ERIC EJ780540: An Application of the Matching Law to Social Dynamics

2007·0.72 MB·English

by  ERIC

JOURNALOFAPPLIEDBEHAVIORANALYSIS 2007, 40, 589–601 NUMBER4 (WINTER2007)
AN APPLICATION OF THE MATCHING LAW TO SOCIAL DYNAMICS
JOHN C. BORRERO, STEPHANY S. CRISOLO, QIUCHEN TU, WESTON A. RIELAND,
NOE¨L A. ROSS, MONICA T. FRANCISCO, AND KENNY Y. YAMAMOTO
UNIVERSITYOFTHEPACIFIC
Using a procedure similar to the one described by Conger and Killeen (1974), we evaluated
levelsofattendingfor25collegestudentswhoparticipatedineithera20-min(n512)or30-
min (n 5 13) discussion on juvenile delinquency. Confederates delivered statements of
agreement(e.g.,‘‘Iagreewiththatpoint’’)accordingtoindependentvariable-intervalschedules.
Pooled results were evaluated using three generalized formulations of the matching law, and
showedthatmatchingwasmorelikelyduringthefirst5 minofthediscussionthanduringthe
last 5 min. Individual data for 7 of 9 participants were better described by the generalized
response-rate matching equation than by the generalized time-allocation matching equation
whenresponse allocation was characterizedin terms offrequencyrather than duration.
DESCRIPTORS: choice, matching law, social dynamics, conversation, agreement, verbal
behavior
_______________________________________________________________________________
Response allocation under concurrent sched- Behavior-analytic research on choice has
ules of reinforcement has been the subject of shown that there are a number of factors that
appreciable basic and applied behavior-analytic may contribute to response allocation (e.g.,
research (Fisher & Mazur, 1997). This may be reinforcer quality, reinforcer magnitude), per-
due in part to the ubiquitous nature of haps the most widely studied of which is
concurrent schedules in the natural environ- reinforcerrate.Giventwoconcurrentlyavailable
ment. As suggested by McDowell (1988, 1989) response alternatives (all other variables being
and others, at any moment, organisms have equal),responseallocationhasbeenshowntobe
the opportunity to engage in one of several a function of relative reinforcer rates associated
concurrently available responses (e.g., read with each alternative. This frequently observed
a newspaper, mow the lawn, or go for a run). linearrelationbetweenrelativeresponserateand
Similarly, a pigeon may peck one of two relativereinforcer rate is known as the matching
concurrently available keys, or engage in law, and was first described by Herrnstein
grooming, and so on. Which one of two or (1961). Herrnstein assessed the responding of
more available alternatives is selected describes pigeonswhenkeypeckingwasexposedtoaseries
choice(Catania,1998),andbyobservingchoice of concurrent variable-interval (VI) schedules.
and subsequent preference, we look next to the For example, one pair of schedules arranged
variables that control response allocation.
reinforcersontheleftkeyaccordingtoaVI75-s
schedule while reinforcers on the right key were
This experiment was completed as a senior project by
thesecondandthirdauthorsunderthesupervisionofthe arranged according to a VI 270-s schedule.
first. We thank Andrew Samaha for his assistance in Across all pairs of concurrent-schedule arrange-
softwaredevelopment.WealsothankPaulineCabalesand
ments, relative response allocation occurred in
Hong Nguyen for their assistance in completing this
project. Portions of this research were presented at the linear relation to relative reinforcer rates, when
25th meeting of the California Association for Behavior theappropriatechangeoverdelaywasincludedas
Analysis in Burlingame. Monica Francisco is now at the
partoftheprocedure.Theseresultswereassessed
Universityof Kansas.
in terms of the following equation:
DirectcorrespondencetoJohnC.Borrero,whoisnow
attheDepartmentofPsychology,UniversityofMaryland
R r
Baltimore County, 1000 Hilltop Circle, Baltimore, 1 ~ 1 ; ð1Þ
Maryland21250(e-mail: [email protected]). R z R r z r
1 2 1 2
doi:10.1901/jaba.2007.589–601
589
590 JOHN C. BORRERO et al.
whereR andR representtherateofresponding obstructions). The b parameter describes altera-
1 2
totheleftandrightkeys,respectively,andr and tions in response allocation that are not
1
r represent the rate of reinforcement for accounted for by differences in relative re-
2
responses to the left and right keys, respectively. inforcer rates. In both nonhuman and human
Equation 1 is often referred to as the pro- laboratories, bias may result from qualitatively
portional matching equation or the strict different stimuli (e.g., food vs. water), differ-
matching equation. ences in effort associated with the two response
Based on certain deviations from strict alternatives (e.g., difficult math problems vs.
matching as described by Herrnstein (1961), mastery level math problems), and seemingly
Baum (1974) proposed what is now known as immutable preferences for one alternative
the generalized matching equation, or more relative to the others (e.g., a strong preference
formally, for the color green; Baum; Neef, Shade, &
Miller, 1994).
(cid:1) (cid:2) (cid:1) (cid:2)
R r
log 1 ~s log 1 zlogb; ð2Þ In some instances, behavior may be more
R2 r2 appropriately captured in terms of its duration.
For example, Baum and Rachlin (1969)
where R , R , r , and r represent the same
1 2 1 2 assessed the behavior of pigeons in terms of
features of the environment described in
timespentononesideoranotherofamodified
Equation 1. The s parameter describes sensitiv-
operant chamber as a function of relative
ity (the slope), and the b parameter describes
reinforcer rates. Baum and Rachlin assessed
response bias (the intercept). The generalized
matching using the following equation:
matching equation takes into account perfor-
mance sensitivity (s) given a one-unit change in (cid:1)T (cid:2) (cid:1)r (cid:2)
log 1 ~s log 1 zlogb; ð3Þ
the relative reinforcer ratio. For example, if an
T r
2 2
initial reinforcer ratio of 2:1 (e.g., VI 30 s VI
60 s; twice as much reinforcer availability on where T and T represent time allocated to
1 2
Response Alternative 1) were altered to a ratio ResponseAlternatives1and2,respectively,and
of 3:1 (e.g., VI 30 s VI 90 s; three times as r and r are as described in Equations 1 and 2.
1 2
much reinforcer availability on Response Alter- In general, relative time allocation matched
native1),one wouldexpect a concomitantone- relative reinforcer rates; however, considerable
unit change in relative response allocation. bias was observed.
Although an s parameter equal to unity (or Oliver, Hall, and Nixon (1999) assessed the
log 1 5 0) occurs infrequently in the published aggressive and communicative behavior exhib-
literature, s values of less than 1 are the most ited by a young boy in terms of its duration as
frequently reported in the literature and are a function of the relative duration of reinforcer
termed undermatching (a less than one-unit access associated with the two response alter-
increase in relative response ratios given a one- natives (aggression and communication) using
unit increase in relative reinforcer ratios; e.g., the following equation:
Madden, Peden, & Yamaguchi, 2002). Mea-
(cid:1) (cid:2) (cid:1) (cid:2)
suresofsthatexceed1(e.g.,Aparicio,2001)are log T1 ~s log t1 zlogb; ð4Þ
less frequently reported and are termed over- T t
2 2
matching (a greater than one-unit change in
relative response ratios given a one-unit change whereT andT areasdescribedinEquation3,
1 2
inrelativereinforcerratios).Forexample,inthe and t and t represent duration of reinforce-
1 2
study by Aparicio, overmatching was associated ment associated with Response Alternatives 1
with increased response effort (e.g., climbing and 2, respectively. This seems to have been
MATCHING AND SOCIAL DYNAMICS 591
a particularly appropriate model because ag- municative responses). Rather, the limits of the
gression was shown to be sensitive to negative matching law remain a subject of ongoing
reinforcement in the form of escape from behavior-analytic research.
instructional demands. It is likely that the Although there have been numerous demon-
duration of escape would be a more relevant strations of the matching relation with nonhu-
reinforcement parameter than its rate. Also mans (responding for primary reinforcers),
noteworthy is that the data used to assess the there have been considerably fewer studies
matching relation were gathered in the partic- involving humans and attention as reinforce-
ipant’s natural classroom environment during ment(e.g.,Pierce&Epling,1983).Likethekey
interactions with his teacher. The results pecks of pigeons or the academic engagement
reported by Oliver et al. were consistent with of students, communicative exchanges during
matching and illustrated how the phenomenon conversation (i.e., verbal behavior, Skinner,
could be modeled using parameters of re- 1957) should also be amenable to evaluations
inforcement other than rate, as well as quanti- of matching. In one such study Snyder and
fications of behavior in terms other than rate. Patterson(1995)evaluatedinteractionsbetween
Equation 1 and its proportional variations socially aggressive boys and their mothers as
have been applied infrequently in more recent well as boys who were not socially aggressive
experimental research (relative to Equations 2, andtheirmothers.Theresearchersaccumulated
3, and 4), in part because of the increased 10 hr of interactions for each mother–child
explanatory utility of the latter equations. dyad and then conceptualized maternal termi-
Specifically, the generalized matching equations nation of the conflicts as the reinforcer for
describe whether, and to what extent, behavior selection of various tactics (e.g., positive verbal,
deviates from perfect matching. Further, the negative verbal) adopted by their children.
generalized equations describe potential sources These data were then evaluated in terms of
of these deviations (e.g., bias to one alternative the matching relation; results suggested that the
or insensitivity to reinforcer rates). likelihood of a particular tactic was in part
Although the response alternatives described determined by the likelihood of reinforcement
by Herrnstein (1961) and Baum (1974) in- associated with each of those tactics, a conclu-
volvedkeypecksexhibitedbypigeons,thework sion consistent with the matching law.
ofOliveretal.(1999)andBorreroandVollmer In a similar study, Dishion, Spracklen,
(2002) have demonstrated that relative mea- Andrews, and Patterson (1996) evaluated the
sures of communication and problem behavior interactions of adolescent boys while focusing
exhibited by individuals with developmental on the content of these discussions (e.g.,
disabilities can also be expressed in terms of the discussion of illegal behavior, discussions of
matching relation. Other applications of the family and school that did not involve in-
matching law(see Davison& McCarthy, 1988, appropriate activities, termed rule breaking and
for an extensive review) have involved assess- normative, respectively) and the responses of
ments of academic responding of individuals the listener (e.g., laughingor pausing). Datafor
with and without developmental disabilities 181 dyads were assessed using Equation 1, and
(Mace, McCurdy, & Quigley, 1990) and the researchers found that relative rates of rule
collegiate (Vollmer & Bourret, 2000) and breaking were well accounted for by relative
professional (Reed, Critchfield, & Martens, rates of laughing. Stated differently, Dishion et
2006) sports performance. Thus, the matching al. suggested that the content of naturally
law is not limited by conceptualizations of occurring conversations between adolescents
response alternatives (e.g., key pecks or com- was a function of the extent to which listeners
592 JOHN C. BORRERO et al.
reinforced (laughed at) the conversation con- participants was assessed during seven 1-hr
tent. sessions. For 2 of 6 participants, matching was
The studies by Synder and Patterson (1995) observedduringthelast30 minofexperimental
and Dishion et al. (1996) are particularly sessions (coefficients of determination ranged
important because they speak to the durability from .45 to .69). Also noteworthy was the
ofthematchingphenomenon(intermsofsocial observation that 3 of 6 participants allocated
dynamics) when reinforcer rates are not exper- relatively more verbal behavior and time to the
imentally manipulated.However,these analyses confederate who provided relatively less agree-
involved between-groups comparisons; thus, ment.
conclusions regarding matching at the level of Taken together, the results reported by
the individual cannot be discerned from these Conger and Killeen (1974) and Pierce et al.
results. However, the extent to which adults (1981) leave the matter of matching during
differentially attend to, or engage with, others communicativeexchangesunresolvedwhendata
in social exchanges has also been evaluated are evaluated at the level of the individual. The
when reinforcer rates were experimentally present study was designed to replicate the
programmed (Beardsley & McDowell, 1992). proceduresreportedbyCongerandKilleen,and
CongerandKilleen(1974)evaluatedlevelsof later by Pierce et al., by evaluating levels of
attending for 5 college students who were attending, given concurrent schedules of agree-
invited to participate in a 30-min discussion. ment, for a larger sample of college students,
using contemporary (Equations 2, 3, and 4)
According to independently programmed con-
variations of the matching equation (McDow-
current VI schedules, confederates delivered
ell, 2005).
statementsofagreement(e.g.,‘‘Iagreewiththat
point’’) following a participant’s comments.
Data for the first and last 5 min of each session METHOD
were then evaluated using a variation of
Participants and Setting
Equation 1 (a classic iteration of the matching
Participants were 25 undergraduate college
equation) and pooled for all participants.
students who were enrolled in a small private
Results showed that during the relatively brief
universityandhadcompletednomorethantwo
discussions, participants’ relative response allo-
college-level psychology courses. The mean age
cation (between each of the confederates) was
of participants was 20.2 years, and each had
well described by relative rates of agreement
completed a mean of 3 years of college-level
duringthelast5 minofthesession.Duringthe
course work. Forty-eight percent of participants
first5 minofthediscussion,however,nolinear were female. Prior to the experimental session,
relation was observed. These data seemed to participants were asked to sign an informed
support the notion that matching is a steady- consent form (approved by the university
state phenomenon (e.g., Baum, 1974) that institutional review board) in a room near the
requires some exposure to experimental con- experimental session room. Participants were
tingencies before it occurs. told that contingent on their consent, they
Pierce, Epling, and Greer (1981) extended would participate in a discussion to assess
the work described by Conger and Killeen college students’ understanding of the factors
(1974) by using Equations 2 and 3 (more contributing to juvenile delinquency. Two
contemporary models of the matching relation) confederates also completed the informed
andby conducting moreextended experimental consent process. Next, participants were re-
sessions. Using procedures similar to those of mindedthatthediscussionwouldbevideotaped
CongerandKilleen,theresponseallocationof6 (also included in the informed consent form).
MATCHING AND SOCIAL DYNAMICS 593
After the consent form was signed, an experi- Procedure and Data Analysis
menter directed the participant and the two While seated in the experimental setting, the
confederates into the session room. Sessions moderatorreadthefollowinginstructionstothe
were conducted in a laboratory that measured participants at the beginning of the discussion:
approximately 5 m by 5 m. Materials included
Before this session begins, we ask that you do not
a desk, four chairs (one for the participant, one
disclose any personal information about yourself
for each confederate, and one for a moderator regarding any of the topics to be discussed. To
responsible for evoking discussion), and posters further control for this, we also ask that all
experiences shared be in third person such as ‘‘I
on the walls (included to evoke discussion).
know this person who …’’ This is to further insure
Only 1 participant at a time was involved in your confidentiality. Thank you.
a discussion session. The participant was
Participants were asked not to disclose any
strategically seated with his or her back to
personal information regarding any of the
a one-way mirror, with each confederate seated
topics to be discussed. After the instructions,
approximately 1.5 m to either side of the
the moderator began the experimental session
participant. The moderator was seated directly
with the question, ‘‘What do you think are
acrossfromtheparticipant(approximately1 m)
some factors that influence juvenile delinquen-
and facilitated conversation (described in more
cy?’’ or a similarly phrased question.
detail below).
During the discussion, confederates emitted
infrequent verbal responses that were not in
Response Measurement and
response to a statement made by the partici-
Interobserver Agreement
pant.Givenanextendedlullintheconversation
Data were collected on comments made by
(e.g., 30 s), the moderator attempted to evoke
the participants (any vocal responses in refer-
discussion using the following list of discussion
ence to the topic); attending, defined as eye
topics:
contact between the participant and either
confederate or the moderator; and orientation Factor 1: Drug and alcohol use
of the body toward either confederate or the Factor 2: Peers and cliques
moderator. Data were collected separately for Factor 3: Quality of school system or school
environment
attending to Confederate 1, Confederate 2, and
Factor 4: Unfavorable home environment
the moderator. Data were also collected on
Factor 5: Subculture participation
statements of approval delivered by each
confederate (e.g., ‘‘I think you are right’’). Both Confederates participated in the conversation
frequency and duration data were collected on (directed to the participant) (a) following
handheld computers for each of the aforemen- a verbal response from a participant that (b)
tionedmeasuresbybothprimaryandsecondary occurred after the VI interval associated with
observers for 88% of all sessions. Duration of each confederate elapsed. Confederates were
participant responses was scored given an signaled by colored flashlights operated by
instance of attending and ended the moment experimenters on the opposite side of the one-
attending to either confederate or the moder- way mirror. For example, Confederate 1 was
ator ceased. Agreement coefficients were calcu- signaled by a blue light, and Confederate 2 was
lated by dividing the smaller frequency (or signaled by a yellow light. The signal indicated
durationin seconds) by thelarger frequency (or that a VI schedule for one confederate had
duration in seconds) in each 10-s interval and elapsed, and that a statement of agreement
multiplying by 100%. Mean agreement coeffi- could be delivered after a participant’s current
cients for all measures exceeded 80% (range, or next response. The lights were not visible to
81% to 94%). the participant. It was possible to have a signal
594 JOHN C. BORRERO et al.
delivered at a time when the opportunity to also evaluated response allocation in terms of
deliveranagreeablestatementwasnotavailable. Equations 2 and 3 in an attempt to determine
For example, a VI interval might have elapsed whether duration of response allocation or rate
during a period in which the participant was ofresponseallocationwouldbebetterdescribed
not talking. Thus, the confederate delayed by relative rates of statements of agreement.
delivery of an agreeable statement until a par-
ticipant’s next response. For this reason,
RESULTS
programmed and obtained reinforcer rates were
Figure 1 depicts the results of the matching
not identical. Confederates were instructed not
analyses using Equations 2, 3, and 4. The left
to attend (look at, orient toward, or speak) to
column depicts results of the analyses during
the participant under any other circumstances.
the first 5 min of the discussion for all
Between reinforcer deliveries, the confederates
participants. The middle column depicts data
either looked down, at each other, or at the
according to each equation during the last
moderator.
5 minofthediscussionforallparticipants.The
Statements of agreement were delivered
right column depicts data according to each
according to independent VI schedules (i.e.,
equation during the entire 20- or 30-min
VI 120 s VI 300 s for 20-min discussions, and
discussion for all participants.
VI 30 s VI 120 s for 30-min discussions).
When evaluated as pooled data (across all
Distributions of the VI schedules were de-
participants) using Equation 2, results illustrate
termined using the method described by
undermatching (i.e., s , 1), with no notewor-
FleshlerandHoffman (1962).Thefidelity with
thy b values. Results using Equations 3 and 4
which confederates delivered statements of
also were generally similar, in that coefficients
agreement was not assessed and cannot be
of determination were modest, but were larger
discerned. Data were reported in either 5-min
in all cases during the first 5 min of the
components or for the entire session. For the
discussion than in the last 5 min. One analysis
20-min discussions, the confederate who ini-
(Equation 3, from the first 5 min of the
tially delivered statements of agreement accord-
discussion) produced a slope greater than 1
ing to the VI 120-s schedule switched to the VI
and considerable bias (b 5 20.372).
300-sscheduleafter10 min,andtheconfederate
Figure 2 depicts data for 4 participants who
who initially delivered statements of agreement
completed the 30-min discussion, in 5-min
according to the VI 300-s schedule provided
intervals. Data for individuals who completed
statements of agreement according to the VI
the 30-min discussion were selected for further
120-s schedule. During the 30-min sessions, analysis if there were at least five data points to
confederatesswitchedschedulesafter10 min.At evaluate (i.e., the numerator or denominator
theconclusionofthesession,theparticipantwas was nonzero for at least five 5-min intervals
debriefed and was awarded extra credit in because the logarithm of zero is undefined).
a required seminar for his or her participation. Data depicted in each row reflect analyses for
Data for all participants were then evaluated individual participants. The left column depicts
using Equations 2, 3, and 4. Data were results according to Equation 2, and the right
expressed in several ways. First, data were columndepictsresultsaccordingtoEquation3.
pooled for all participants and plotted during Equations2and3wereselectedtocomparethe
thefirst 5 min of thediscussion, during the last time-allocation and response-rate variations of
5 min of the discussion, and during the entire thegeneralizedmatchingequationduringsocial
20- or 30-min discussion. Second, for partici- interaction.ForParticipants15,18,20,and17,
pantswhocompletedthe30-mindiscussion,we Equation 2 produced relatively larger s param-
MATCHING AND SOCIAL DYNAMICS 595
Figure1. Theleftcolumndepictspooleddataforallparticipantsduringthefirst5 minofthediscussionaccording
toEquations2,3,and4(fromtoptobottom).Themiddlecolumndepictspooleddataforallparticipantsduringthelast
5minofthediscussionaccordingtoEquations2,3,and4(fromtoptobottom).Therightcolumndepictspooleddata
forallparticipantsduringtheentire20-or30-mindiscussionaccordingtoEquations2,3,and4(fromtoptobottom).
Dasheddiagonal lines representperfect matching, andsolid linesrepresent bestfit lines.
eters(indicatingthattheyweremoresensitiveto Figure 3 depicts results for the remaining 5
changes in relative reinforcer ratios when participants who completed the 30-min discus-
statements made by the participants were sion, in 5-min intervals. Results are similar to
expressed in terms of relative rate of occur- those depicted in Figure 2, with two notable
rence), smaller b parameters (indicating that exceptions. First, Participants 26 and 27
factors not captured by relative reinforcer ratios exhibited considerable bias to one of the two
had a negligible impact on relative response confederates (b 5 20.648, 20.560, and b 5
allocation), and larger coefficients of determi- 0.286, 0.193, respectively, for Equations 2 and
nation.Participants20and17producedperfect 3 and Participants 26 and 27). Based on the
matching when expressed using Equation 2. availabledata,wecannotdeterminewhythese2
Note that three data points for Participant 20 participantsmighthavedemonstratedsuchbias.
are plotted in coordinates (0, 0), and thus, only Second, Participants 27 and 14 were the 2
three data points are visible. participants for whom Equation 3 produced
596 JOHN C. BORRERO et al.
Figure 2. Data depicted according to Equations 2 and 3 for 4 participants whose data were selected for further
analysis. All data are for participants who completed the 30-min discussion. Dashed diagonal lines represent perfect
matching, andsolidlines represent bestfit lines.
larger coefficients of determination (relative to on the limited range of relative reinforcer rates
Equation 2); however, the difference observed and not based on the model assessed.
for Participant 14 was rather small. For For 7 of 9 participants who completed the
Participant 27, these differences may be better 30-mindiscussion,Equation2providedabetter
explained in terms of the spread in relative account of response allocation than did Equa-
reinforcer ratios. That is, relative reinforcer tion 3, suggesting that characterizations of
ratios were highly concentrated such that response allocation in terms of relative rate or
evaluations of matching might be limited based duration may influence summaries based on
MATCHING AND SOCIAL DYNAMICS 597
Figure 3. Data depicted according to Equations 2 and 3 for 5 participants whose data were selected for further
analysis. All data are for participants who completed the 30-min discussion. Dashed diagonal lines represent perfect
matching, andsolidlines representbest fitlines.
598 JOHN C. BORRERO et al.
relative reinforcer rates. In other words, not the first 5 min than in the last 5 min of the
only is selection of an appropriate model discussion), suggesting that participants in the
important, but the way in which responding is currentinvestigationwereimmediatelysensitive
characterized may also contribute to findings in to reinforcer rates. As noted previously, Conger
support of the matching relation. andKilleenappliedavariationofEquation1(a
proportional equation), which has been shown
to be of less explanatory utility. Thus, if data
DISCUSSION
reported by Conger and Killeen were reex-
The matching relation was assessed during
pressed using generalized matching equations,
experimentally arranged conversations among
the findings may not be commensurate. A
college students. To extend the classic work of
second discrepancy lies in the rather low
Conger and Killeen (1974) and Pierce et al.
coefficients of determination obtained in the
(1981), three iterations of the matching equa-
current study (at the between-subjects level)
tion were assessed at the between-subjects level.
relative to those reported by Conger and
Each equation was applied to capture relevant
Killeen. However, this discrepancy may not be
features of social dynamics (i.e., relative dura-
unique to these two studies. Consider an
tions of response allocation, relative rates of
experiment in which 13 pigeons respond on
response allocation, relative durations of agree-
a pair of five VI schedules, during which each
ment, and relative rates of agreement). At the
pair of VI schedules is presented for 5 min. If
between-subjects level, positive correlations
one were to assume stable responding and then
betweenrelativeresponseallocationandrelative
select (at random) pairs of schedules and plot
reinforcer rates were obtained, despite the way
the data across subjects, low coefficients of
in which behavior and statements of agreement
determination would be expected. However,
were expressed. This general finding is consis-
when those data are reexpressed at the level of
tentwiththosereportedbyCongerandKilleen.
the individual subject, considerably higher
Inadditiontothebetween-subjectsanalyses,the
coefficients of determination would likely be
matching relation was also assessed at the level
obtained. Differences of this sort may even be
of the individual, using Equations 2 and 3.
expectedgivendifferencesintermsofsensitivity
These two models were selected to determine
whether rate or duration of response allocation and bias (as reflected in Figures 2 and 3).
was better accounted for by relative rates of Therefore, although low coefficients of de-
agreement. Results of these analyses were termination were obtained at the between-
indicative of matching using one or both of subjectslevelinthecurrentinvestigation(which
the models for allparticipants. These results are might be expected), improvements were ob-
also consistent with those reported by Pierce et served at the level of the individual (which also
al., although matching was observed for might be expected).
relatively more participants in the current It is also possible that the 20-min discussions
investigation than in the study by Pierce et al. in the current investigation did not allow
The present findings also differ from those sufficient time for participants’ behavior to
reportedinpriorwork.Forexample,whendata come under the control of the programmed
were pooled, Conger and Killeen (1974) found schedules,andthus,influencedtheutilityofthe
that closer approximations to matching were equations in describing the pooled data.
observed during the last 5 min of the 30-min Matching is a steady-state phenomenon. In
discussionthaninthefirst5 min.Resultsofthe fact, analyses conducted for the 20-min partic-
present investigation found just the opposite ipants and the 30-min participants separately
(i.e., closer approximations to matching during showedthatmoreofthevariancewasaccounted