
Experiment Visual Descriptive Normative MRC 
 
1 (N:P) 3/3 3/3 2/3 2/3 
2 (IP:P) 3/3 3/3 3/3 3/3 
3 (TN:TP) 3/3 3/3 3/3 1/3 
4 (TN:TN) 1/3 2/3 0/3 0/3 
152 
Figure Captions 
Figure 1.  The logarithms of the response (left panels) and time (right panels) allocation 
ratios plotted against the logarithms of the obtained reinforcement ratios for each subject 
of Experiment 1.  Lines were fit to the data from each phase by the method of least 
squares.  Closed circles and heavy lines represent the data from the concurrent VC 
schedules of ?standard? positive versus ?standard? positive reinforcement and closed 
triangles and light lines represent the data from the concurrent VC schedules of 
?standard? negative versus ?standard? positive reinforcement.  Note the different scales 
on the axes of SO104?s plot for responses. 
Figure 2.  The logarithms of the response (left panels) and time (right panels) allocation 
ratios plotted against the logarithms of the obtained reinforcement ratios for each subject 
of Experiment 2.  Lines were fit to the data from each phase by the method of least 
squares.  Closed circles and heavy lines represent the data from the concurrent VC 
schedules of ?standard? positive versus ?standard? positive reinforcement and closed 
diamonds and light lines represent the data from the concurrent VC schedules of 
?inverse? positive versus ?standard? positive reinforcement. 
Figure 3.  The logarithms of the response (left panels) and time (right panels) allocation 
ratios plotted against the logarithms of the obtained reinforcement ratios for each subject 
of Experiment 3.  Lines were fit to the data from each phase by the method of least 
squares.  Open circles and heavy lines represent the data from the concurrent VC 
schedules of ?total feedback? positive versus ?total feedback? positive reinforcement and 
closed squares and light lines represent the data from the concurrent VC schedules of 
?total feedback? negative versus ?total feedback? positive reinforcement. 
153 
Figure 4.  The logarithms of the response (left panels) and time (right panels) allocation 
ratios plotted against the logarithms of the obtained reinforcement ratios for each subject 
of Experiment 4.  Lines were fit to the data from each phase by the method of least 
squares.  Open circles and heavy lines represent the data from the concurrent VC 
schedules of ?total feedback? positive versus ?total feedback? positive reinforcement and 
open squares and light lines represent the data from the concurrent VC schedules of ?total 
feedback? negative versus ?total feedback? negative reinforcement. 
Figure 5.  Slope estimates (top panel) and slope estimate differences (bottom panel) of 
each matching function for each subject of each experiment.  In the top panel, dark bars 
represent the slope estimates for the ?baseline? phase matching functions and light bars 
represent the slope estimates for the ?experimental? phase matching functions.  In the 
bottom panel, bars represent the difference between the ?experimental? matching 
function slope estimate and the ?baseline? matching function slope estimate.  The 
horizontal line in the bottom panel demarcates the normative criterion (a = .388) used as 
the primary evaluative tool for the present investigation. 
Figure 1 
 
Responses Time 
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
154 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
-3
-2
-1
0
1
2
3
-3 -2 -1 0 1 2 3
-2
-1
0
1
2
-2 -1 0 1 2
 
% Conc N:P 
? Conc P:P 
TB101 
TM102 
SO104 
Lo
g
 Allocation Ratio 
(
N:P = N/P; P:P = L/R
)
 
 
Log Reinforcement Ratio (N:P = N/P; P:P = L/R) 
Figure 2 
 
Responses Time 
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
155 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
" Conc IP:P 
? Conc P:P 
GE105 
MJ106 
GR108 
Lo
g
 Allocation Ratio 
(
IP:P = IP/P; P:P = L/R
)
 
 
Log Reinforcement Ratio (IP:P = IP/P; P:P = L/R) 
Figure 3 
 
Responses Time 
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
156 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
! Conc TN
? Conc
:TP 
 TP:TP 
JE109 
SL110 
NN111 
Lo
g
 Allocation Ratio 
(
TN:TP = TN/TP; TP:TP = L/R
)
 
 
Log Reinforcement Ratio (TN:TP = TN/TP; P:P = L/R) 
Figure 4 
 
Responses Time 
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
157 
-2
-1
0
1
2
-2 -1 0 1 2
-2
-1
0
1
2
-2 -1 0 1 2
 
' Conc TN
? Conc
:TN 
 TP:TP 
MJ112 
JL113 
SS114 
Lo
g
 Allocation Ratio 
(
L/R
)
 
 
Log Reinforcement Ratio (L/R) 
Figure 5 
 
 
 
 
 
 
-0.5
0.0
0.5
1.0
1.5
2.0
TB101 TM102 SO104 GE105 MJ106 GR108 JE109 SL110 NN111 MJ112
Exp. 1 (N:P) Exp. 2 (IP:P) Exp. 3 (TN:TP) E
Sl
o
p
e
Baseline Experimental
-0.5
0.0
0.5
1.0
1.5
2.0
TB101 TM102 SO104 GE105 MJ106 GR108 JE109 SL110 NN111 MJ112
Exp. 1 (N:P) Exp. 2 (IP:P) Exp. 3 (TN:TP) E
S
l
opes
 Di
f
f
er
enc
e
Series1
158 
JL113 SS114
xp. 4 (TN:TN)
 
JL113 SS114
xp. 4 (TN:TN)
 
a
(EXP)
-a
(BL)
 = .388 
159 
Appendix A 
Intake, Instructions, and Training 
 The first visit to the laboratory began with presentation of the informed consent 
agreement.  Volunteers were asked to read, but not sign it right away, so that they could 
have a chance to see the task before committing to participate.  After they had read the 
informed consent, and had any questions answered, they were shown the workroom and 
the particular workstation at which they would be working.  Following this brief spatial 
orientation, they were presented the following set of general task instructions: 
Instructions to the Subject 
1) You cannot take a break during a working session. 
 The total time you spend in the lab will be divided into short working 
sessions.  In between these sessions, you will have the option to take a break, go 
to the restroom, or ask questions.  If you do not need a break and would like to 
continue working then you should just remain in the ?run room.?  You should 
realize that money cannot be earned while you are on a break; therefore it is in 
your best interests to take few, if any, breaks. 
2) Your task will be to click on the moving boxes using the mouse pointer and the 
left button on the mouse. 
 After you click the <Ready> button on the first screen you see, your 
?work? screen will appear.  On this ?work? screen, you will notice boxes moving 
around on two different sides of the screen.  Your job is to use the mouse to click 
on these moving boxes.  Once you start working on one side, the other side of the 
screen will turn black.  This means that your mouse is turned on for the white 
160 
side, and turned off for the black side.  Either side can be black or white, 
depending on where you are working at the moment. 
 Clicking on the white side will help you earn money, or avoid losing 
money.  Clicking on the black side will not help you, because the mouse is turned 
off for that side.  While a side is black, you cannot earn money that may be 
available there.  Similarly, while a side is black, you cannot avoid money losses 
that happen there. 
 To change a side from black to white, you will need to click several times 
on the small ?Change? box in the middle of your screen.  When you have clicked 
this box enough times, the black side will turn white, and the mouse will be 
turned on there.  The mouse will be off for the other side. 
 Thus, the mouse is always on for only one side at a time.  You can change 
sides whenever you want by clicking on the ?Change? box.  There are no rules for 
how you should respond except that you want to maximize the number of points 
you get as quickly as you can. 
3) The experimenters will keep a running tally of your total money earned. 
 At the end of each session, a message will be displayed informing you of 
how much money you have accrued for that session.  The experimenter will 
record this amount.  At the end of each session, the experimenter will add the 
amount from that session to your previous cumulative total to get a running total.  
It is based on this cumulative amount that you will be paid. 
4) Please do not hesitate to ask the experimenter any questions you may have. 
161 
They were then given a 1 min task demonstration with concurrent VC5 schedules of 
positive reinforcement (reinforcer magnitude = 1?) programmed for both work areas.  
Language used to address any questions they had did not deviate significantly from the 
written instructions.  If the volunteers were interested in participating in the experiment 
following the demonstration, they were asked to sign the informed consent. 
 Two 1 min training sessions followed agreement to participate.  The training 
sessions provided free-operant forced-choice arrangements where the ?Change? box was 
inoperative and only one side had a schedule programmed.  Opposite sides were used for 
each training session and the first side used was varied across subjects.  All sessions were 
programmed with VC5 schedules and reinforcer magnitudes of 1? and subjects were 
informed that the ?money? they would earn during the training sessions would not count 
toward their final earnings total.  Different instructions had to be given for each training 
session for each experiment (except Experiments 3 and 4 required the same instructions) 
to accord with the ?gain vs. loss? and ?feedback asymmetry? variations of the different 
conditions and were as follows: 
For Experiment 1, training session 1: 
Sometimes clicking your mouse on a box will earn you money.  If you should 
earn money, a flashing message will show this on your screen.  The upcoming 
session provides an example with only one side of the screen active. 
For Experiment 1, training session 2: 
Sometimes clicking your mouse on a box will keep you from losing money, but 
there will be no message to show you that you have avoided losing money.  
162 
Sometimes a message will show you that you have lost money.  The upcoming 
session provides an example with only one side of the screen active. 
For Experiment 2, training session 1: 
Sometimes clicking your mouse on a box will earn you money.  If you should 
earn money, a flashing message will show this on your screen.  The upcoming 
session provides an example with only one side of the screen active. 
For Experiment 2, training session 2: 
Sometimes clicking your mouse on a box will earn you money, but there will be 
no message to show you that you have earned money.  Sometimes a message will 
show you that you have missed a chance to earn money.  The upcoming session 
provides an example with only one side of the screen active. 
Since Experiments 3 and 4 used the same contingency structures (just no differential 
outcome in Experiment 4), the same instructions were given for both. 
For Experiments 3 and 4, training session 1: 
Sometimes clicking your mouse on a box will earn you money.  If you should 
earn money, a flashing message will show this on your screen.  Sometimes a 
message will show you that you have missed a chance to earn money.  The 
upcoming session provides an example with only one side of the screen active. 
For Experiments 3 and 4, training session 2: 
Sometimes clicking your mouse on a box will keep you from losing money.  If 
you should avoid losing money, a flashing message will show this on your screen.  
Sometimes a message will show you that you have lost money.  The upcoming 
session provides an example with only one side of the screen active. 
163 
 Each training session was designed to give the subject experience with each of the 
four types of consequences that would be presented in the experiment (two types of 
feedback for each of the two types of consequences) and the experimenter prompted the 
subject in whatever way was necessary to ensure this.  For example, if the subject was 
training on a VC5 schedule of positive reinforcement, and was clicking the mouse rapidly 
enough to earn every positive reinforcer, the experimenter prompted the subject not to 
respond for a few moments just to experience the feedback (or lack thereof) for not 
responding. 
 After the second training session was completed, subjects were given the 
following final set of instructions prior to beginning the experiment proper: 
From now on, both sides of your screen will be active.  Note that clicking the two 
boxes may affect your earnings differently.  You can respond as much or as little 
as you like wherever you like and use whatever strategy you like overall.  It is up 
to you to figure out how to work each side to your best advantage. 
After the subject read the final set of instructions, all instructions were removed, the 
background noise began (their own music in most cases), the door to the workroom was 
shut, and the experiment began. 
Appendix B 
Raw Data Averaged from the Four-Session Stable Data 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 1 TB101 P5:P1 316.50 136.50 328.76 150.45 31.25 6.25 7.25 1.50 6 
 P1:P2 187.25 267.25 200.14 278.36 9.75 23.00 5.75 10.50 7 
1
6
4
 
 N5:P1 379.50 31.75 428.96 49.39 37.25 6.00 2.75 1.75 10 
 P1:N2 166.25 199.25 214.46 263.84 13.25 25.50 2.50 6.25 15 
 P1:P5 42.50 400.00 54.17 424.68 5.25 36.00 2.25 3.00 10 
 P5:N1 415.25 40.50 429.67 48.39 37.25 4.00 2.25 3.50 7 
 N1:P2 155.50 278.25 176.45 301.81 11.50 26.25 4.00 6.00 15 
 P2:P1 211.50 158.25 264.98 213.67 26.00 13.25 6.75 2.75 9 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 TM102 P1:P5 387.75 774.00 170.05 309.29 7.00 31.25 1.00 7.50 5 
 P2:P1 742.50 483.50 282.99 196.04 26.75 13.75 5.00 2.25 9 
1
6
5
 
 N2:P1 298.75 286.50 239.79 239.51 26.00 14.75 6.75 1.25 6 
 N1:P5 19.75 391.75 29.42 449.67 4.25 38.50 3.25 .50 9 
 P5:P1 309.25 103.25 345.04 133.91 33.75 5.75 6.00 2.00 11 
 P2:N1 362.50 79.50 381.44 97.38 30.75 10.00 2.00 5.75 8 
 P1:N5 97.50 874.75 78.21 401.00 7.00 37.50 1.00 2.00 11 
 P1:P2 416.50 585.50 199.36 279.85 10.75 23.00 5.25 9.75 6 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 SO104 P1:P5 82.00 382.50 111.47 367.56 5.50 34.25 2.25 4.00 17 
 P2:P1 439.75 254.00 293.21 185.56 28.00 13.25 6.00 3.00 15 
1
6
6
 
 N2:P1 607.75 27.00 442.55 35.23 30.75 6.50 2.00 9.00 5 
 N1:P5 270.50 298.50 233.25 245.71 7.50 30.75 .50 8.50 22 
 P5:P1 417.25 242.25 285.92 192.96 32.75 6.50 6.00 1.50 6 
 P2:N1 257.75 231.75 241.66 237.46 26.25 13.50 5.50 2.75 14 
 P1:N5 9.25 997.50 16.78 462.01 2.50 38.00 4.50 1.50 16 
 P1:P2 315.25 382.00 218.61 260.34 13.75 28.25 2.75 4.50 5 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 2 GE105 P5:P1 292.00 194.50 274.83 203.27 28.25 7.50 9.75 .50 12 
 IP5:P1 831.75 31.75 430.30 47.93 36.25 6.75 2.50 .75 13 
1
6
7
 
 P1:IP2 33.75 716.50 57.63 421.11 9.00 30.25 6.50 2.50 6 
 P2:P1 262.75 240.50 241.49 236.73 26.50 14.75 6.00 1.00 5 
 IP1:P2 422.75 136.25 334.38 144.07 15.50 18.50 .50 13.50 16 
 P1:P5 165.00 215.25 216.69 261.11 7.50 29.75 .25 8.50 6 
 P5:IP1 243.00 218.75 240.79 237.46 30.50 7.50 8.25 .50 16 
 P1:P2 220.25 232.50 236.19 239.11 14.00 25.00 1.75 7.75 5 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 MJ106 P2:IP1 913.50 190.25 386.43 92.38 30.25 9.25 2.25 6.75 18 
 P1:P5 351.75 710.00 167.98 310.68 6.50 32.00 1.50 6.50 11 
1
6
8
 
 IP2:P1 1026.25 41.50 444.90 33.74 32.50 6.25 .75 9.00 9 
 P5:P1 650.50 361.00 299.97 179.23 30.25 7.00 9.25 1.00 13 
 P1:P2 324.50 582.50 185.43 293.74 12.75 28.00 2.75 4.75 18 
 P1:IP5 47.75 937.00 51.31 427.12 6.50 36.00 1.25 2.00 7 
 IP1:P5 219.75 848.00 109.38 368.11 5.25 34.75 2.50 4.25 7 
 P2:P1 493.00 424.25 250.92 227.86 24.00 13.25 8.50 2.75 7 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 GR108 P1:P2 583.00 620.25 231.90 247.41 14.50 23.00 1.50 9.25 13 
 P5:IP1 934.25 386.75 322.63 156.67 34.50 6.50 4.75 1.00 8 
1
6
9
 
 IP1:P2 347.00 811.00 159.15 320.29 13.25 28.50 2.25 5.00 6 
 P2:P1 712.00 560.50 266.51 212.69 26.75 12.75 6.00 3.25 6 
 P5:P1 789.00 501.75 285.92 193.58 31.50 7.25 8.00 .75 5 
 P1:IP2 142.50 1063.75 95.08 384.26 12.75 29.00 2.75 3.00 11 
 IP5:P1 1279.00 114.25 420.11 59.37 38.00 5.75 1.00 2.25 7 
 P1:P5 482.50 789.00 186.83 292.29 6.75 30.00 1.25 8.75 6 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 3 JE109 TP5:TP1 272.75 168.00 291.38 187.95 32.25 7.00 6.75 .75 18 
 TN5:TP1 376.50 49.00 404.63 73.82 35.50 6.25 3.00 1.50 10 
1
7
0
 
 TP1:TN2 76.25 312.75 118.36 360.51 12.50 31.00 3.25 2.75 8 
 TP2:TP1 217.75 193.25 247.97 231.23 25.00 14.00 7.25 1.75 15 
 TN1:TP2 124.25 293.50 151.89 327.21 13.75 28.75 2.00 4.50 7 
 TP1:TP5 104.25 321.25 130.96 348.31 7.00 34.25 1.00 5.50 8 
 TP5:TN1 349.25 73.50 382.84 96.25 34.50 7.00 5.25 1.00 6 
 TP1:TP2 177.25 235.25 215.59 263.52 13.25 27.25 2.75 5.00 11 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 SL110 TP2:TN1 490.25 281.50 290.31 188.75 29.25 12.25 3.75 3.50 8 
 TP1:TP5 113.50 813.50 78.90 400.24 6.00 35.25 1.75 3.00 10 
1
7
1
 
 TN2:TP1 432.25 300.75 277.34 201.51 25.25 14.25 6.75 1.75 9 
 TP5:TP1 866.50 126.50 398.16 80.93 36.50 6.50 1.25 1.25 7 
 TP1:TP2 358.25 683.50 172.68 306.52 12.25 26.50 3.50 5.75 20 
 TP1:TN5 97.50 878.25 73.56 405.65 6.50 37.00 1.25 1.50 14 
 TN1:TP5 22.00 1082.00 23.30 456.12 5.50 38.25 2.25 1.00 6 
 TP2:TP1 711.25 254.75 338.45 140.80 30.00 11.25 3.00 4.50 21 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 NN111 TP1:TP2 483.00 697.75 205.55 273.91 11.00 26.25 4.25 6.50 9 
 TP5:TN1 878.00 46.25 452.85 26.64 38.50 4.75 .75 2.75 19 
1
7
2
 
 TN1:TP2 221.50 1074.50 97.81 381.50 11.00 28.75 4.50 3.75 13 
 TP2:TP1 710.25 520.25 275.94 203.42 27.25 13.50 5.00 2.50 14 
 TP5:TP1 1185.50 138.75 422.44 57.05 36.00 5.50 2.50 2.50 13 
 TP1:TN2 55.00 1235.00 36.14 443.36 9.00 32.75 6.50 .50 9 
 TN5:TP1 1229.50 74.00 446.17 33.29 38.75 5.25 00.00 2.50 9 
 TP1:TP5 227.25 818.50 105.43 374.03 5.00 33.75 2.25 5.25 13 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 4 MJ112 TP5:TP1 427.75 47.00 425.57 53.72 35.50 4.75 3.00 3.00 10 
 TN1:TN2 126.00 310.00 144.52 334.80 9.00 26.50 6.25 6.50 5 
1
7
3
 
 TP1:TP2 120.50 330.50 132.73 346.68 10.25 27.25 5.50 6.50 14 
 TN5:TN1 439.50 24.25 450.03 29.09 37.75 4.25 1.00 3.00 15 
 TP2:TP1 388.25 57.50 410.52 68.72 29.50 9.00 2.75 6.75 10 
 TP1:TP5 12.75 447.75 17.37 462.01 4.25 37.75 3.00 .75 8 
 TN2:TN1 370.50 66.25 395.94 83.61 30.25 11.25 1.75 4.50 15 
 TN1:TN5 37.25 422.50 43.62 435.82 6.25 36.75 1.75 1.75 5 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 JL113 TP1:TP2 453.50 711.75 189.78 289.58 12.75 26.75 3.25 5.00 9 
 TN5:TN1 666.25 135.50 380.91 98.44 36.75 7.00 2.25 .75 7 
1
7
4
 
 TN2:TN1 443.50 159.00 332.54 146.89 30.25 14.00 2.75 1.75 13 
 TP1:TP5 79.50 388.00 95.70 383.76 6.75 36.5 1.00 2.50 9 
 TP5:TP1 542.50 67.00 408.28 71.06 37.00 6.75 2.00 1.25 7 
 TN1:TN2 189.50 682.00 124.18 355.29 13.75 29.00 2.25 3.50 23 
 TP2:TP1 824.50 201.00 363.54 116.00 31.50 12.50 1.75 3.25 20 
 TN1:TN5 76.25 969.75 58.97 420.32 7.25 37.50 .50 1.75 5 
(Table Continues) 
 
Table (con?t) 
 
 
 Number of Number of 
  Number of  Time in Reinforcers Reinforcers Number of 
 Condition     Responses        Schedule (s)         Obtained              Missed        Sessions 
Exp. Subject (Left:Right) Left Right Left Right Left Right Left Right to Stability 
 
 SS114 TP1:TP5 160.50 427.75 143.49 335.68 7.50 35.00 .50 3.50 16 
 TP2:TP1 508.00 232.50 287.80 191.29 30.75 14.75 3.50 1.25 9 
1
7
5
 
 TN5:TN1 981.50 95.75 383.22 95.92 36.50 7.00 2.50 1.00 6 
 TP1:TP2 242.25 455.00 188.18 290.88 14.00 29.50 1.75 3.75 17 
 TN1:TN2 203.50 725.00 132.74 346.79 14.25 29.25 1.50 3.00 19 
 TN1:TN5 177.25 711.25 132.48 347.03 7.25 35.75 .50 3.25 5 
 TP5:TP1 535.25 115.50 378.48 100.88 36.00 7.00 2.75 .75 13 
 TN2:TN1 685.25 306.25 308.07 171.26 29.00 14.25 2.75 1.75 9 
 
176 
CHAPTER 3 
EXTENDED GENERAL DISCUSSION 
 Placing the present results into proper context requires a brief review of the 
prevailing models of free-operant choice.  The generalized matching relation (GMR) is 
the most widely accepted account, but it has two major limitations.  First, the GMR 
makes limited predictions, constrained specifically to the relationship between behavior 
(and time) allocation and relative reinforcement frequency.  It is silent on the differential 
effects of all other potential choice controlling variables.  Although the estimates of the 
fitted parameters of the GMR offer measures of these effects, the GMR makes no 
predictions about the means by which those variables interact to determine the parameter 
values.  Second, the GMR theoretically applies only to free-operant choice. 
 Davison and Nevin?s (1999) quantitative model of contingency discriminability 
theory (CDT), the discriminative law of effect (DLOE), improves upon the GMR in both 
respects.  First, the most notable conceptual improvement of the DLOE over the GMR is 
that it distinguishes between antecedent stimulus effects and consequence effects on 
behavior.  In effect, it partitions the a parameter of the GMR, which is really a catch-all 
measure of anything that influences sensitivity to reinforcement, into d
sb
 and d
br
, and 
proposes mechanisms by which they differentially influence responding (stimulus 
generalization and response induction, respectively).  It is in this sense that the DLOE 
makes more specific predictions than the GMR.  Second, the DLOE is more general than 
177 
the GMR.  It is able to account for many data from the extensive conditional 
discrimination literature because it explicitly invokes conditional stimulus control effects. 
 That said, it should be noted that a variant of the GMR, the concatenated GMR 
(Baum & Rachlin, 1969; Rachlin, Logue, Gibbon, & Frankel, 1986; see Davison & 
McCarthy, 1988 for a review), explicitly invokes several important response-
consequence choice-controlling variables (e.g., reinforcer magnitude, delay, or quality).  
Unfortunately, this model has not received much empirical attention, leaving it largely a 
conceptual exercise to date.  Moreover, the model has been criticized as being 
tautological (for an argument that exceeds the scope of the present discussion, see 
Rachlin, 1971).  The DLOE does not explicitly address all of the choice-controlling 
variables mentioned in the concatenated GMR.  It states simply that the parameter 
representing response-consequence contingency discriminability, d
br
, will influence the 
degree of response induction.  Consequently, Davison and Nevin (1999) acknowledge, ?a 
substantial research effort will be required to identify independent functions for the 
discriminability and value of the consequences of choice? (p. 472).  The implication, 
therefore, is that for now the model is restricted to making qualitative predictions 
regarding the effects of other response-consequence choice-controlling variables, but that 
it is at least principle possible to specify quantitatively how they interact to contribute to 
d
br
.  The present investigation provides a data set that might be an early step toward that 
aim.  It confirms the qualitative prediction made by Davison and Nevin (1999, pp. 444-
445) that concurrently available different types of reinforcers should increase behavioral 
sensitivity as suggested by research on the differential outcomes effect (Trapold, 1970).  
These data, in combination with future data, should provide a basis for future quantitative 
178 
analyses of how reinforcement type interacts with other response-consequence variables 
to influence d
br
.  The present investigation also provides a procedure and general research 
strategy that may prove useful in further addressing the concatenation of the variables 
assumed to influence d
br
. 
Studies of Reinforcer Magnitude as a Framework for Studies of Reinforcer Type 
 While there have been studies in the context of the matching relation involving 
concurrently available different types of reinforcement (e.g., Farley & Fantino, 1978; 
Hollard & Davison, 1971; Logue & deVilliers, 1981; Miller, 1976; Ruddle, Bradshaw, 
Szabadi, & Foster, 1982), the primary purpose of those studies was to demonstrate the 
ubiquity of the matching relation rather than to ask questions regarding the relationships 
among choice-controlling variables (cf. Bron, Sumpter, Foster, & Temple, 2003).  
Furthermore, from the perspective of the present investigation, those studies suffered 
from either of two limitations.  First, some studies employed nonhuman animals as 
subjects, requiring the use of reinforcers that cannot be easily compared on a per-unit 
basis (e.g., food and electric current, Hollard & Davison, 1971; Logue & deVilliers, 
1981).  Second, some studies used easily scalable conditioned reinforcers of different 
types, but did not employ a control phase of concurrently available same type reinforcers 
by which to judge relative effects (e.g., Ruddle, et al., 1982).  The present investigation 
and closely related studies (Critchfield & Lane, 2005; Magoon & Critchfield, 2005) are 
the first to use easily scalable reinforcers to make within-subject comparisons of the 
effects of concurrently available different types of reinforcers in relation to those of 
concurrently available same type reinforcers in free-operant choice.  Several recent 
studies, however, have examined the effects of magnitude of reinforcement using similar 
179 
procedures.  A brief review of those studies might inform the means by which DLOE 
model development, in terms of d
br
, might proceed to include reinforcement type. 
 Landon, Davison, and Elliffe (2003) arranged a concurrent schedule switching-
key procedure in which pigeons' key-pecking responses were reinforced.  Relative 
frequency of reinforcement and overall absolute magnitude of reinforcement were held 
equal and constant across conditions but relative magnitude was varied.  Landon et al. 
found that pigeon?s pecking behavior undermatched relative reinforcer magnitude ratios 
and did so to a greater degree than the same birds undermatched to relative reinforcer 
frequency in a different study involving the same subjects (see Landon, et al., 2003, 
Table 2 for the relevant comparison).  Two of their conclusions were that behavior is less 
sensitive to reinforcer magnitude than it is to reinforcer frequency and that the effects of 
these two variables are independent. 
 McLean & Blampied (2001) arranged a two-key concurrent schedules procedure 
in which pigeons? key-pecking responses were reinforced.  Relative frequency of 
reinforcement was varied across identical ranges for two phases, one in which the 
concurrently available reinforcers were of identical magnitude, and one in which the 
concurrently available reinforcers were of different magnitude.  In the phase with 
different magnitudes of reinforcement, there was a pronounced bias for the larger 
magnitude reinforcers, while there was no systematic bias in the other phase.  There were 
no systematic slope differences between the two phases.  While McLean and Blampied?s 
results corresponded well with Landon et al.?s (2003) conclusion that reinforcement 
frequency and magnitude effect behavior independently, their results did not agree with 
180 
Landon et al.?s conclusion that behavior is less sensitive to reinforcer magnitude than it is 
to reinforcer frequency. 
 Critchfield & Merrill (2005) extended McLean and Blampied?s work to human 
subjects using procedures modeled closely after those of the present investigation.  One 
of their phases arranged concurrently available schedules of positive reinforcement with 
equal magnitude reinforcers and the other arranged concurrently available schedules of 
positive reinforcement with different magnitudes of reinforcement.  Their results 
mirrored those of McLean and Blampied (2001) in that the phase with the different 
magnitudes of reinforcement showed a clear bias toward the larger magnitude reinforcers, 
the other phase showed no bias, and there were no slope differences between phases. 
 The three studies just discussed illustrate how within subject comparisons of 
matching functions can be used to analyze the separate effects of frequency and 
magnitude of reinforcement on behavior.  The results of all three studies converge on the 
conclusion that magnitude of reinforcement exerts an independent effect from that of 
reinforcement frequency.  Landon et al. (2003) came to this conclusion because nonzero 
slopes resulted when only relative magnitude of reinforcement was varied.  McLean and 
Blampied (2001) and Critchfield and Merrill (2005) came to the same conclusion when 
there were intercept but not slope differences between phases when the range of relative 
reinforcement frequency was held constant across phases but magnitude was the same 
within one phases and different within the other.  In all three cases, the parameters of 
matching functions were the metrics by which effects were evaluated. 
 The present investigation adopted this same general strategy to assess independent 
and interactive effects between frequency and type of reinforcement.  The difference 
181 
between outcomes of Experiments 1-3 and Experiment 4 suggest independence of 
reinforcer-frequency effects and reinforcer-type effects that is similar to the independence 
found between reinforcer-frequency effects and reinforcer-magnitude effects.  
Experiment 1 (like Critchfield & Lane, 2005, and Magoon & Critchfield, 2005) 
demonstrated this independence generally, while Experiments 2 and 3 attempted to 
determine which specific aspects of the positive and negative reinforcement 
contingencies (i.e., gain vs. loss and/or feedback asymmetry) were responsible for 
reinforcer-type effects.  Hybrid contingencies were arranged such that reinforcers 
differed only in terms of money gain versus money loss (Experiment 3), or only in terms 
of feedback asymmetry (Experiment 2).  Both factors proved to be sufficient and neither 
proved necessary to create a slope effect. 
 It would be premature to assume that the effects resulting from positive and 
negative reinforcement manipulation apply to all instances of concurrently available 
different types of reinforcement given that analogous manipulations with other pairs of 
nonidentical reinforcer types are virtually nonexistent in the literature (cf. Bron et al., 
2003).  That feedback asymmetry and money gain vs. money loss created the slope effect 
of interest in this investigation lends optimism to the notion that the present findings 
reflect a general phenomenon, but only new studies using different types of 
reinforcement other than positive versus negative can address this more directly.  As an 
example, consider a study with human subjects that arranged two-ply concurrent 
schedules of positive reinforcement with points exchangeable for money in both 
components in one phase (as in the ?baseline? phases of Experiments 1 and 2 of the 
present investigation), and concurrent schedules of positive reinforcement with points 
182 
exchangeable for college course extra credit in one component (with college students as 
subjects, of course) and points exchangeable for money in the other component in the 
other phase.  The DLOE predicts that the latter phase would result in a matching function 
steeper than that of the former.  The scaling of the consequences to each other would not 
be important to the experimental question as the primary interest would be type 
difference effects on slopes, though it would be interesting to see if there was any bias.  
Replication of the slope differences as seen in Experiments 1-3 of the present 
investigation, Magoon and Critchfield (2005), and Critchfield and Lane (2005) would 
further support the proposition that any reinforcer type difference between concurrent 
operants enhances response-consequence contingency discriminability and therefore 
sensitivity to reinforcement.  Similar experiments can be easily imagined using 
nonhumans as subjects. 
 Most generally, the literature just reviewed indicates that traditional, free-operant, 
concurrent schedules procedures are well suited to evaluating the independent effects of 
reinforcement frequency and other choice-controlling variables.  Separate studies have 
shown that reinforcement-frequency effects are independent of both reinforcement-
magnitude effects and reinforcement-type effects.  Currently unknown is whether these 
two types of effects are independent of each other. 
 Anecdotal evidence suggests that reinforcer-type manipulations are functionally 
different from reinforcer-magnitude manipulations.  Both McLean and Blampied (2001) 
and Critchfield and Merrill (2005) found that reinforcer-magnitude manipulations did not 
create slope effects like those created in the present investigation by reinforcer-type 
manipulations.  The DLOE apparently does not predict this distinction (note that, in 
183 
general, the seminal article of Davidson and Nevin, 1999, is vague about the exact role of 
reinforcement magnitude in the model).  In the conceptual framework of the DLOE, 
implications of the findings just described are clear:  Differences of reinforcer type 
appear to qualify as differential outcomes, while differences of reinforcer magnitude do 
not.  This suggests the need for additional research.  It can be predicted that when both 
reinforcer magnitude and reinforcer type are manipulated parametrically, their effects 
will be independent. 
 Relevant experiments would be easy to design.  For example, reinforcer 
frequency and magnitude could be held constant across phases, while reinforcer type was 
manipulated.  The ?baseline? of such an experiment could consist of concurrently 
available schedules of positive reinforcement with relative reinforcement frequency ratio 
fixed at 1:1 and relative magnitude of reinforcement ratios varied across a range of values 
(as in Landon et al., 2003).  The ?experimental? phase could consist of identical 
schedules except that reinforcer type (e.g., positive vs. negative) would be different for 
the two concurrent operants.  The findings of Landon et al. (2003) predict a nonzero 
slope for the ?baseline? function, based strictly on the effects of varied relative reinforcer 
magnitudes.  Any increase in slope in the experimental phase would indicate an additive 
effect of reinforcer type.  Extending this general research strategy to other response-
consequence choice-controlling variables and their various combinations could provide 
the means by which d
br
 could be unpacked and the DLOE could be expanded into a 
concatenated DLOE. 
184 
Comments on the DLOE 
 On reinforcer type versus magnitude.  The DLOE predicts that any difference 
between response-consequence contingencies of concurrent operants should heighten 
discriminability and increase behavioral sensitivity.  The findings of Critchfield and 
Merrill (2005) and McLean and Blampied (2001) clearly indicate this is not universally 
true.  Their concurrent different-reinforcer phases consisted of different magnitudes of 
reinforcement, ?+6? and ?+2? in the former case and 6 sec vs. 2 sec access to food in the 
latter.  Although both studies showed a systematic bias toward the larger reinforcer, 
neither showed an increased sensitivity.  This state of affairs seems irreconcilable with 
the DLOE specifically and CDT generally.  As Critchfield and Merrill (2005) noted, ?it 
seems illogical ? particularly in the context of contingency discrimination theory ? that a 
large reinforcer can be preferred over a small one without being simultaneously 
discriminated from it? (p. 17).  Thus, in some cases concurrently available different 
reinforcement increases sensitivity and in other cases it does not.  It is worth investigating 
the various dimensions of ?type? of reinforcement that are capable of producing the 
effects found in the current investigation. 
 Reinforcer type differences and bias.  Another issue raised by the present results 
concerns the systematic bias found for all subjects in Experiment 2.  Figure 1 illustrates 
the intercept values (top panel) and between-phase intercept differences (bottom panel) 
for each subject in the four experiments.  In the top panel of Figure 1, dark bars represent 
the intercepts of ?baseline? phases and light bars represent the intercepts of 
?experimental? phases.  In the lower panel of Figure 5, bars represent intercept 
differences between regression functions ("experimental" phase intercept minus 
185 
?baseline? phase intercept).  In light of Magoon and Critchfield?s (2005) results regarding 
bias, the nonsystematic results of Experiments 1, 3, and 4 are unsurprising, but the results 
from Experiment 2 clearly indicate a systematic bias toward ?inverse? positive 
reinforcement. 
 On first consideration, since the effects in Experiment 2 are similar to those from 
experiments where magnitude and frequency were manipulated (e.g., Critchfield & 
Merrill, 2005; McLean & Blampied, 2001), it is possible to speculate that the different 
magnitude reinforcers used in Experiment 2 (i.e., 2? for all conditions) somehow 
interacted with frequency in a similar way to how concurrently available different 
magnitude reinforcers do.  This seems unlikely, though, in the context of Experiment 4 
that also used different magnitude reinforcers (i.e., 7.5?).  Aside from this, there is no 
apparent explanation for these effects, but current procedures seem well suited to 
examine further this outcome.  As an example of how they might, consider an 
arrangement where concurrent ?standard? negative reinforcement was programmed for 
both response options in the ?baseline? phases, and ?inverse? negative reinforcement was 
programmed for one option and ?standard? negative reinforcement was programmed for 
the other in the ?experimental? phases (admittedly subject retention would be an issue to 
overcome).  If the same bias was found toward the ?inverse? negative reinforcement 
phase as was found toward the ?inverse? positive reinforcement phase in Experiment 2 of 
the current investigation, that might indicate that feedback asymmetry affects bias, but 
only when there are no ?gains and losses? differences.  This is another example of the 
flexibility of the current procedures to address a variety of research questions. 
186 
 On the provisional status of the DLOE.  Although Davison and Nevin?s (1999) 
quantitative model of the DLOE appears to be an improvement over previous models of 
choice in terms of its increased precision and scope, even its authors acknowledge that, 
?the probability of [their] having lit upon the correct model [is] probably something 
rather less than 1 in 10
6
? (Davison & Nevin, 1999, p. 475).  A viable quantitative 
statement of CDT is probably a long way off.  Given the number of variables invoked 
and the range of outcomes to which it is designed to be applied, even some of the 
qualitative statements of the DLOE will undoubtedly need to be refined.  Bearing this in 
mind, several conceptual critiques of the DLOE warrant mention. 
 The first is specific to the concerns of the present investigation and other work 
with concurrent schedules.  Davison and Nevin (1999) argued that, ?conventional two-
key concurrent schedules are arranged in the presence of a single stimulus condition, so 
S
1
 and S
1
 are equivalent? (p. 469), thereby allowing the parameter representing stimulus-
response contingency discriminability (d
sb
) to be dropped.  In quantitative terms, this 
yields Equation 18 in Chapter 1 (also Equation 18 in Davison and Nevin's report).  This 
simplifying assumption, while conceptually and practically convenient, appears to be at 
odds with the claim that, ?response differentiation will be reflected in both parameters:  
For example,?, increasing the separation between correct responses would increase both 
d
sb
 and d
br
? (Davison & Nevin, 1999, p. 445).  If it is true that response differentiation 
increases d
sb
, then it seems difficult to justify Equation 18 under any concurrently 
available two-response procedure.  In fact, the only circumstance where it might be 
plausible to consider d
sb
 = 1 would be in an unsignaled Findley switching-key procedure 
(Findley, 1958).  However, this apparent contradiction does not change the fundamental 
187 
premise of CDT proper that variables that increase response-consequence contingency 
discriminability should heighten behavioral sensitivity.  A test of this qualitative 
prediction would only seem to require that all possible effort be made to minimize d
sb
 
effects and to hold any antecedent stimuli constant across conditions.  That was the 
approach taken in the present investigation. 
 A related issue is that the model does not seem able to account for discriminative 
effects of reinforcement frequency.  Most fundamentally, the model (refer to Equation 18 
for ease of understanding) allows relative frequency of reinforcement (R
1
:R
2
) to vary 
even in the case that d
br
 is one.  This prediction makes intuitive sense, in that if an 
organism is unable to discriminate which response results in reinforcement, all other 
things being equal, responding should be equally distributed despite changing relative 
reinforcement frequencies.  However, in light of what is known about the discriminative 
functions of reinforcement (e.g., Lattal, 1975), it seems that any reinforcement 
discrepancies across alternatives should result in d
br
 being at least marginally larger than 
one.  Furthermore, just from an intuitive sense of the model, it seems as if the 
discriminative functions of reinforcement should contribute to d
sb
 as well as to d
br
.  Since 
reinforcers can serve a discriminative function, any time d
br
 is >1 because of 
reinforcement (not response) factors, the potential exists for d
sb
 also to be > 1.  The model 
appears to imply that the values of d
sb
 and d
br
 are determined independently, though once 
determined, they are allowed to interact. 
 Concatenating the DLOE.  Two other issues must be addressed if there is to be 
future research into the interaction of response-consequence choice-controlling variables.  
The concatenated GMR grants equivalent weight and function to all dimensions of 
188 
reinforcement (e.g., magnitude, delay, type, and frequency), but the DLOE seems to 
imply that all dimensions but frequency interact with each other to determine d
br
 and only 
then interact with frequency.  This conceptualization does not give equal weight and 
function to all dimensions of reinforcement.  It, in effect, makes all other reinforcement 
dimension subservient to frequency.  Of course, it is an empirical question whether the 
dimensions of reinforcement enter in to the relation as specified by the concatenated 
GMR or by some other means.  In fact, in light of Critchfield and Merril?s (2005) results, 
it may be that magnitude interacts directly with bias (log c) but not with d
br
, though 
again, as pointed out by Critchfield and Merrill, it seems logically difficult to accept that 
magnitude could influence preference (i.e., bias) without the difference being 
discriminated.  Furthermore, Landon et al.?s (2003) results suggest that frequency 
manipulations are not required to heighten response-consequence contingency 
discriminability and thus sensitivity.  These empirical results need to be rectified with the 
current conceptualization of the DLOE.  The manner in which this is done is the subject 
of the final issue of consideration.  Quantitative means by which to evaluate d
br
 in 
relation to a seem of the utmost importance in further model development.  Thus far, 
such comparisons have largely focused on the relative variance accounted for by the two 
parameters (e.g., Davison & Jenkins, 1985).  While this is informative, parametric 
investigations into the relationship between them would seem to offer much greater 
benefits to developing a concatenated DLOE. 
189 
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Bron, A., Sumpter, C. E., Foster, T. M., & Temple, W. (2003).  Contingency 
discriminability, matching, and bias in the concurrent-schedule responding of 
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Behavior, 289-306. 
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differential impact effects in concurrent schedules, delay discounting, probability 
discounting, and risky choice.  Manuscript submitted for publication. 
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heterogeneous reinforcement:  Testing predictions of matching and contingency 
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Davison, M., & McCarthy, D. (1988).  The matching law:  A research review.  Hillsdale, 
NJ:  Erlbaum. 
Davison, M., & Nevin, J. A. (1999).  Stimuli, reinforcers, and behavior:  An integration.  
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Findley, J. D. (1958).  Preference and switching under concurrent scheduling.  Journal of 
the Experimental Analysis of Behavior, 1, 123-144. 
190 
Hollard, V., & Davison, M. C. (1971).  Preference for qualitatively different reinforcers.  
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Landon, J., Davison, M., & Elliffe, D. (2003).  Concurrent schedules:  Reinforcer 
magnitude effects.  Journal of the Experimental Analysis of Behavior, 79, 351-
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Lattal, K. A. (1975).  Reinforcement contingencies as discriminative stimuli.  Journal of 
the Experimental Analysis of Behavior, 23, 241-246. 
Logue, A. W., & deVilliers, P. A. (1981).  Matching of behavior maintained by 
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Magoon, M. A., & Critchfield, T. S. (2005).  Concurrent-schedules of positive and 
negative reinforcement:  Differential-impact and differential-outcomes effects.  
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McLean, A. P., & Blampied, N. M. (2001).  Sensitivity to relative reinforcer rate in 
concurrent schedules:  Independence from relative and absolute reinforcer 
duration.  Journal of the Experimental Analysis of Behavior, 75, 25-42. 
Miller, H. L. (1976).  Matching-based hedonic scaling in the pigeon.  Journal of the 
Experimental Analysis of Behavior, 26, 335-347. 
Rachlin, H. C. (1971).  On the tautology of the matching law.  Journal of the 
Experimental Analysis of Behavior, 15, 249-251. 
Rachlin, H. C., Logue, A. W., Gibbon, J., & Frankel, M. (1986).  Cognition and behavior 
in studies of choice.  Psychological Review, 93(1), 33-45. 
191 
Ruddle, H. V., Bradshaw, C. M., Szabadi, E., & Foster, T. M. (1982).  Performance of 
humans in concurrent avoidance/positive-reinforcement schedules.  Journal of the 
Experimental Analysis of Behavior, 38, 51-61. 
Trapold, M. A. (1970).  Are expectancies based upon different positive reinforcing events 
discriminably different?  Learning and Motivation, 1, 129-140. 
192 
Figure Caption 
Figure 1.  Intercept estimates (top panel) and intercept estimate differences (bottom 
panel) of each matching function for each subject of each experiment.  In the top panel, 
dark bars represent the intercept estimates for the ?baseline? phase matching functions 
and light bars represent the intercept estimates for the ?experimental? phase matching 
functions.  In the bottom panel, bars represent the difference between the ?experimental? 
matching function intercept estimate and the ?baseline? matching function intercept 
estimate. 
Figure 1 
 
 
 
 
 
-0.5
0.0
0.5
1.0
1.5
2.0
TB101 TM102 SO104 GE105 MJ106 GR108 JE109 SL110 NN111 MJ112 JL113 SS114
Exp. 1 (N:P) Exp. 2 (IP:P) Exp. 3 (TN:TP) Exp. 4 (TN:TN)
In
te
r
c
e
p
t
Baseline Experimental
 
-0.5
0.0
0.5
1.0
1.5
2.0
TB101 TM102 SO104 GE105 MJ106 GR108 JE109 SL110 NN111 MJ112 JL113 SS114
Exp. 1 (N:P) Exp. 2 (IP:P) Exp. 3 (TN:TP) Exp. 4 (TN:TN)
In
t
e
r
c
e
p
t
s
 D
i
ff
e
r
e
n
c
e
Series1
 
193