The Psychological Record, 2000, 50, 721-744
ESTABLISHING EQUIVALENCE CLASSES WITH MATCH-TO-SAMPLE
FORMAT AND SIMULTANEOUS-DISCRIMINATION FORMAT
CONDITIONAL DISCRIMINATION TASKS
PAUL M. SMEETS
DERMOT BARNES-HOLMES
Leiden University
National University of Ireland, Maynooth
VERONICA CULLINAN
University College Cork
This study compared standard stimulus equivalence training
and testing in the match-to-sample format to a simultaneousdiscrimination format. Experiment 1 compared the formats
between groups in both adults and 5-year-old children. There were
no differences on symmetry tests. There was a difference between
children and adults on a one-node equivalence test. Results were
positive for all of the adults in the match-to-sample and simplediscrimination formats. Results were positive for all children in the
match-to-sample format, but for only half of them in the simplediscrimination format. Transfer tests for discriminative control were
conducted with participants who had positive equivalence test
results. Transfer was less reliable in children than in adults, but
there were no differences between formats. Experiment 2
replicated the results with children in a within-subject design.
Studies on stimulus equivalence typically use match-to-sample tasks
for establishing arbitrary conditional discriminations. Match-to-sample
tasks consist of two or more comparisons (e.g., B1 and B2) and a sample
(e.g., A 1). Responding to Comparison B1 is reinforced when given
Sample A 1, responding to Comparison B2 is reinforced when given
Sample A2 (A1-B1, A2-B2}.Numerous studies have shown that, after
being trained on multiple match-to-sample tasks with common sets of
stimuli (e.g., A 1-B1, A2-B2; A 1-C1, A2-C2), verbally able humans
frequently relate all directly and indirectly linked stimuli conditionally with
one another: B1-A 1, B2-A2, C1-A 1, C2-A2 (symmetry), and B1-C1, B2C2, C1-B1, C2-B2 (symmetric transitivity). Responding in accordance
with symmetry and symmetric transitivity is, in a conditional discrimination
context, accepted as evidence for the formation of two stimulus
equivalence classes: A 1-B1-C1 and A2-B2-C2 (Barnes & Holmes, 1991;
Fields, Adams, Newman, & Verhave, 1992; Sidman, 1992).
Moreover, when a discriminative function is trained to one member of
an equivalence class, that function will transfer to the other members of
Reprint requests may be sent to Paul M. Smeets, Behavior Analysis Unit, Department
of Psychology, Leiden University, P. O. Box 9555, 2300 RA Leiden, The Netherlands. (E-mail:
[email protected]).
722
SMEETS ET AL.
that class (Barnes & Keenan, 1993; de Rose, Mcllvane, Dube, Galpin, &
Stoddard, 1988; Hayes, Devany, Kohlenberg, Brownstein, & Shelby, 1987;
Wulfert & Hayes, 1988). For example, after training adults on A-B and A-C
match-to-sample tasks (A 1-B1, A2-B2; A 1-C1, A2-C2) and obtaining
symmetric transitivity (B1-C1, B2-C2; C1-B1, C2-B2), Hayes et al. (1987)
trained the participants to clap when given B1 and to wave when given B2.
Subsequent tests showed transfer from B to C via A: C1-clap and C2-wave ..
Recently, researchers have begun to use alternatives to the standard
match-to-sample procedure. Some of these alternatives include match-tosample tasks with stimulus compounds (Markham & Dougher, 1993;
Schenk, 1993; Smeets, Schenk, & Barnes, 1995; Stromer & Stromer,
1990), sequence training (Sigurdardottir, Green, & Saunders, 1990),
simple-discrimination training (Schenk, 1995; Smeets& Barnes, 1997),
and exposure to strings of sequentially presented stimuli (Barnes,
Smeets, & Leader, 1996; Leader, Barnes, & Smeets, 1996; Smeets,
Leader, & Barnes, 1997).
Although these studies indicate that stimulus equivalence may be
derived from many procedures other than match-to-sample training
(Saunders & Green, 1992; Sidman, 1994), the variables that allow the
match-to-sample procedure to produce equivalence are not well
understood. Several formats of conditional discrimination tasks can be
distinguished: match-to-sample, go/no-go (D'Amato & Colombo, 1985),
and simultaneous discrimination (see below). In each of these formats,
participants are trained and/or tested on if-then stimulus-stimulus
relations. Two questions that we have started to address are as follows: Is
the match-to-sample task more effective than other conditional
discrimination formats in producing stimulus equivalence? Is the matchto-sample task perhaps more effective with mentally young populations
(Le., young children, persons with mental retardation) than with
intellectually advanced populations?
Cullinan, Barnes, and Smeets (1998) compared match-to-sample
and go/no-go procedures on their efficacy to produce equivalence
relations. Twenty adults participated. Ten participants received standard
match-to-sample training (A 1-B1, A2-B2; B1-C1, B2-C2). Ten other
participants received training on go/no-go discrimination tasks with two
sequentially presented stimuli: first an A stimulus and then a B stimulus
(A 1---+B 1, A 1---+B2, A2---+B 1, A2---+B2) or first a B stimulus and then a C
stimulus (B1---+C1, B1---+C2, B2---+C2, B2---+C1). The participants received
positive feedback for pressing a computer board key when two sameclass stimuli were shown (A 1---+B1---+PRESS, A2-B2---+PRESS,
B1---+C1---+PRESS, B2---+C2---+PRESS) and for not pressing the key when
two stimuli of different classes were shown (A 1---+B2---+NO PRESS,
A2---+B1---+NO PRESS, B1---+C2---+NO PRESS, B2---+C1---+NO PRESS). All
participants received match-to-sample and go/no-go discrimination tests
measuring symmetry (match-to-sample: e.g., B1-A 1, B2-A2; go/no-go:
e.g., B1---+A 1---+PRESS, B1---+A2---+NO PRESS, B2-A2---+PRESS, B2A 1---+NO PRESS) and symmetric transitivity (match-to-sample: C1-A 1, C2-
EQUIVALENCE CLASS FORMATION
723
A2; go/no-go: C1-.A 1-.PRESS, C1-.A2-.NO PRESS, C2-.A2-.PRESS,
C2-.A1-.NO PRESS). Both formats were equally effective (100%) in
generating symmetry, but go/no-go produced less symmetric transitivity
(10/20 participants) than match-to-sample (16/20 participants). Similar
findings were obtained in a follow-up study (Cullinan, Barnes-Holmes, &
Smeets, 2000).
Schematically, the go/no-go procedure was similar to the matchingto-sample procedure. In go/no-go, for example, the participants received
points for pressing when B 1 followed A 1 and for not pressing when B2
followed A 1. In match-to-sample, the participants received points for
responding to B 1 and for not responding to B2 when given A 1. Given
these similarities, one might expect both procedures to be equally
effective in producing equivalence. Yet, there are also procedural
differences. First, go/no-go involved twice as many different stimulus
combinations for training and testing as match-to-sa~ple. The relatively
large number of go/no-go stimulus combinations could have been difficult
to discriminate and may have thus interfered more with the symmetric
transitivity performances than with the easier to establish symmetry
performances (Fields et aI., 1992). Second, the stimulus configurations
and response requirements differed across tasks. In match-to-sample,
the participants were required to point to the correct comparison in the
presence of the incorrect comparison. The go/no-go configurations
showed only one "comparison" and required participants to respond or
not respond to a third stimulus (key). Perhaps, pointing to a correct
comparison among incorrect comparisons facilitates discrimination
learning and stimulus class formation. Finally, the go/no-go training could
have led to the formation of eight compounds, four controlling pressing
(A 1B1, A2B2, B1 C1, B2C2) and four controlling nonpressing (A 1B2,
A2B1, B1 C2, C2B1). If so, participants would be expected to respond
, correctly on symmetry trials (e.g., press when given B1-.A 1) and to
respond inconsistently on symmetric transitivity trials (e.g., C1-.A 1)
.(Cullinan et aI., 1998, 2000; Dube & Mcllvane, 1996).
Awaiting the outcome of ongoing go/no-go follow-up research, we
intiated the present study comparing the efficacy of match-to-sample
format and simultaneous-discrimination format conditional discrimination
tasks on equivalence formation in children and adults. The match-tosample procedures were standard: Baseline training (A 1-B 1, A2-B2; A 1C1, A2-C2) followed by symmetry tests (B1-A 1, B2-A2; C1-A 1, C2-A2)
and symmetric transitivity tests (B1-C1, B2-C2; C1-B2, C2-B2). During
the simultaneous-discrimination format procedure four simultaneous
discrimination (baseline) tasks were trained, two with complex AB stimuli
(AB/AB) "a nd two with complex AC stimuli (AC/AC). When using AB/AB
discrimi"nation tasks, participants were trained to respond to A 1B1 and
not to A1B2, and to respond to A2B2 and not to A2B1 (A1B1+/A1B2-,
A2B2+/A2B1-). When using AC/AC discrimination tasks, participants
were trained to respond to A 1C1 and not to A 1C2, and to respond to
A2C2 and not to A2C1 (A1C1+/A1C2-, A2C2+/A2C1-). Following
724 .
SMEETS ET AL.
acquisition, the participants received simultaneous-discrimination format
BAIBA and CAICA symmetry tests (B1A1+/B1A2-, B2A2+/B2A1-,
C1A1+/C1A2-, C2A2+/C2A1-), and BC/BC and CB/CB symmetric transitivity
tests (B1C1+/B1C2-, B2C2+/B2C1-, C1B1+/C1B2-, C2B2+/C2B1-).
Participants who demonstrated symmetry and symmetric transitivity were
trained to emit a specified response (R) in the presence of one member of
each class (B1-R1, B2-R2) and were subsequently tested for transfer (A 1-R1,
A2-R2, C1-R1, C2-R2).
The simultaneous-discrimination format could be more effective than the
go/no-go format because, like in match-to-sample, (a) multiple choice stimuli
are used, (b) participants are required to respond to the choice stimuli rather
than to a third stimulus (key), and (c) the number of different stimulus
configurations (tasks) used in training and testing is the same as in matchto-sample. On balance, the simultaneous-discrimination procedure has the
same disadavantage as the go/no-go procedure in that it permits the
participants to respond exclusively to the S+ stimuli (A 1B1, A2B2, A1C1 ,
A2C2) and treat these stimuli as compounds. If so, the participants should
be expected to respond consistently to the S+ stimuli used in symmetry
tasks (B1 A1, B2A2, C1 A1, C2A2) and inconsistently to the S+ stimuli used
in symmetric transitivity tasks (B1 C1, B2C2, C1 B1, C2B2).
The study consisted of two experiments. Experiment 1 used a
between-subject design with children and adults. Experiment 2 used a
within-subject design with children only. The study addressed the
following two questions. First, are both formats equally effective in
producing derived stimulus relations in children and adults? If not, does
the simultaneous-discrimination format procedure yield similar results as
the go/no-go procedure (Cullinan et aI., 1998; 2000)? Second, is transfer
affected by the formats (match-to-sample, simultaneous dicrimination)
previously used for training and testing conditional discriminations?
Experiment 1
Method
Participants
Sixteen Dutch preschool children and eight Dutch first-year students
of a teachers' college participated. All children were 5 years and all adults
18 years old. None of them had participated in similar research before.
Each population was divided into two groups: two groups of 8 children
(Groups 1 and 2) and two groups of 4 adults (Groups 3 and 4). Group 1
(Participants 1-8) consisted of 4 boys and 4 girls with a mean age of 5
years and 3 months (range: 5yr/1 mo - 5yr/5mo). Group 2 (Participants 916) consisted of 3 boys and 5 girls of the same mean age (range: 5yr/1 mo
- 5yr/6mo). Group 3 (Participants 17-20) consisted of 2 males and 2
females, and Group 4 (Participants 20-24) of 1 male and 3 females.
All participants served on a voluntary basis. Children were recruited
through contacts with the school and with parents' approval. Adults were
EQUIVALENCE CLASS FORMATION
725
recruited through personal contacts and were paid for their participation
(about US $12).
Setting, Sessions, Experimenter, and Observers
The children were seen in a quiet room of the school building.
Sessions were conducted individually, once or twice a day, lasted from 5
to 18 min (M = 9.8), and were conducted over a period of 9 to 13 days.
The lengths of the sessions were dependent on the child's on-task
behavior, the time permitted by the teachers, and time pressure to
conclude the experiment before school vacation. An adult female served
as experimenter. The experimenter and child .were seated at the same
table facing one another. Prior to her participation in this study, the
experimenter had received extensive training on the correct execution of
the test and training procedures with special emphasis on the prevention
of any cues (facial expression, eye darting) that could influence the
participants' responses. During the training trials, the experimenter looked
at the participant's face when giving instructions and delivering
programmed consequences. During the remainder of these trials (Le.,
when presenting stimuli and while the participants responded), the
experimenter gazed at the center of the stimulus card. Precautions were
taken to prevent the participants from observing the experimenter's
recordings on the data sheets. Seven other adults served as reliability
observers, one at a time. The reliability observer was present in the same
room but was situated such that she could clearly observe the subject's
responses, but not the experimenter's data sheet.
The adults were seen in a similar setting (Le., a quiet room of the college
building) but required only one session (M = 43 min, range: 41-48).
Stimuli, Tasks, and Materials
The stimuli consisted of rectangles that were solid black, gray,
speckled, or filled with black and white squares, and of black symbols.
They were 2 to 3 cm long and/or wide and centered in square windows (3
x 3 cm). The stimuli were shown singly (single-element stimuli) or
presented as combinations (two-element complex stimuli). Figure 1
shows the single-element stimuli and some examples of complex stimuli.
The stimuli are labeled with alphanumerics. These codes were not shown
to the participants and are used for descriptive purposes only. Singleelement stimuli are identified as single alphanumerics (e.g., A 1, C1).
Complex stimuli are identified by multiple alphanumerics (e.g., A 1B1,
C1 A 1), with the first and second one occupying the left and right
positions, respectively. For example, A 1B 1 indicates a complex stimulus
composed of elements A 1 and B 1, A 1 left and B 1 right; B 1A 1 indicates a
complex stimulus composed of the same elements but with B 1 left and A 1
right. The A, B, and C stimuli and combinations thereof were used in
Experiments 1 and 2. The D, E, and F stimuli, and combinations thereof,
were used in Experiment 2 only.
SMEETS ET AL.
726
Al
A2
Dl
D2
Bl
B2
Cl
C2
Et
E2
Fl
F2
,e
A
AIBI
CtAl
*
CtBt
Figure 1. Single-element stimuli and exemplars of complex stimuli.
Three types of discrimination tasks were used: ·match-to-sample
format conditional discriminations, simultaneous-discrimination format
conditional discriminations, and successive simple discriminations (see
Figure 2). The match-to-sample and simultaneous-discrimination tasks
were used for establishing baseline performances and measuring
symmetry and transitivity. The successive simple discriminations were
used for transfer training and· testing.
The match-to-sample tasks were composed of th.ree single-element
stimuli: two horizontally aligned choice stimuli (e.g., 81 and 82), distanced
9.0 cm, and a sampl,e stimulus (A1) centered below (see first panel in Figure
2). These stimuli were presented on white cards (14.5 x 21.0 cm). These and
all other stimulus materials were laminated in clear acrylic.
The simultaneous-discrimination tasks consisted of two horizontally
aligned complex choice stimuli with a common element (e.g., A181 and
A182, A282 and A281 , see second panel of Figure 2). The stimuli were
distanced 7.0 cm and presented on same size cards used for the matchto-sample tasks.
The successive discrimination tasks involved smaller white cards (5.0
x 5.0 cm) show.ing one single-element stimulus (e.g., 81) (see third panel
of Figure 2).
Additional materials were (a) a quadrant (32.5 x 32.5 cm) with three
rectangles (5.0 x 5.0 cm), one at the center, one at the upper left corner,
and one at the bottom right corner (see fourth panel of Figure 2); and (bl
a tray with beads and a standing glass tube showing a mark. Filling the
tube up to the mark required 50 beads.
727
EQUIVALENCE CLASS FORMATION
Bl
Bl
B2
Al
B2
A2
Match-to-sample fonnat conditional discrimination
AlB!
AIB2
A2B2
A2B!
Simultaneous-discrimination format conditional discrimination
Bl
At
Cl
Single discriminative stimuli for successive simple discriminations
D
Quadrant
Figure 2. Schematic presentation of stimulus materials.
Response Criteria and Programmed Consequences
During the match-to-sample and simultaneous discrimination tasks, the
participants were required to point to one (single-element or two-element
complex) comparison. Duri"ng the successive discrimination tasks, the
participants were required to place a stimulus card (showing a singleelement stimulus) on the upper left or bottom right rectangle of the quadrant.
Responses were recorded as correct, incorrect, or invalid. Responses
were scored correct or incorrect when a participant pointed to the
SMEETS ET AL.
728
designated corre'ct or incorrect comparison (match-to-sample and
simultaneous discrimination tasks) or placed the given stimulus card on
the correct or incorrect rectangle of the quadrant (successive
discrimination tasks). Responses were scored invalid when a participant
(a) pointed to a sample (match-to-sample tasks), (b) responded without
looking at the stimuli (all tasks), or (c) responded to both comparisons
(e.g., placed a card first on the bottom right and then on the upper left
rectangle). Only four invalid responses were recorded, three times in
Experiment 1 (all on training trials), and once in Experiment 2 (test trial).
All responses to training trials were followed by programmed
consequences. Children's correct responses were followed by praise and
the delivery of a token ("Good, take a bead."), incorrect responses by mild
punishment ("Wrong, no bead."), and invalid responses by corrective
feedback (e.g., "No, look at the pictures when pointing."). Following an
accumulation of 50 beads, the children were invited to exchange the
beads for a preselected color picture (cartoon character, sportscar,
. animal). The adults received only verbal feedback ("correct," "incorrect").
Responses on test trials were without programmed consequences.
Following each (correct, incorrect, or invalid) response, the experimenter
silently presented the next stimulus card.
Reliability
The reliability observers checked 1208 training trials (24.0%) and 576 test
trials (24.0%). The experimenter and observers disagreed on one test trial.
Table 1
Basic Training and Testing Sequence in Experiment 1
Match-To-Sample Format
Step 1 Train
Step 2 Train
Step 3 Train
A1-B1,
A1-C1,
A 1-B1,
A1-C1,
Step 4 Test
A1-B1,
A1-C1,
Step 5 Test
B1-A1,
C1-A1,
Step 6 Test
B1-C1,
C1-B1,
Step 7 Train
B1-R1,
Step 8 Test
B1-R1,
A 1-R1,
C1-R1,
Stimultaneous-Discrimination Format
Baseline Training
A2-B2
Step 1 Train A1 B1+/A1 B2-,
A2-C2
Step 2 Train A1C1+/A1C2-,
A2-B2
Step 3 Train A1 B1+/A1 B2-,
A2-C2
A1C1+/A1C2-,
Baseline Testing
A2-B2
Step 4 Test A1 B1+/A1 B2-,
A2-C2
A 1C1 +/A 1C2-,
Testing Symmetry
B2-A2
Step 5 Test B1 A 1+/B1 A2-,
C1A1+/C1A2-,
C2-A2
Testing Symmetric Transitivity
B2-C2
Step 6 Test B1 C1 +/B1 C2-,
C2-B2
C1 B1+/C1 B2-,
Transfer Training
B2-R2
Step 7 Train
B1-R1,
Testing Transfer
B2-R2
Step 8 Test B1-R1, B2-R2
A2-R2
A 1-R1, A2-R2
C2-R2
C1-R1, C2-R2
A2B2+/A2B1A2C2+/A2C1A2B2+/A2B1A2C2+/A2C1A2B2+/A2B1A2C2+/A2C1B2A2+/B2A 1C2A2+/C2A 1B2C2+/B2C1C2B2+/C2B 1B2-R2
EQUIVALENCE CLASS FORMATION
729
Procedures
Each participant was trained and tested on match-to-sample or
simultaneous discrimination tasks, and eventually also on transfer tasks.
The training and testing sequence was the same for both formats:
Training and testing of baseline tasks, testing symmetry and symmetric
transitivity, training and testing transfer (see Table 1). Group 1 (children;
Participants 1-8) and Group 3 (adults; Participants 17-20) received
match-to-sample tasks (match-to-sample program). Group 2 (children;
Participants 9-16) and Group 4 (adults; Participants 21-24) received
simultaneous discrimination tasks (simultaneous discrimination program).
Each program consisted of eight steps. Criterion performance on each
step was required for going to the next step.
Match-to-Sample Program
Step 1. A-B baseline training. The participants were trained to match
Samples A 1 and A2 with Comparisons 81 and 82, respectively (A 1-81,
A2-82). On each trial, the experimenter presented a card showing
Comparisons 81 and 82 and Sample A 1 or A2. The revised blocked-trial
procedure was used (Smeets & Striefel, 1994). Three substeps were
used. When dealing with children, the experimenter started Step 1A by
showing a stimulus card while saying, "We are going to playa game in
which you have to point to one of these two pictures (experimenter
pointed to 81 and 82). Sometimes this one is right (experimenter pointed
to 81), sometimes that one (experimenter pointed to 82). Each time you
point to the right one, you get a bead. I'll show you how it goes. Look here
(experimenter pointed to Sample A 1), point to this (experimenter pointed
to 81). Now you point." After two demonstration trials (A1-81 and A2-82),
the experimenter presented 20 no-help trials ("Now you have to do it on
your own."): 10 A1-81 quasirandomly mixed with 10 A2-82 trials. The
instructions for the adults were the same except that references to playing
a game and earning beads were omitted. During this substep, the
locations of the 8 stimuli were fixed, 81 always left and 82 always right
(see Figure 3). The samples, A 1 and A2, varied unsystematically over
trials. Step 1B was the same except that (a) no demonstrations wete
given, and (b) the locations of the 8 stimuli were reversed (81 always right
and 82 always left) (see Figure 3). Step 1C was the same as Step 18
except that the locations of the 8 stimuli varied quasirandomly over trials.
Criterion performance for each substep was set at 19/20 no-help trials of
a block correct. Participants who did not demonstrate criterion
performance received another block of trials (2 demonstration trials and
20 no-help trials in Step 1A, 20 no-help trials in Steps 18 and 1C).
Step 2: A-C baseline training. The procedures were the same as in Step
1, except that the participants were trained to match Samples A 1 and A2
with Comparisons C1 and C2, respectively (A 1-C1, A2-C2) (see Figure 3).
Step 3: Mixed A-B and A-C baseline training. Same as Steps 1C and
2C except that each training block consisted of quasirandomly mixed A 181, A2-82, A 1~C1, and A2-C2 trials (five of each).
SMEETS ET AL.
730
CONDITIONAL DISCRIMINATIONS
Simultaneous Discriminination Format
Match-to-Sample Format
I
BASELINE TASKS
+
+
Bl
B2
C2
B2
+
Cl
A2
C2
Step2B
Bl
A2Bl
+
C2
Al
AIC2
A2B2
+
AlCI
A2C2
CI
Step2B
+
AlB2
AlBl
+
AlC2
AlCl
Al
+
+
Bl
A2
AICI
+
SteplB
+
B2
AlB2
A2
SteplB
B2
AlBl
Al
+
Bl
+
+
Cl
Al
AC/AC
Step2A
AD/AD
SteplA
A-C
Step2A
A-B
SteplA
+
CI
C2
AlB2 .
+
AlB I
A2C2
AlCI
A2
Figure 3. Schematic presentation of baseline tasks.
Step 4: A-B and A-C baseline testing. This step assessed whether the
participants continued to respond accurately on all baseline tasks (A-B
and A-C) when the programmed consequences were withheld and
served to prepare the participants for the critical tests in Steps 5, 6, and
8. Step 4 consisted of two test blocks (Blocks 1 and 3) and two training
blocks (Blocks 2 and 4). Thus, each test block was immediately followed
by a training block. Each test block consisted of eight A-B and eight A-C
trials. Each training block consisted of two A-8 and two A-C trials. When
dealing with children, the experimenter introduced each test block as
follows, "Now I am no longer going to say whether you are right or wrong.
I will also give you no beads (experimenter removed the bead containers
from the table). Later, we will play the game with beads again. Do your
best." When dealing with adults, the experimenter informed the
participants that, until further notice, she would refrain from giving
feedback ("No feedback"). From that moment on, the experimenter silently
presented one stimulus card after another and refrained from making
verbal or nonverbal comments about the participants' performance.
731
EQUIVALENCE CLASS FORMATION
Immediately before each training block, the experimenter put the bead
containers on the table and told the children they could earn beads again
or, when dealing with adults, simply said "Feedback."
Participants who responded correctly on 15/16 A-B test trials, 15/16
A-C test trials, and on 7/8 training trials proceeded to Step 5. Participants
who did not meet criterion on the test trials received Step 4 again. Those
who. also failed to meet criterion on training trials returned to Step 3
(mixed A-B and A-C training) before receiving Step 4 again.
Step 5: a-A and C-A symmetry tests. This step examined whether the
participants continued to relate the directly linked stimuli with one another
when their functions (samples and comparisons) were reversed (B1-A 1,
B2-A2; C1-A 1, C2-A2) (see Figure 4). Step 5 was the same as Step 4
except that each test block consisted of two B1-A 1, two B2-A2, two C1A 1, and two C2-A2 trials quasi randomly mixed with eight baseline trials
(two A 1-B1, two A2-B2, two A 1-C1, and two A2-C2 trials) . .
CONDITIONAL DISCRIMINATIONS
Simultaneous Discrimination Format
Match-to-Sample Format
I SYMMETRY TASKS I
StepS
StepS
C-A
B-A
BAIBA
7
7
?
Al
Al
A2
Bl
A2
?
BlAI
ClAI
BIA2
CIA2
Cl
7.
Al
CAICA
?
Al
A2
B2
A2
?
B2At
?
C2A2
B2A2
C2A2
C2
ISYMMETRY TRANSITIVITY TASKS I
Step 6
Step 6
B-C
C-B
?
C2
Cl
B2
C2
B2
7.
BlCl
81C2
ClBl
ClB2
Cl
7
Cl
CBlCB
?
?
Bl
Bl
BCIDC
?
Bl
B2
7.
?
B2Cl
B2C2
-
C2B2
C2B2
C2
Figure 4. Schematic presentation of symmetry and transitivity tasks. The question marks (?)
above comparisons denote the class-consistent correct stimuli.
732
SMEETS ET AL.
Criterion was met when a participant responded correctly on 7/8 8-A
and 7/8 C-A symmetry trials, 15/16 baseline test trials (A-8, A-C), and on 7/8
training trials (A-8, A-C). Participants who did not meet the symmetry
criterion received Step 5 again. Participants who responded also
inaccurately on the baseline test trials, returned to Step 4 before receiving
Step 5 again. Those who failed on test and training trials received Steps 3,
4, and 5 again.
Step 6: B-C and C-B symmetric transitivity tests. This ·step examined
whether the participants related the indirectly linked 8 and C stimuli
conditionally with one another. Step 6 was identical to Step 5 except that each
test block consisted of two 81-C1, two 82-C2, two C1-81, and two C2-82
trials (see Figure 4) mixed with eight baseline test trials (same as in Step 5).
Criterion was met when a participant responded correctly on 7/8 8-C and
7/8 C-8 symmetric transitivity trials, 15/16 baseline test trials (A-8, A-C), and
on 7/8 training trials. Participants who failed to demonstrate criterion
performance on the symmetric transitivity trials received Step 6 once more.
Participants who also failed to demonstrate criterion performance on the
baseline test trials returned to Step 4 before receiving Step 6 again. Those
who failed on test and training trials returned to Steps 3 and 4 before
receiving Step 6 again. Participants who failed to reach criterion during the
second presentation of Step 6 did not receive Steps 7 and 8.
Step 7: B-R transfer training. This step was designed to establish
discriminative functions for one member of each class. Training consisted
of 2 demonstration trials followed by 20 no-help trials. The experimenter
introduced this step by presenting the quadrant (see panel 4 of Figure 2)
and two cards, one showing 81 and one showing 82. During each
demonstration trial, the experimenter first placed a stimulus card at the
center rectangle and then at the upper left rectangle (81) or at the bottom
right rectangle (82) (8 1-R 1, 82-R2) and invited the participant to do the
same. During the no-help trials the experimenter placed the stimulus card
at the center rectangle and waited for the participant to place that card on
one of the peripheral rectangles. Criterion was set at 19/20 nO-help
responses correct.
Step 8: B-, A-, C-R transfer test. This step assessed whether the
discriminative functions of the 8 stimuli transferred to same-class A and
C stimuli (A 1-R1, C1-R1, A2-R2, C2-R2). Four trial blocks were used, two
test blocks of 16 trials and two training blocks of 4 trials. Each test block
consisted of two A 1-R1, two C1-R1, two A2-R2, and two C2-R2 trials
quasirandomly mixed with four 81-R1, and four 82-R2 trials. Each training
block consisted of two 81-R1 and two 82-R2 trials. Transfer was assumed
if a pa·rticipant responded correctly on 7/8 A-R test trials, 7/8 C-R test
trials, 15/16 8-R test trials, and on 7/8 training (8-R) trials. Participants
who did not reach the test criteria received Step 8 again. Those who failed
on the test and training trials returned to Step 7 before receiving Step 8
again. Table 2 shows the numbers and types of trials for each step of the
match-to-sample program and simultaneous-discrimination program.
733
EQUIVALENCE CLASS FORMATION
Table 2
Numbers of Trials in Each Step of Match-to-Sample (MTS)
and Simultaneous Discrimination (SO) Program
MTS
SO
Steps
Step
Step
Step
Step
Step
Step
Step
Step
Step
Step
Step
Step
1A
1B
1C
2A
2B
2C
3
4
5
6
7
8
Train Train Test Test Test Test Test Test Train
A-B A-C A-B A-C
B-A C-A B-C C-B B-R
ABIAB AC/AC ABIAB AC/AC BAlSA CAICA BCIBC CBlCB B-R
Test Test
B-R C&A-R
B-R C&A-R
20
20
20
10
20
20
20
10
4
4
4
4
4
4
16
16
8
8
8
8
8
8
8
8
20
8
16
16
Notes. AB/AB =A1 B1+/A1 B2-, A2B2+/A2B1-. Notations for AC/AC, BAlBA, CAlCA, BC/BC,
and CB/CB are the same as for ABIAB. A-B = A 1-B 1, A2-B2. Notations for A-C, B-A, C-A,
B-C, and C-B are the same as for A-B. B-R = B1-R1, B2-R2. C&A-R = C1-R1, C2-R2, A 1R1, A2-R2.
Simultaneous Discrimination Program
Except for the stimulus configurations and minor instructional
changes (to suit the stimulus configurations), the procedures were
identical to those of the match-to-sample program. In Step 1 (AB/AB
training), the participants received two simultaneous discrimination tasks
with complex AB stimuli, A1B1 vs. A1B2 (A 1B1/A 1B2) and A2B2 vs. A2B1
(A2B2/A2B1). Pointing to A 1B1 and to A2B2 was reinforced
(A 1B1 +/A2B1-, A2B2+/A2B1-). As in the match-to-sample program, Step
1 consisted of three substeps. During Steps 1A and 1B, the left-right
locations of the stimuli were fixed (see Figure 3). In Step 1A, A1B1 was
presented always left and A2B2 always right (A 1B1+/A 1B2-, A2B 1/A2B2+). In Step 1B, the locations were reversed, A1B1 right and A2B2
left (A 1B2-/A 1B1 +, A2B2+/A2B1-). In Step 1e, the locations of the stimuli
varied quasi randomly across trials.
Step 2 was the same as Step 1 but with complex AC stimuli (AC/AC
training). The participants were trained to point to A 1C1 and not to A 1C2,
and to point to A2C2 and not to A2C1 (A1C1+/A1C2-, A2C2+/A2C1-)
(see Figure 3). Steps 3 and 4 involved mixed AB/AB and AC/AC training
and testing, respectively.
Steps 5 and 6 assessed symmetry (BAlBA, CAlCA) and symmetric
transitivity (BC/BC, CB/CB). In Step 5, each test block consisted of eight
symmetry trials: two B1A1+/B1A2-, two B2A2+/B2A1-, two C1A1+/C2A1-,
and two C2A2+/C2A 1- trials (see Figure 4). These trials were quasirandomly
mixed with eight baseline trials: two A1B1+/A1B2-, two A2B2+/A2B1-, two
A1C1 +/A 1C2-, and two A2C2+/A2C1- trials. Each training block consisted of
four baseline trials (two AB/AB and two AC/AC trials). Step 6 was the same
734
SMEETS ET AL.
except that each test block incorporated eight symmetric transitivity trials:
two B1C1+/B1C2-, two B2C2+/B2C1-, two C1B1+/C1B2-, and two
C2B2+/C2B1- trials (see Figure 4).
Steps 7 and 8, transfer training and testing, were the same as in the
match-to-sample program.
Results
Children
Baseline training and testing. Both child groups learned the baseline
tasks (Steps 1, 2, and 3) without majqr difficulties (Table 3). All children
continued to respond accurately on these tasks during testing and
training in Steps 4, 5, and 6.
Table 3
Numbers of Baseline Training Trials in Steps 1 to 3 of Experiment 1
Children
Group 1
1.
2.
3.
4.
5.
6.
7.
8.
M
140
140
140
140
180
140
140
200
152.5
Adults
Group 2
9.
10.
11.
12.
13.
14.
15.
16.
Group 3
220
160
140
140
140
140
140
180
157.5
17.
18.
19.
20.
Group 4
140
140
140
140
140
21.
22.
23.
24.
140
140
140
140
140
Note. Groups 1 and 3, match-to-sample format. Groups 2 and 4, simple-discrimination format.
Symmetry and symmetric transitivity. Tables 4 and 5 show the
numbers of correct responses by each group on the first and second
presentation of the symmetry, symmetric transitivity, and transfer tests. All
children responded accurately during the first or second presentation of
the symmetry test (B-A, C-A: Group 1; BAlBA, CAlCA: Group 2).
Seven children of Group 1 (87.5%) demonstrated match-to-sample
format symmetric transitivity (B-C, C-B), all during the first test
presentation. Only 4 children of Group 2 (50%) evidenced simultaneousdiscrimination format symmetric transitivity (BC/BC, CB/CB), 2 during the
first presentation (Participants 9 and . 12) and 2 during the second
presentation (Participants 10 and 11). Participant 4 (Group 1)
mismatched during the first presentation (B1-C2, B2-C1; C1-B2, C2-B1)
and responded unsystematically during the second presentation.
Participants 13, 14, 15, and 16 (Group 2) showed stimulus preference
(Le., systematically selected stimuli with a same B or C element) or
position preference.
Training and testing transfer. All 11 children, 7 of Group 1 and 4 of
Group 2, who passed the symmetry and symmetric transitivity tests
received transfer training (B1-R1, B2-R2). All of them learned the training
EQUIVALENCE CLASS FORMATION
735
tasks in one session (20 training trials). Of these children, 7 also
demonstrated transfer (A 1-R1, C1-R1, A2-R2, C2-R2), 5 (71.4%) of
Group 1 (Participants 1, 2, 5, 6, and 8) and 2 (50%) of Group 2
(Participants 9 and 10), all during the first test presentation.
Participant 3 (Group 1) responded unsystematically during the first
test presentation. During the second presentation, she responded
correctly when given Class-1 stimuli (81-R1, A 1-R1, C1-R1), and when
given 82 (82-R2), but responded at chance level when given A2 and C2.
Participant 11 (Group 2) responded un~ystematically both presentations.
Participant 12 (Group 2) emitted R1 when given 81 and R2 when given
all other stimuli (82, A 1, A2, C1, and C2).
Adults
All adults completed the training and testing sequences (training and
testing of baseline tasks, symmetry and symmetric transitivity tests,
transfer training and testing) in a (near) error free fashion, irrespective of
the types of conditional discrimination tasks that were used (see Tables 3,
4, and 5). Collectively, these participants responded correctly on all but 9
of the 2560 training and test trials.
Experiment 2
The results of Experiment 1 suggested that, when used with children,
the match-to-sample format tasks are superior to simultaneousdiscrimination format tasks in establishing stimulus equivalence and, to a
lesser extent also, in generating transfer. This conclusion, however, could
be criticized due to the between-group design that was used in
Experiment 1. Since this design permits the outcome to be affected by
Table 4
Numbers of Correct Test Responses in Match-to-Sample Program in Experiment 1
Participants
Symmetry
Test 1
8-AC-A
1
2
3
4
5
6
7
8
5
7
8
7
7
8
8
8
8
8
8
7
8
8
8
8
17
18
19
20
8
8
8
8
8
8
8
8
Symmetry
Test 2
8-AC-A
8
8
Sym-Trans
Test 1
8-CC-8
Sym-Trans
Test 2
8-CC-8
Group 1 - Children
7 8
7 8
8 8
0 0
3
7 8
8 8
8 8
8 8
Group 3 - Adults
8
8
8 8
8 8
8 8
Note. A&C-R = A 1-R1, C1-R1, A2-R2, C2-R2.
Transfer
Test 1
A&C-R
Transfer
Test 2
A&C-R
15
16
11
12
4
16
16
9
16
16
16
16
16
9
SMEETS ET AL.
736
Table 5
Numbers of Correct Test Responses in Simultaneous Discrimination Program in Experiment 1
Participants
Symmetry
Test 1
BAIBA CAICA
9
10
11
12
13
14
15
16
21
22
23
24
Note. A&C-R
8
8
8
8
8
8
8
8
7
7
7
7
8
8
8
8
8
8
8
8
7
8
7
8
Symmetry
Test 2
BAIBA CAICA
Sym-Trans
Test 1
BCIBC CB/CB
Group 2 - Children
7
8
6
5
5
6
7
8
2
5
4
4
2
8
4
5
Group 4 - Adults
8
8
7
8
8
8
8
8
Sym-Trans
Test 2
BC/BC CB/CB
8
8
4
5
4
4
8
8
Transfer
Test 1
A&C-R
Transfer
Test 2
A&C-R
15
16
7
7
8
8
4
5
4
4
16
16
16
16
= A 1-R1, C1-R1, A2-R2, C2-R2.
extraneous variables (e.g., intelligence, attention span, sensitivity to
reinforcement), Experiment 2 was designed to replicate the child-based
findings using a within-subject design.
Method
Eight new children, 4 boys and 4 girls, participated. Their ages ranged
from 5 years 1 month to 5 years 7 months (M= 5yr/4mo). The participants
were divided into four pairs: Participants 1 and 2 (Pair 1), Participants 3
and 4 (Pair 2), Participants 5 and 6 (Pair 3), and Participants 7 and 8 (Pair
4). Each pair received two programs, one with match-to-sample format
tasks and one with simultaneous-discrimination format tasks. The matchto-sample tasks involved single-element A, B, and C stimuli, or D, E, and
F stimuli for training and testing symmetry and symmetric transitivity (see
Figure 1). The simultaneous-discrimination format tasks involved complex
AB, AC, BA, CA, BC, and CB stimuli, or complex DE, DF, ED, FD, EF, and
FE stimuli for training baseline tasks, and testing symmetry and
symmetric transitivity. Both programs used single-element A, B, and C, or
D, E, and F stimuli for transfer training and testing. The order in which the
two formats were used and the stimuli that were used with each format
were counterbalanced across pairs (see Table 6). Participants who
demonstrated symmetry and symmetric transitivity with A, B, and C
stimuli (match-to-sample tasks) or with complex BA, CA, BC, and CB
stimuli (simultaneous discrimination tasks) received transfer training on B
stimuli and transfer tests with B, A, and C stimuli. Participants who
demonstrated symmetry and symmetric transitivity with D, E, and F
stimuli (match-to-sample tasks) or with complex ED, FD, EF, and FE
stimuli (simultaneous discrimination tasks) received transfer training on E
737
EQUIVALENCE CLASS FORMATION
stimuli and transfer tests with D, E, and F stimuli. Table 6 shows the
training and test sequence for each pair. The procedures for each
program were the same as in Experiment 1. Each participant required 10
to 12 sessions, 5 to 18 min each, over a period of 15 to 17 days.
The reliability observers checked 839 training trials (27.20/0) and 704
test trials (31.9%). The experimenter and observers disagreed on one
training trial.
Table 6
Basic Training and Testing Sequence in Experiment 2
Steps
1-3
4
5
6
Participants 1and 2
Participants 3 and 4
Participants 5 and 6
Participants 7 and 8
Simult-Discrim Format
Simult-Discrim Format
Match-to-Sample Format
Match-to-Sample Format
Baseline Training
A1B1t1A1B2-, A2B2t1A2B1- D1E1-HD1E2-,02E2+iV2E1- A1-B1, A2-B2
A1C1t1A2C1-, A2C2t1A2C1- D1F1-HD1F2-,02F2+iV2F1- A1-C1, A2-C2
Baseline Testing
A1B1t1A1B2-, A2B2t1A2B1- D1E1-HD1E2-,02E2+iV2E1- A1-B1, A2-B2
A1C1t1A1C2-, A2C2t1A2C1- D1F1-HD1F2-,02F2+iV2F1- A1-C1, A2-C2
Testing Symmetry
B1A1+tB1A2-, B2A2+!B2A1- E1D1+i£102-, E202+i£2D1- B1-A1, B1-A2
C1A1tlC1A2-, C2A2tIC2A1- F1D1+Jf102-, F202+IF2D1- C1-A1, C2-A2
Testing Symmetric Transitivity
B1C1+tB1C2-, B2C2t1B2C1- E1F1+i£1F2-, E2F2+i£2F1- B1-C1, B2-C2
C1B1t1C1B2-, C2B2t1C2B1- F1E1+Jf1E2-, F2E2+Jf2E1- C1-B1, C2-B2
Transfer Training
E1-R1 , E2-R2
B1-R1 ,B2-R2
B1-R1 , B2-R2
Testing Transfer
B1-, A1-, C1-R1
E1-, D1-, F1-R1
B1-, A1-, C1-R1
B2-,A2-, C2-R2
E2-, 02-, F2-R2
B2-,A2-,C2-R2
D1-E1 , O2-E2
D1-F1 , O2-F2
D1-E1 , O2-E2
D1-F1 , O2-F2
E1-D1 , E2-02
F1-D1 , F2-02
E1-F1 , E2-F2
F1-E1 , F2-E2
I
7
E1-R1 , E2-R2
r
8
Match-to-Sample Format
Match-to-SampIe Format
Simu~-Discrim Format
E1-, 02-, F2-R2
E2-, 02-, F2-R2
Simu~-Discrim Format
Baseline Training
1-3
D1-E1,02-E2
D1-F1 , O2-F2
A1-B1, A2-B2
A1-C1, A2-C2
D1E1-HD1E2-,02E2+iV2E1:- A1B1t1A1B2-, A2B2+IB2B1D1F1-HD1F2-,02F2+iV2F1- A1C1t1A1C2-, A2C2t1A2C1Baseline Testing
4
D1-E1,02-E2
D1-F1 , O2-F2
5
E1-D1, E2-D2
F1-D1, F2-02
6
E1-F1, E2-F2 .
F1-E1, F2-E2
7
E1-R1 , E2-R2
8
E1-,D1-, F1-R1
E2-, 02-, F2-R2
A1-B1, A2-B2
A1-C1, A2-C2
D1E1-HD1E2-,02E2+iV2E1D1F1-HD1F2-,02F2+iV2F1Testing Symmetry
B1-A1, B2-A2
E1D1+i£102-, E202+i£2D1C1-A1, C2-A2
F1D1+IF102-, F202+Jf2D1Testing Symmetric Transitivity
B1-C1, B2-C2
E1F1+i£1F2-, E2F2+i£2F1C1-B1, C2-B2
F1E1+Jf1E2-, F2E2+IF2E1Transfer Training
B1-R1, B2-R2
E1-R1, E2-R2
Transfer Testing
B1-, A1-, C1-R1
E1-, D1-, F1-R1
B2-, A2-, C2-R2
E2-, 02-, F2-R2
A1B1t1A1B2-, A2B2t1A2B1A1C1t1A1C2-, A2C2t1A2C1B1A1+!B1A2-, B2A2+!B2A1C1A1t1C1A2-, C2A2t1C2A1B1C1+tB1C2-, B2C2t1B2C1C1B1t1C1B2-,C2B2t1C2B1B1-R1, B2-R2
B1-, A1-, C1-R1
B2-, A2-, C2-R2
SMEETS ET AL.
738
Results
The results were very similar to those of Experiment 1. Again, all
participants required no or only a few extra training trials to learn the
baseline tasks (Table 7). All participants continued to respond accurately
on these tasks during training and testing conditions in Steps 4 to 6.
Table 7
Numbers of Baseline Training Trials in Steps 1 to 3 of Experiment 2
Children
MTS
SO
1
2
3
4
5
6
7
8
M
140
140
140
160
140
160
140
140
140
140
140
140
140
140
140
140
140
145
Note. MTS = match-to-sample format. SO = simple-discrimination format. Children 1-4
received SO first. Children 5-8 received MTS first.
Table 8 shows the numbers of correct responses on the first
presentation of the symmetry test (there was no need to present this test
twice), and on the first and second presentation of the symmetric
transitivity and transfer tests. All participants demonstrated criterion
performance during the first presentation of the symmetry test ·
irrespective of its format. The performances on the symmetric transitivity
tests, however, varied across participants and task formats. Four
participants (1,3,6, and 8) responded accurately on the match-to-sample
format and simultaneous-discrimination format transitivity tests. The other
4 participants (2, 4, 5, and 7) responded accurately on the match-tosample format symmetric transitivity test, 2 (4 and 7) during the first
presentation and 2 (2 and 5) during the second presentation, but not on
the simultaneous-discrimination format symmetric transitivity test, even
after having demonstrated symmetric transitivity with the match-tosample format tasks (Participants 5 and 7). Three of these participants
evidenced position preference (Participant 2) or stimulus preference
(Participants 4 and 5). The performance of Participant 7 did not suggest
any form of systematic stimulus control. Thus, like in Experiment 1, the
match-to-sample format tasks were superior to the simultaneousdiscrimination format tasks in producing symmetric transitivity.
Transfer training was implemented 12 times, 4 times with stimuli that
had been used in simultaneous-discrimination format tasks (Participants
1, 3, 6, and 8) and 8 times with stimuli that had been used in match-tosample format tasks (all 8 participants). All participants learned the
successive discriminations (B1-R1, B2-R2 or E1-R1, E2-R2) in one
session. The following tests showed that transfer was not affected by the
format of tasks (match-to-sample, simultaneous discrimination) in which
the stimuli had previously participated. Transfer was observed nine times
(75%), three out of four times (75%) with stimuli that had been used in
simultaneous-discrimination format tasks and six out of eight times (75 % )
with stimuli that had been used in match-to-sample format tasks. Two of
739
EQUIVALENCE CLASS FORMATION
Table 8
Numbers of Correct Responses of Each Participant (P) on
Symmetry, Symmetric Transitivity, and Transfer Tests
Tasks
P1
P2
P3
P4
Tasks
P5
P6
P7
P8
8
8
8
8
8
8
8
8
16
16
7
8
8
7
6
2
8
MTS Format
SO Format
Sym Test
BAiBA
CAiCA
EO/EO
FO/FO
8
8
BC/BC
CB/CB
EF/EF
FE/FE
8
8
8
8
8
4
4
8
8
BC/BC
CB/CB
EF/EF
FE/FE
A&C-R
O&F-R
7
6
3
16
16
A&C-R
O&F-R
B-A
C-A
E-O
7
F-O
7
Sym-Trans Test 1
B-C
C-B
E-F
4
F-O
4
Sym-Trans Test 2
B-C
C-B
E-F
6
F-E
4
Transfer Test 1
A&C-R
O&F-R
Transfer Test 2
A&C-R
O&F-R
MTS Format
8
8
6
6
7
7
8
8
8
7
10
16
9
SO Format
Sym Test 1
E-O
F-O
B-A
C-A
7
8
E-F
F-E
B-C
C-B
7
7
7
8
7
8
6
5
8
7 ·
E-F
F-E
B-C
C-B
7
7
O&F-R
A&C-R
13
O&F-R
A&C-R
13
16
16
EO/EO
FO/FO
BAiBA
8
CAiCA
8
Sym-Trans Test 1
EF/EF
FE/FE
BC/BC
8
CB/CB
8
Sym-Trans Test 2
EF/EF
FE/FE
BC/BC
CB/CB
Transfer Test 1
O&F-R
16
A&C-R
Transfer Test 2
O&F-R
A&C-R
7
7
3
6
8
8
8
8
7
5
5
5
6
12
16
12
Note. MTS =match-to-sample. SD =simple discrimination. A&C-R =A 1-R1 , C1-R1 , A2-R2, C2-R2.
SMEETS ET AL.
740
these failures implied transfer to only one stimulus of each class
(Participant 1: E1-F1-R1, E2-D1-D2-F2-R2; Participant 6: E1-D1-R1, E2D2-F1-F2-R2).
Discussion
For both age groups, the match-to-sample format and simultaneousdiscrimination format tasks were equally effective in establishing baseline
performances and symmetry, but not in establishing symmetric transitivity
(Table 9). All 8 adults (Experiment 1) learned the baseline tasks and
demonstrated symmetry, symmetric transitivity, and transfer irrespective of
the task format that was used for generating class formation. All 16 children
(Experiments 1 and 2) learned the baseline tasks and demonstrated
symmetry. Almost all of them (N = 15) demonstrated match-to-sample
format symmetric transitivity while only half of them (N = 8) demonstrated
simultaneous-discrimination format symmetric transitivity. Transfer training
and testing was conducted 23 times, 15 times after match-to-sample format
equivalence, and 8 times after simultaneous-discrimination format
equivalence. Transfer was observed 16 times (69.6%): 11/15 times (73.3%)
with stimuli that had participated in match-to-sample format tasks and 5/8
times (62.5 %) with stimuli that had participated in simultaneousdiscrimination format tasks. Thus, transfer occurred less often with children
than with adults but was not affected by the task formats in which the stimuli
had previously participated.
Table 9
Numbers and Percentages of Children (Experiments 1 and 2) and of Adults
(Experiment 1) Demonstrating Symmetry, Symmetric Transitivity, and Transfer
Tests
Symmetry
Sym-Trans
Transfer
Note. MTS
Children
MTS Format
SD Format
16 (100%)
16 (100 %)
15 (93.8%)
8 (50.0%)
11 (73.3%)
5 (62.5%)
Adults
MTS Format
4 (100%)
4 (100%)
4 (100%)
SD Format
4 (100%)
4 (100%)
4 (100 %)
=match-to-sample, SD =simultaneous discrimination.
These findings, combined with those reported here, tentatively suggest
that the simultaneous-discrimination format is superior to the go/no-go
format in producing equivalence relations in adults and possibly also in
children. (In the study by Cullinan et aI., 1998, for example, go/no-go format
training and testing produced symmetric transitivity 3/10 times [300/0] in
adults; in the present study, simultaneous-discrimination format training and
testing produced symmetric transitivity in all 8 (1 00%) adults and 8/16 times
[50%] in children.} Yet, this conclusion could be challenged because of the
different testing protocols that were used. In the studies by Cullinan etal.
(1998, 2000), symmetry and symmetric transitivity were tested
simultaneously. In the current study, symmetry was tested before symmetric
transitivity. Studies have shown that symmetric transitivity occurs more
readily when tested after symmetry rather than with symmetry (Bush,
EQUIVALENCE CLASS FORMATION
741
Sidman, & de Rose, 1989; Fields et aI., 1992, and Smeets et aI., 1997).
Although the match-to-sample equivalence performances did not seem to
be affected by these protocols (almost all participants in the studies by
Cullinan et aI., 1998, 2000, and in the present study demonstrated matchto-sample symmetric transitivity), the symmetric transitivity performances on
nonmatching-to-sample (go/no-go, simultaneous-discrimination) · format
tasks may have been affected by these protocols.
The discrepant child performances on simultaneous-discrimination
format symmetry tests (100 % success) and symmetric transitivity tests
(50% success) could be related to the training. The simultaneousdiscrimination format training allowed the children to treat the baseline .
tasks as simple discriminations and thus some of them may have
responded exclusively to the complex S+ stimuli (A 1B1, A2B2, A 1C1,
A2B2). In fact, the children could have learned to point to only two specific
compounds (e.g., A 1B1 and A 1C1) and to all compounds with no element
in common (A2B2, A2C2), and not to point to any compounds with one
element in common (A 1B2, A2~1, A 1C2, A2C1). If correct, the accurate
performances on the symmetry tests (i.e., selecting B1 A 1, B2A2, C1 A 1,
C2A2) (a) could be accounted for by primary stimulus generalization, (b)
should be seen as "false positives" for symmetry, and (c) formed no basis
for symmetric transitivity (i.e., selecting B1C1, B2C2, C1 B1, C2B2).
The failures on the simultaneous-discrimination format symmetric
transitivity tests could also be a function of the task format that was used for
testing. In the studies by Cullinan et al. (1998, 2000), adults who had been
trained on go/no-go format conditional discriminations performed better on
match-to-sample format symmetric transitivity tests than on go/no-go format
symmetric transitivity tests. In the present study, all participants received
training and testing with same format tasks: match-to-sample format training
and testing or simple-discrimination format training and testing. Future child
research should explore whether simultaneous-discrimination format
conditional discrimination training followed by match-to-sample format tests
is more effective in producing symmetric transitivity than when followed by
simultaneous-discrimination format tests.
However, even if it was shown that children's failures on the
transitivity tests are a function of the task formats used for training and/or
testing, it would still not be clear why, for young children, match-to-sample
tasks are more effective than simultaneous-discrimination format tasks.
The children's performances on the simultaneous-discrimination format
tasks could be related to developmental status per se .. Developmental
studies examining the integrality/separability question have reported that,
as children grow older, there is a general trend from responding to
compound aspects of the stimuli to responding to stimulus components,
or from holistic to featural perception (Shepp, Barrett, & Kolbet, 1987;
Smith & Kemler, 1977; Tighe & Tighe, 1978; Zeaman & Hanley, 1983; but
see Rudy, 1991). Alternatively, the superiority of match-to-sample could
have resulted from the matching tasks being often used in formal and
informal educational settings (e.g., school textbooks and commercially
available games) to teach picture-to-word equivalences and other forms
742
SMEETS ET AL.
of categorization (e.g., matching names of food items). With this
educational history, the match-to-sample format itself may act as a
powerful contextual cue for equivalence responding (de Rose, 1996;
Dymond & Barnes, 1995; Hayes, Gifford, & Wilson, 1996; Wulfert &
Hayes, 1988) in a way that nonmatching-to-sample tasks can not. This
difference may be critical for young children who do not have a protracted
history of problem solving activities like teenagers or adults. For the latter
populations, a novel format may be less likely to disrupt predicted
relational responding because they have a "richer history" of problem
solving exemplars to draw on when presented with testing tasks.
Following transfer training, all adults and a modest majority of the
children evidenced class-consistent transfer irrespective of the task
formats in which the stimuli had previously participated. This finding
supports the conclusion that the symmetry and symmetric transitivity
performances, notably those measured with simultaneous discrimination
tests, constituted stimulus equivalence (Sidman, 1994; Sidman & Tailby,
1982). This conclusion could be challenged also because previous
research has shown that transfer between compound elements may
occur without equivalence (Schenk, 1995; Smeets, Barnes, Schenk, &
Darcheville, 1996). For example, in the study by Smeets et al. (1996)
involving children and adults with mental retardation, training of a
simultaneous A discrimination task (A 1+/A2-) reliably produced transfer
from A to B and from B to C via AB and BC compounding (A 1B 1+/A2B2-,
B1 +/B2-, B1 C1 +/B2C2-, C1 +/C2-) even though most of these participants
failed to match the directly and indirectly paired compound elements with
one another (A 1-B1-C1, A2-B2-C2). The same could have occurred in the
present study (transfer from B to A and from A to C), except that all Band
C stimuli were compounded with all A stimuli (e.g., A 1B1, A 1B2, A2B2,
A2B1). Thus, it would be difficult to explain why the responses trained with
B 1 would transfer to A 1, the element that appeared with B 1 in the S+
compounds, and not to A2, the element that appeared with B1 in the Scompound, unless A 1, B1, and C1 formed an equivalence class.
In conclusion, the present findings indicate that (a) simultaneousdiscrimination format conditional discrimination tasks are as effective as
match-to-sample format conditional discrimination tasks for generating
equivalence relations in adults but less effective than match-to-sample
tasks when used with young children, and (b) transfer was a function of
age and not of the task format (match-to-sample, simultaneous
discrimination) that was used for measuring equivalence. Furthermore,
current findings tentatively suggest that simultaneous-discrimination
format conditional discriminations are more effective in producing
equivalence than go/no-go format conditional discriminations (Cullinan et
aI., 1998, 2000).
EQUIVALENCE CLASS FORMATION
743
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