ENHANCING EQUIVALENCE CLASS FORMATION BY PRETRAINING OF OTHER EQUIVALENCE CLASSES

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1 The Psychological Record, 1997, 47, ENHANCING EQUIVALENCE CLASS FORMATION BY PRETRAINING OF OTHER EQUIVALENCE CLASSES DAWN M. BUFFINGTON 1,3, LANNY FIELDS 2, 3, and BARBARA J. ADAMS 1, 3 1 Queens College/CUNY, 2The College of Staten Island/CUNY, and 3The Graduate School and University Center/CUNY This study investigated how the learning of one set of equivalence classes enhances the learning of new equivalence classes. Fifty-two undergraduate students were divided into four groups. Subjects in Group 1 received no pretraining. Using the simple-to-complex procedure followed by incremental expansion of class size, subjects in Groups 2, 3, and 4 learned 3-, 4-, and 5- member equivalence classes, respectively. After pretraining, two new 3-member equivalence classes were established by the concurrent training of all baseline relations and the concurrent presentation of all emergent relations probes to assess class formation (the simultaneous protocol). With no pretraining, 58% of subjects formed the new classes under the simultaneous protocol. After pretraining of the 3-, 4-, and 5-member classes, the new classes were formed by 62, 85, and 100% of the subjects, respectively. Pretraining of 4- and 5-member classes produced a small increment in the percentage of subjects who showed the immediate emergence of the new classes. Pretraining of the 5- member classes produced a large increment in percentage of subjects who formed classes with repeated testing. Thus, pretraining influenced immediate and delayed emergence of equivalence classes. With no pretraining, during the tests used to assess the formation of the new classes, 12% of subjects showed disruption of baseline performances, relational responding produced by symmetry probes was lower than that produced by baseline relations, and very low levels of relational responding were evoked by 1-node probes. These data demonstrated the effects of nodal distance. Pretraining did not ameliorate the disruption of baseline performances. Pretraining of 4- and 5-member classes produced moderate increments in the relational responding evoked by symmetry probes. Pretraining of 5-member classes produced large increments in the relational responding evoked by 1-node probes. This paper was prepared with the support of Contract MDA C-132 from the Army Research Institute. We thank Kenneth F. Reeve, Devorah Rosen, and Donna Landon-Jimenez for their critical comments and assistance in the preparation of this manuscript. Reprints can be obtained from Lanny Fields, The College of Staten Island, 2800 Victory Boulevard, Staten Island, NY

2 70 BUFFINGTON ET AL. In studies of the emergence of equivalence classes, the conditional relations that are the prerequisites of the classes and the emergent relations probes can be introduced in a serial order or on a concurrent basis. A great deal of information is available regarding class formation when training and testing trials are introduced serially. Little is known about class formation when training trials are introduced concurrently and are then followed by the concurrent introduction of all testing trials. The purpose of the present experiment is to explore the factors that influence class formation under the latter conditions. Two serial protocols that have been used to form equivalence classes are the complex-to-simple procedure (CTS) and the simple-tocomplex (STC) procedure (Adams, Fields, & Verhave, 1993). Complexto-simple protocols were introduced earlier than the simple-to-complex protocol and have been used in far more experiments. In the complex-to-simple procedure, all baseline relations are trained to criterion in a serial manner prior to the presentation of the emergent relations tests. The first emergent relation test conducted involves the presentation of equivalence probes, which assess the combined effects of symmetry and transitivity (Fields, Adams, Newman, & Verhave, 1992; Fields & Verhave, 1987; Sidman, 1990; Sidman & Tail by, 1982). If subjects fail that test, it is followed by the presentation of other probes that assess transitivity alone and/or symmetry alone (Fields, Adams, et al, 1992). After subjects pass one of these tests, the equivalence tests are reintroduced. Once the equivalence test is passed, the classes are said to have formed. Using the complex-to-simple procedure, between 70 and 100% of subjects form equivalence classes (Bush, Sidman, & de Rose, 1989; Devany, Hayes, & Nelson, 1986; Fields, Adams, et al, 1992; Fields, Adams, Verhave, & Newman, 1993; Kennedy & Laitinen, 1988; Lazar, Davis-Lang, & Sanchez, 1984; Saunders, Wachter, & Spradlin, 1988; Sidman, Kirk, & Willson-Morris, 1985; Spradlin, Cotter, & Baxley, 1973). In addition, there is a large amount of intersubject variability in the number of trials required to pass the emergent relations tests for the subjects who form classes (Adams et al, 1993; Fields et al, 1992). With the simple-to-complex procedure, each emergent relation is assessed immediately after the demonstration of all its baseline relations. Under these conditions, at least 95% of the subjects pass the emergent relations tests almost immediately (Adams et al, 1993; Fields, Newman, Adams, & Verhave, 1992; Fields, Reeve, Adams, & Verhave, 1991; Lynch & Cuvo, 1995; Schusterman & Kastak, 1993). When this protocol is used, equivalence classes are formed with relatively little intersubject variability (Adams et al, 1993; Fields et al, 1991; Fields, Newman, et al, 1992). Although most studies of equivalence class formation have used serial protocols, these are not the only ways of presenting trials for training and testing. Fields, Landon-Jimenez, Buffington, & Adams (1995) studied the formation of two 5-member classes using the

3 PRETRAINING ENHANCES EQUIVALENCE 71 simultaneous protocol (SIM). First, all baseline conditional relations were introduced in a single block of randomly presented trials. This training block was repeated until all baseline conditional relations were learned. It was followed by the presentation of all symmetry, transitivity, and equivalence probes in a single emergent relations test block. All 12 college students who participated in the study learned the baseline conditional discriminations. Only two of them (17%), however, passed the emergent relations tests and formed equivalence classes. Relative to the serial protocols, a much smaller proportion of subjects formed equivalence classes under the simultaneous protocol. The low yield was surprising considering the fact that college students were the subjects in the experiment. The low yields occasioned by the simultaneous protocol, however, provide an opportunity for identifying variables that increase the likelihood of equivalence class formation by normal adults, and for discovering some of the behavioral processes responsible for equivalence class formation. When learning under a specific set of conditions is unlikely, the learning can be enhanced by appropriate pretraining. This has been demonstrated in the shaping of new responses (Catania, 1992; Galbicka, 1994; Lane, Kopp, Sheppard, Anderson, & Carlson, 1967; Pear & Legris, 1987; Platt, 1973). The prior training of component skills also enhances the emergence of problem-solving repertoires (Goldstein, 1985; Johnson & Layng, 1992; Nakajima & Sato, 1993) and learning of conditional discriminations (Hively, 1962; Saunders & Spradlin, 1989, 1990, 1993; Sidman & Stoddard, 1967; Zygmont, Lazar, Dube, & Mcllvane, 1992). Wulfert, Dougher, and Greenway (1991) found that the prior training of subjects to attend to the relational properties of stimuli enhanced likelihood of equivalence class formation. Adams et al. (1993) found that the likelihood of successful expansion of class size was influenced by the protocol used to establish initial equivalence classes. Specifically, expansion of class size from three to five members was far more likely after the establishment of the initial 3-member classes using the simple-to-complex protocol instead of the complex-to-simple protocol. In the current experiment, we showed that learning one set of equivalence classes using the simple-to-complex protocol followed by expansion in class size increased the likelihood of learning new equivalence classes under the simultaneous protocol. A detailed analysis of the emergent relations test performances showed how pretraining influenced the behavioral processes responsible for equivalence class formation. Method Subjects Fifty-two undergraduate students from Queens College participated in this study, and each student was assigned to one of four groups that differed in terms of pretraining condition. The students were volunteers from Introductory Psychology courses and had no prior experience with

4 72 BUFFINGTON ET AL. the research area. The students received partial course credit for participating in the study. The credit, however, was not contingent upon performance in the experiment. Each student participated in one to two experimental sessions over the course of 1 to 2 weeks, with each session lasting 1-2 hr in length. Apparatus and Stimuli The experiment was conducted on an IBM compatible microcomputer. The stimuli were presented to the subjects on the computer screen. Each subject was required to make all responses by touching keys on the computer keyboard. Both the recording of responses and the presentation of stimuli were controlled by software designed to study equivalence classes. Table 1 Stimuli Used in Each of the Equivalence Classes ---- Condition Stimulus Symbol Stimulus Symbol Class 1 Class 2 3MEM 4MEM LEO HUK POV m A1 B1 C1 01 MEV GUO ZOJ A2 B2 C2... ~~~n~nl1hlh mmm m mm m mmm m mmmmmm : 02 5MEM BAF m 01 E1 3SIM OIJ TUW COH Class 3 X3 Y3 Z3 VIF KUY XOL Class 4 Note. In the 4MEM and 5MEM conditions, the stimuli used as A, B, and C were the same as those listed under the 3MEM condition. The stimuli used to form equivalence classes under the simultaneous protocol are listed to the right of the 3SIM designator in the leftmost column. The stimuli used in the formation of each of the equivalence classes are presented in Table 1 with a corresponding symbolic letter/number notation (Fields, Verhave, & Fath, 1984). All stimuli were composed of ASCII characters and were 3 mm wide and 5 mm high on the computer screen. The classes used in pretraining were designated as Classes 1 and 2. Nonsense words, referred to symbolically as A, B, and C, were the stimuli used in the 3-member classes established in pretraining. When 4-member classes were formed in pretraining, the same stimuli served as the A, B, and C members of the classes with lines made up of contiguous strings of ASCII 176 characters (::n serving as the 0 members of each class. The line in Class 1 was 1 character in length and the line in Class 2 was 25 characters in length. When 5-member X4 Y4 Z4

5 PRETRAINING ENHANCES EQUIVALENCE 73 classes were formed in pretraining, the same stimuli served as the A, B, and C members of the classes with new nonsense syllables serving as the D stimuli and lines made up of contiguous strings of ASCII 176 characters C:::) serving as the E members of each class. The classes established under the simultaneous procedure were designated Classes 3 and 4. The nonsense words that constituted the stimuli in the simultaneously trained classes differed from those used in pretraining, and they were referred to symbolically as X, Y, and Z. Procedure Trial structure, contingencies, and responses within a trial. Each trial began when the words "Press Enter" appeared on the screen. After the subject pressed enter, a sample stimulus was displayed in the upper portion of the computer screen. The subject was then required to press the space bar to display the comparison stimuli on the screen. All stimuli were displayed in a triangular pattern, with the sample stimulus at the vertex of the triangle, and each comparison stimulus at the corners of the base of the triangle. During each trial, the sample stimulus and the positive comparison stimulus (Co+) were from the same class, whereas the negative Table 2 Order of Training and Testing Trials Cond Operation Relation % Feedback Sa Co+ Co- No. Trials --- 3MEM Train AB Baseline 100 A1 B1 B2 8 Train AB Baseline 75,25,0 A1 B1 B2 4 Test BA Symmetry 0 B1 A1 A2 8 A1 B1 B2 8 Train BC Baseline 100 A1 B1 B2 2 B1 C1 C2 6 Train BC Baseline 75,25,0 A1 B1 B2 2 " " " B1 C1 C2 2 Test CB Symmetry 0 A1 B1 B2 4 B1 C1 C2 4 C1 B1 B2 8 Test BAiCB Symmetry 0 A1 B1 B2 4 B1 C1 C2 4 B1 A1 A2 4 C1 B1 B2 4 Test AC Transitivity 0 A1 B1 B2 4 B1 C1 C2 4 A1 C1 C2 8 Test CA Equivalence 0 A1 B1 B2 4 B1 C1 C2 4 C1 A1 A2 8 Mixed Test BL,S, T, E 0 A1 B1 B2 4 B1 C1 C2 4 B1 A1 A2 2 C1 B1 B2 2 A1 C1 C2 2 C1 A1 A2 2

6 74 BUFFINGTON ET AL. 4MEM Train CO Baseline 100 A1 B1 B2 2 B1 C1 C2 2 C Train CO Baseline 75,25,0 A1 B1 B2 2 B1 C1 C2 2 C Mixed S, T, E 0 B1 A1 A2 2 C1 B1 B2 2 A1 C1 C2 2 C1 A1 A C1 C2 6 B A B1 B A1 A2 6 5MEM Train OE Baseline 100 A1 B1 B2 2 B1 C1 C2 2 C E1 E2 6 Train OE Baseline 75,25,0 A1 B1 B2 2 B1 C1 C2 2 C E1 E2 2 Mixed Test S, T, E 0 E C1 E1 E E1 E2 2 A1 E1 E2 2 E1 C1 C2 2 E1 B1 B2 2 E1 A1 A2 2 3SIM Train XYIYZ Baseline 100 X3 Y3 Y4 12 Y3 Z3 Z4 12 Train XYIYZ Baseline 75,25,0 X3 Y3 Y4 2 Y3 Z3 Z4 2 Mixed Test BL,S, T, E 100 X3 Y3 Y4 4 Y3 Z3 Z4 4 0 Y3 X3 X4 2 Z3 Y3 Y4 2 X3 Z3 Z4 2 Z3 X3 X4 2 Note. The stimuli used as samples and comparisons in trials for Classes 1 and 3 were represented symbolically. Each row indicates one configuration which contains a sample, a positive, and a negative comparison, all of which were presented together. The stimuli in each configuration were presented the number of times indicated in the column headed "No. Trials." The comparisons in each configuration appear equally often on the left and the right. A parallel set of trials with samples from Classes 2 and 4 were also presented in the experiment, although they were not listed in this Table. The trials for Classes 2 and 4 were presented in the same block as the trials for Classes 1 and 3, respectively. For example, the 3MEN block used for training AB contains (A! B1 B2), (A1 B2 B1), (A2 B2 B1), and (A2 B1 B2) trials. BL, S, T, and E refer to baseline conditional discriminations, symmetry, transitivity, and equivalence probes, respectively.

7 PRETRAINING ENHANCES EQUIVALENCE 75 comparison stimulus (Co-) was from the other class. The subject selected the comparison on the left by pressing the 1 key and selected the comparison on the right by pressing the 2 key. After the subject made a response, a feedback message was displayed on the screen. If the subject selected the Co+, the word "right" appeared on the screen until the subject pressed the R key. If the subject selected the Co-, the word "wrong" appeared on the screen until the subject pressed the W key. During non informative feedback trials, the letter E appeared on the screen after the subject's response and remained there until the subject pressed the E key. The letter E was presented regardless of comparison selection. It merely indicates the END of a trial. In addition, the E key was selected because it is between the Rand W keys on a QWERTY keyboard. Trial block structure and contingencies. Each phase of training and testing consisted of a block of trials. The type and number of trials presented in each block are listed in Table 2. The trials in each block were presented in random order without replacement. Each Co+ and Co- appeared equally often on the left and right sides of the computer screen within each block. During the initial phases of training, each trial in a block was presented with informative feedback. Each block was repeated until all trials within the block occasioned class-consistent comparison selections; this performance was defined as the mastery criterion. After the mastery criterion was reached, the percentage of trials in a block that produced informative feedback was reduced from 100% to 75% to 25% and, finally, to 0% across blocks, provided there was no change in the accuracy of responding. If the subject did not meet the mastery criterion within three blocks at a given feedback level, (s)he was returned to the prior level of feedback until 100% accurate responding was achieved. All trials in the test blocks used in pretraining were presented without informative feedback. In the test blocks presented under the simultaneous protocol, the emergent relations trials were presented without informative feedback, and all baseline review trials occasioned informative feedback. Start-up training. All subjects were taught the keyboard skills required to progress through each trial in the experiment. To facilitate this process, semantically related English words were used as samples and comparisons along with five instructional prompts. The prompts were deleted in a serial manner as training progressed (Fields et ai., 1990). Pre tra ining. Subjects in different groups received different levels of pretraining prior to the simultaneous training and testing of two 3-member equivalence classes. The four levels of pretraining were (a) NONE, (b) 3MEM, (c) 4MEM, and (d) 5MEM. NONE: Subjects in this group did not receive any pretraining prior to learning Classes 3 and 4 under the simultaneous protocol. 3MEM: Subjects in this group learned the two 3-member classes (Classes 1 and 2) in pretraining. The classes were established using the simple-to-complex protocol (Adams et ai., 1993). Subjects first learned two AS relations. After subjects mastered AS, symmetry for the trained relations was assessed with SA probes. Then, SC was trained for each class, and

8 76 BUFFINGTON ET AL. symmetry for these trained relations was assessed with CB tests. After a combined review of BA and CB symmetry trials, transitivity was tested with AC probes. Following the tests for transitivity, equivalence was assessed with CA probes. Finally, a mixed review of all baseline, symmetrical, transitive, and equivalence relations was conducted. 4MEM: Subjects in this condition learned 4-member classes in pretraining. Initially 3-member classes were trained with the simple-tocomplex procedure described in the preceding paragraph. After the 3- member classes were established, a third relation (CD) was trained. Once CD was learned, a mixed block of emergent relations tests was presented to assess expansion of the class size to four members. This block contained trials assessing symmetry (BA, CB, DC), transitivity (AC, BD, AD), and equivalence (CA, DB, DA). The block was repeated until all emergent relations tests were passed, or for a maximum of six blocks. 5MEM: Subjects in this condition learned 5-member classes in pretraining. After learning two 4-member equivalence classes using the 4MEM procedure described above, a fourth baseline conditional relation (DE) was trained. After DE was learned, a mixed block of emergent relations was presented to assess the expansion of class size to five members. Trials assessing symmetry (ED), transitivity (CE, BE, and AE), and equivalence (EC, EB, and EA) were presented in this block. The block was repeated until all emergent relations tests were passed, or for a maximum of six blocks. Simultaneous training and testing: 3SIM. After pretraining was completed, Classes 3 and 4 were established using simultaneous training and testing. First, the conditional relations XY and YZ were introduced in a single training block. Each trial type was presented an equal number of times within the block. Trials were presented in random order without replacement. The training block was repeated until the mastery criterion was met. During the initial phases of training, each trial in a block was presented with informative feedback. Each block was repeated until all trials within the block occasioned class-consistent comparison selections; this performance was defined as the mastery criterion. After the mastery criterion was reached, the percentage of trials in a block that produced informative feedback was reduced from 100% to 75% to 25% and, finally, to 0% across trials. Following this training, the baseline conditional relations (XY and YZ), as well as the symmetry (YX and ZV), transitivity (XZ), and equivalence (ZX) probes were presented in a single test block. Trials were presented in random order without replacement. The 3SIM test block was repeated until criterion was met or for a maximum of five blocks. During this test block, informative feedback was presented for selections made on each baseline trial. Noninformative feedback was presented for selections made on each emergent relations test trial. Results Class formation in pre tra ining. Table 3 lists the number of blocks needed to learn the baseline relations and to pass the emergent

9 PRETRAINING ENHANCES EQUIVALENCE 77 Table 3 Number of Presentations of Each Training and Emergent Relations Test Block in Each Phase of the Experiment for All Subjects Classes Established During Pretraining -- 3MEM 4MEM 5MEM 3SIM BA Group Subj AB BA BC CB CB AC CA 3MIX CD 4MIX DE 4MIX Trn Tst P/F - MIN NONE MEM 316* MEM ** MEM

10 78 BUFFINGTON ET AL. Note. MIN is the minimum number of blocks that could be presented to complete a condition. 3MEM, 4MEM, and 5MEM refer to the number of class members in each class established during pretraining. AB, BC, CD, and DE refer to baseline relations that were directly trained in various portions of pretraining. BA, CB, AC, and CA, were single emergent relations probes presented during the formation of the 3-member classes during pretraining. 3MIX, 4MIX, and 5MIX were the mixed test blocks presented to confirm the emergence of the 3-member classes, or assess the expansion of class size to four members and five members, respectively. The "Trn" and "Tst" columns listed under the 3SIM heading designate the training block and the testing block presented under the simultaneous protocol. A + or - under the "P/F" column indicates whether the subject did (+) or did not (-) form classes under the SIM protocol. * The data for Subject 316 in the 3MEM group were excluded from the statistical analysis because of a variation in experimental procedure that reduced the number of programmed training blocks and would have inappropriately reduced the group average. ** For Subject 377, the 12 blocks listed for the AC test were caused by an experimenter error which involved the presentation of additional baseline and transitivity test blocks. relations test for subjects in each phase of pretraining. The row labeled MIN lists the minimum number of blocks that could be presented in each phase of the experiment. Data for subjects in the NONE, 3MEM, 4MEM, and SMEM pretraining conditions are shown in the successive horizontal segments of Table 3. The baseline relations were learned rapidly in all phases of pretraining: within a few blocks of the minimum scheduled for presentation. In addition, the majority of subjects passed the serially presented emergent relations tests and the mixed review tests quite rapidly: in one or two blocks. There was also a low level of intersubject variability in performances within and across groups for a given type of relation. Baseline relations and emergent relations performances under 3SIM conditions. During the training component of the simultaneous protocol, all subjects in each group learned the baseline conditional relations (see third from last column in Table 3). Pretraining, therefore, did not influence the percentage of subjects who learned the baseline conditional relations under simultaneous training conditions. Figure 1 shows how pretraining influenced the mean number of blocks needed to learn the baseline relations and the intersubject variability within each group. The number of blocks needed to learn the baseline relations under simultaneous training conditions was an inverse function of pretraining class size. Compared to no pretraining, the largest class size (SMEM) used in pretraining resulted in a 42% reduction in the number of blocks needed to learn baseline relations. The differences in the mean number of blocks to acquisition across all experimental conditions were statistically significant, as demonstrated by an independent groups ANOVA, F(3, 34) = , p < When all pairwise comparisons were analyzed using the Hayter Fisher Least Significant Difference procedure, the mean number of blocks needed to learn the baseline relations in the NONE group differed significantly from the mean number of blocks needed to learn the baseline relations in the 4MEM and SMEM groups. Other differences were not significant. Intersubject variability in the number of blocks needed to learn the baseline relations during simultaneous training was also an inverse function of pretraining. This functional relation was statistically

11 PRETRAINING ENHANCES EQUIVALENCE RVER AGE NUMBER OF BLOCKS I--,.- I-- l- 10 ~ rl- I-... l- 5 f- I- r- - -f- f0- r- o I I I J NONE 3MEM 4MEM 5MEM PRETRAINING Figure 1. The mean number of blocks required to learn the 3SIM baseline conditional discriminations plotted as a function of pretraining condition. Plus and minus one standard error of the mean for each group is represented by the "I" beam at the top of each bar. Table 4 Correlations Between Baseline Acquisition and Class Formation TRN-P/F TRN-BLKS to Pass PBS P CC P NONE MEM MEM SMEM NA NA Note. Point-biserial (PBS) correlations between number of blocks needed to learn the baseline conditional discriminations in the training component of the simultaneous protocol and relative frequency of forming classes for each pretraining condition. Correlation coefficients (CC) between number of blocks needed to learn the baseline relations during the training component of the simultaneous protocol and number of blocks to pass the emergent relations tests in the 3SIM protocol for each pretraining condition. The values in the p columns indicate the exact probabilities of obtaining the listed coefficients due to chance.

12 80 BUFFINGTON ET AL. significant, as measured by the Brown-Forsythe procedure, F(3, 34) = , P < Compared to no pretraining, the largest class size used in pretraining resulted in an 82% reduction in variability. All subjects learned the baseline relations during simultaneous training. Only some of these subjects, however, formed equivalence classes within the five test blocks presented in the simultaneous protocol. A comparison of the individual subject data in the third from last and the last columns of Table 3 showed that passing of the emergent relations tests was not predicted by the number of blocks needed to learn the baseline relations, as indicated by the point-biserial correlations listed on the left-hand side of Table 4. For those subjects who passed the tests and formed classes, there was no correlation between speed of learning the baseline relations and the number of blocks needed to pass the emergent relations tests, as indicated by the correlations listed on the right-hand side of Table 4. Thus, neither the likelihood of equivalence class formation nor the rate of passing the emergent relations tests under the simultaneous protocol were influenced by rate of learning the baseline conditional discriminations. 100 ~ - % SUBJECTS WHO PRSS 3S1M TESTS l- r-- 75 r- - I ~ r 25 I-- r r-- "'" 1 I I o 1 NONE 3MEM 4MEM 5MEM PRETRR1NING Figure 2. The percentage of subjects who passed the 381M emergent relations tests plotted as a function of pretraining condition. -

13 PRETRAINING ENHANCES EQUIVALENCE 81 Effects of pretraining on emergence of new equivalence classes. Figure 2 shows how pretraining influenced the percentage of subjects who passed the emergent relations tests within five blocks and formed Classes 3 and 4 under the simultaneous protocol (data for Figure 2 were obtained from the last two columns of Table 3). Only 58% of the subjects with no pretraining (NONE group) passed the 3SIM emergent relations tests. (Data were presented for only 12 subjects because the data for one subject were lost). There was a minimal increase in the percentage of subjects who passed the 3SIM emergent relations test in the 3MEM group. A large increase in the percentage of subjects who passed the 3SIM emergent relations tests was observed in the 4MEM group. Finally, all of the subjects with 5MEM pretraining passed the 3SIM emergent relations % SUBJECTS WHO ENTER THE 1st OR 3rd TEST BLOCK RND THEN PRSS THE 3SIM TEST BLOCKS 1 OR 2 BLOCKS 3 TO 5 N N 3 4 PRETRRINING 5 Figure 3. The left side of the figure portrays the percentage of subjects who passed the emergent relations tests in the first two 3SIM test blocks, plotted as a function of pretraining condition. Percentages were calculated using all subjects in a group. The right side of the figure contains data for those subjects who passed the emergent relations tests in the last three 3SIM test blocks. Percentages were calculated using those subjects who failed to pass the tests in the first two blocks. tests. This trend was statistically significant (Chi Square = 8.284, P < 0.04). The major enhancement occurred after 4MEM pretraining; yield increased from 62% after 3MEM pretraining to 85% after 4MEM pretraining. Some subjects formed Classes 3 and 4 rapidly and others formed classes more slowly. Rapid class formation is defined by passing the emergent relations test within the first two test blocks presented in the simultaneous protocol. Slow class formation is defined by passing of the

14 82 BUFFINGTON ET AL. emergent relations test blocks in three to five presentations of the test blocks. Figure 3 illustrates the effects of pretraining on both rapid and slow class formation. The left side of Figure 3 illustrates how pretraining influenced the percentage of subjects who formed equivalence classes rapidly under the simultaneous protocol. This calculation was based on all subjects in a group. Approximately half of the subjects who received no pretraining or pretraining of 3-member classes formed the 3SIM classes within two blocks. Pretraining of 4- or 5-member classes resulted in a 20% increase in the percentage of those subjects who formed the 3SIM classes. This trend, however, did not reach statistical significance (chi square = 2.42, P = 0.12). The right side of Figure 3 illustrates how pretraining influenced the percentage of subjects who formed equivalence classes slowly under the simultaneous protocol. This calculation was based on all of the subjects in a group who did not pass the tests by the second test block, and thus entered the third test block. Classes were formed with repeated testing under the 3SIM condition by only 17% of the subjects who received either no pretraining or pretraining of 3-member classes. In both of these conditions, if the tests were not passed within two blocks, it was very unlikely that repeated testing with up to 5 blocks would result in class formation. In contrast, after the establishment of 4-member classes in pretraining there was a doubling in the percentage of subjects who formed 3-member classes under 3SIM protocol. Finally, after the pretraining of 5-member classes, all subjects who required at least three presentations of the test block formed classes under the 3SIM protocol. This difference was statistically significant, as measured with a chisquare test that compared the 5MEM data with the combined data for the other three conditions (chi square = 8.67, P < 0.003). Analysis of Relational Control Measurement of relational control. For some subjects, performances in the 3SIM test blocks were not always class consistent. This provided the opportunity to analyze relational responding occasioned by the baseline conditional discriminations as well as the emergent relations probes presented under the simultaneous protocol. The traditional method for assessing relational stimulus control is to compute the percentage of trials in a session that are consistent with the experimenter-defined classes. This measure is sufficient when percentage values approach 100 % correct. In contrast, however, when intermediate percentages are obtained, there are many forms of stimulus control that can produce the same intermediate value (Dube, MCilvane, & Green, 1992; Iversen, 1993; Mackay, 1991; Sidman, 1980, 1992). Thus, overall percentage correct is an inadequate measure of intermediate levels of conditional stimulus control (Sidman, 1952). An instance of relational responding that is indicative of an experimenter-defined class has occurred when a comparison from one nominal class is always selected in the presence of a sample drawn from

15 PRETRAINING ENHANCES EQUIVALENCE 83 Table 5 Set of Trials Needed to Measure One Instance of Relational Control Consistent with Experimenter-Defined Classes --- Sample Stimulus Left Side Comparison Right Side Comparison X3 X3* Y4 X3 Y4 Y3* X4 Y3 Y4* X4 Y4* Y4 Note. The asterisk indicates the positive comparison on each trial. the same nominal class, and is never selected in the presence of samples that are not members of the same nominal class (Dinsmoor, 1995a, 1995b; Fields et ai., 1995; Mackay, 1991; Sidman, 1978, 1980, 1992; Sidman et ai., 1985). When a conditional discrimination format is used, an instance of relational responding can be assessed by measurement of performances on more than one trial. When two-choice conditional discrimination trials are used, the minimum number of trials needed to assess relational responding is a group of four trials such as those shown in Table 5. The four trials contain stimuli from each of two potential classes. Two of the stimuli are used as samples. Each sample has the same letter designation and is drawn from a different class (X3 and X4). Each sample stimulus is presented twice. In addition, the same two comparison stimuli are presented on all four trials (Y3 and Y4). For each sample, each comparison appears once on the left and once on the right (X31Y3 Y 4 and X31Y 4 Y3). The set of four such trials is called a behavioral kernel (Fields et ai., 1995). One instance of relational responding that is indicative of experimenter-defined classes has occurred when all four trials in a kernel occasion the selection of comparisons that are consistent with the experimenter-defined classes. An instance of relational responding has not occurred on that kernel if at least one of the trials did not occasion the selection of a comparison that was consistent with the experimenterdefined classes. The kernel, then, provides a quantal, or an all-or-none measure of relational responding, just as the depression of a pigeon key measures the occurrence of one instance of an operant (Sidman, 1986). Intermediate levels of relational control are indexed by determining the percentage of a given type of kernel that produces relational responding. Thus, if eight symmetry kernels are presented and five produce performances that are relational, relational responding would have been occasioned by 62.5% of the symmetry kernels. Other quantally based measures of stimulus control have been considered by Bickel and Etzel (1985), Migler (1964), and Migler and Millenson (1969). Table 6 provides a detailed description of the performances occasioned by the baseline, symmetry, and 1-node kernels presented in each 3SIM test block. The subjects in a column are listed in terms of number of emergent relations test blocks presented during the 3SIM test. Those who formed classes are listed above the dogleg that breaks

16 84 BUFFINGTON ET AL. Table 6 Percentage of Baseline and Emergent Relations Kernels That Occasion Relational Responding in Each 381M Test Block for 8ubjects in Each Pretraining Condition NONE 3M EM Rei Block Rei Block 8ubj BLD NDE Type ubj BLD NDE Type B B N 100 1N B B N 100 1N B B & 100 1N 100 1N B B N 100 1N x B B N N x B B N N B B N N x B x B N N x x B x B N N x x B x x B N N x x B x x B N N o x B x B N N x B N

17 PRETRAINING ENHANCES EQUIVALENCE 85 NONE 3M EM Rei Block Rei Block Subj BLD NDE Type Subj BLD NDE Type B B1 100 S 100 S 100 1N 100 1N B B1 100 S 100 S 100 1N 100 1N B B1 100 S 100 S 100 1N 100 1N B B1 100 S 100 S 100 1N 100 1N B B1 100 S 100 S 100 1N 100 1N B B1 100 S 100 S 100 1N 100 1N B B1 100 S 100 S 100 1N 100 1N B B S 100 S N 100 1N B x B S 100 S N 100 1N x B x B S S N N x x B x B S S N N x x B x x B S S N N x B x x B S S N N Note. The 3SIM test block contained 4 baseline kernels, 2 symmetry kernels, and 2 1-node kernels, as determined from Table 2. "ReI. Type" indicates the type of relation that is being assessed. An ''x'' in the BLD column indicates a subject who showed disruption of baseline responding. An ''X' in the NDE column indicates a subject who showed nodal distance effects.

18 86 BUFFINGTON ET AL. each column, and those who did not are listed below the dogleg. Each data point in Table 6 indicates the percentage of kernels of a given type that occasioned relational responding. Data from the XY and YZ kernels were combined to assess relational control by the baseline relations. Data from the YX and ZY kernels were combined to assess relational control by all symmetry or zero-node emergent relations. Finally, data from the XZ and ZX kernels were combined to assess relational control exerted by 1-node emergent relations used to assess transitivity and equivalence. Because each type of kernel was presented twice in a test block, 0, 50, or 100% of the kernels can occasion relational responding. Disruption of baseline performances. At the end of 381M training, relational responding was occasioned by the baseline kernels for the subjects in all conditions. With the introduction of the 381M emergent relations probes, the relational responding occasioned by the baseline kernels was disrupted for some subjects. Disruption was defined as at least one block in which at least one baseline kernel did not occasion relational responding. Disruption of baseline performance for a subject is indicated with an "x" in the BLD column of Table 6. Nodal distance effects. The stimuli in the symmetry kernels are separated by zero nodes. The stimuli in the transitivity and equivalence kernels are separated by one node. The effects of nodal distance for individual subjects can be assessed by comparing the relational responding occasioned by these kernels in individual test blocks. To assess the effects of nodal distance, either the symmetry and 1-node kernels must produce different levels of relational responding which would show nodal distance effects, or they must occasion equal but intermediate levels of relational responding which would show no effect of nodal distance (Fields, Adams, Verhave, & Newman, 1990). Blocks in which relational responding is evoked by all symmetry and 1-node kernels were excluded because the measurement ceiling prevented the observation of performance differences. In addition, blocks in which no relational responding was evoked by both kernels were excluded because the absence of relational responding has many possible interpretations. According to these criteria, 71 of the 126 test blocks which had been presented to the subjects during the simultaneous protocol could be used to analyze the effects of nodal distance. Relational responding consistent with the experimenter-defined classes was evoked by a higher percentage of symmetry kernels than 1-node kernels in 56 of the 71 blocks. The reverse was true in 13 blocks. The symmetry and the 1- node kernels produced equal levels of relational responding in the remaining 2 blocks. Thus, test performance was an inverse function of nodal distance in 77% of these blocks, an effect that was statistically significant (binomial p < ). When the data in Table 6 were viewed by subject, 24 subjects showed intermediate test performances in at least one emergent relations test block. For 16 of these subjects (identified by the "x" in the NDE column in Table 6), a higher proportion of symmetry kernels consistently occasioned relational responding than

19 PRETRAINING ENHANCES EQUIVALENCE PERCENTRGE OF KERNELS THRT EVOKE RELRTIONRL RESPONDINC IN THE FIRST TWO TEST BLOCKS IN THE SIMULTANEOUS PROTOCOL O~----~ ~------~~~------~~--~ NONE 3MEM 4MEM 5MEM PRETRRININC Figure 4. The percentage of kernels presented in the first two 3SIM test blocks that occasioned relational responding, plotted as a function of type of kernel and pretraining condition. The open bars represent data for baseline kernels, the hashed bars represent data for symmetry kernels, and the filled bars represent data for the 1-node kernels. Each data point is averaged across blocks and subjects in a particular pretraining condition. did the 1-node kernels. The block and subject analyses, then, showed that emergent relations test performances were an inverse function of nodal distance. Effects of pretraining. The effects of pretraining on the behavioral processes involved in the formation of classes under the simultaneous protocol were assessed by analyzing the relational responding occasioned by the baseline, symmetry, and 1-node kernels presented in the first two test blocks of the simultaneous protocol for each pretraining condition. A block was included in the analysis if at least one type of kernel in a block did not always occasion relational responding. Blocks in which all kernels occasioned relational responding were excluded from the analysis because no performance differences could be measured; this ceiling effect precluded the assessment of nodal distance effects. These effects were indexed by averaging the performances evoked by a given type of kernel across subjects in the same pretraining condition in the first two test blocks of the simultaneous protocol. The averages were obtained from the data in Table 6 and are presented in Figure 4. Each pretraining condition contains three bars. The performances occasioned by the baseline kernels, O-node or symmetry kernels, and 1-node kernels are illustrated by the open, striped, and filled bars, respectively.

20 88 BUFFINGTON ET AL. For subjects who received no pretraining, prior to testing, all baseline kernels occasioned relational responding. When testing began in the simultaneous protocol, only 89% of the baseline kernels evoked relational responding. A smaller percentage of symmetry kernels produced relational responding than did the baseline kernels. Most notably, relational responding was evoked by a very small percentage of the 1-node kernels. The disruption of relational responding occasioned by the baseline kernels was not ameliorated by any of the pretraining conditions. This was shown by the unsystematic pattern of responding occasioned by the baseline kernels across pretraining conditions. Pretraining of 3-member classes did not improve the performances occasioned by the symmetry kernels when compared to the symmetry performances observed in the NONE group. In contrast, pretraining of 4- and 5-member classes produced a modest increase in the relational responding occasioned by the symmetry kernels; these performances approximated those produced by the baseline kernels. Finally, relational responding by the 1-node kernels remained very low and similar to that observed during the NONE condition after pretraining of 3- or 4-member classes. In contrast, relational responding evoked by the 1-node kernels increased dramatically after the establishment of 5-member classes in pretraining. To summarize, introduction of the 381M test resulted in the disruption of relational responding by baseline kernels. Pretraining did not influence level of disruption. Pretraining, however, produced a major increase in relational responding by kernels that contained stimuli separated by one node, and a moderate increase in the relational responding by symmetry kernels, which contained stimuli separated by zero nodes. Discussion Five issues will be considered in this section: (a) equivalence class formation during pretraining, (b) the effects of nodal distance seen during the simultaneous protocol, (c) the effects of pretraining on the enhancement of forming new classes under the simultaneous protocol, (d) the behavioral processes that are influenced by pretraining and their involvement with the enhancement effect, and (e) possible confounds and experimental parameters that could have also influenced the results of the experiment. Equivalence class formation during pre training. When 3-member classes were established during pretraining, the probes for each emergent relation were presented serially. Most of the emergent relations probes occasioned class-consistent performances as soon as they were introduced; the performances indicated the immediate emergence of class-consistent responding. Because trial blocks were either not repeated or were repeated very few times, there was neither necessity nor opportunity for performances to be "trained" by trial repetition. Thus, the inadvertent training of conditional discriminative

21 PRETRAINING ENHANCES EQUIVALENCE 89 performances that were not indicative of class formation would appear to be unlikely. It is far more plausible to conclude that the test performances indicate the emergence of 3-member equivalence classes under the simple-to-complex protocol. After establishing the 3-member classes, class size was expanded to 4-members for subjects in the 4MEM and 5MEM groups. The expansion of class size was assessed with a mixed test block that included symmetry, transitivity, and equivalence probes all of which were presented in a random order. Class-consistent performances occurred as soon as the test block was introduced, thereby demonstrating expansion of class size from three to four members. For subjects in the 5MEM group, a further expansion of class size from four to five members was assessed with a mixed test block that included symmetry, transitivity, and equivalence probes that contained the E1 and E2 stimuli, all of which were presented in a random order. Class-consistent performances occurred as soon as the test blocks were introduced, thereby demonstrating expansion of class size from four to five members. Because class-consistent performances were occasioned by all probes as soon as the mixed probe blocks were introduced, it is not possible to account for the data in terms of learning through repeated presentation of probes. It is also very unlikely that the obtained test performances could be accounted for by subject-defined unreinforced conditional selection of comparison stimuli (Saunders, Saunders, Kirby, & Spradlin, 1988). The 4- member test block contained five new emergent relations probes (see Table 2). The binomial probability of all of these probes occasioning performances consistent with the experimenter-defined classes would be equal to (0.5) 5, or p < The 5-member test block contained seven new emergent relations (see Table 2); therefore, the binomial probability of all new probes occasioning performances consistent with the experimenter defined classes would be equal to (0.5)7, or p < Thus, it is likely that the test performances indicated expansions in the size of already established equivalence classes. The emergence of equivalence classes can be confirmed by a post class formation demonstration of the transfer of a behavioral function acquired by one class member to the other class members. The expansion of class size from three to four members can be viewed as such a transfer test (Fields, Adams, & Verhave, 1993). Each D stimulus was linked by training to a C stimulus from one of the putative 3-member classes. After training, the presentation of the D stimuli occasioned the selection of the B and A stimuli from the same putative class. The demonstration of expansion of class size, then, confirmed the interchangeablity of the A, Band C stimuli, and thus their status as an equivalence class. Finally, the formation of 3-member classes and the incremental expansion of class size reported in this experiment replicated the results reported by Adams et ai., (1993) and Fields et al. (1991). The outcomes of both studies were similar in terms of reliability of class formation, expansion

22 90 BUFFINGTON ET AL. of class size, speed of learning baseline relations, speed of passing emergent relations tests, and the levels of intersubject variability in the number of blocks needed to pass tests and to learn the baseline relations. Nodal distance effects under the simultaneous protocol. Each 3SIM test block included symmetry, transitivity, and equivalence probes. The stimuli in the symmetry probes are separated from each other by 0 nodes, whereas the stimuli in the transitivity and equivalence probes are separated from each other by one node. Thus, the test kernels are differentiated by nodal distance. When comparisons were possible, most performances occasioned by the symmetry and 1-node kernels were an inverse function of nodal distance. Although similar effects were described by others (Dube, Green, & Serna, 1993; Fields et ai., 1990; Kennedy, 1991; Kennedy, Itkonen, & Lindquist, 1994; Lazar et ai., 1984; Sidman et ai., 1985; Wulfert & Hayes, 1988), in all of these studies, nodal distance was confounded with training order or number of stimulus presentations (Fields et ai., 1995; Fields, Adams, & Verhave, 1993). Because of the concurrent training of all baseline conditional discriminations in the present study, these variables were not confounded with nodal distance in the current experiment; thus, the effects of nodal distance cannot be accounted for in terms of variables other than nodal distance. These effects were seen for subjects who eventually passed the tests and formed classes, and for subjects who did not form classes. Such data replicate similar findings reported by Fields et al. (1995). Thus, these data suggest that each relation between stimuli in different conditional discriminations is determined by the training cluster (the specific set of conditional discriminations that are directly trained as the baselines of a potential equivalence class), and is an inverse function of nodal distance (Fields & Verhave, 1987), and develops independent of the formation of equivalence classes (Fields, Adams, & Verhave, 1993; Fields, Adams, Newman, & Verhave, 1992; Fields et ai., 1995). Effects of pretraining on equivalence class formation under the simultaneous protocol. All subjects formed 3-member classes under the simple-to-complex protocol. There were no systematic differences in the performances for subjects in each of the groups. Therefore, any performance differences observed during the subsequent phases of the experiment could not be attributed to individual differences in the subjects assigned to each experimental group. The data presented in Figure 1 showed that pretraining of equivalence classes influenced the rate of learning baseline relations under simultaneous training conditions. The enhancement effect could have been a function of the number of previously learned conditional discriminations, regardless of linkage between them and/or the number of previously learned equivalence classes. In either case, the data provide an example of learning set (Harlow, 1949) in a context that is more complex than that typically used to study learning set. The data in Figure 2 showed that the percentage of subjects who formed equivalence classes under the simultaneous protocol was a

23 PRETRAINING ENHANCES EQUIVALENCE 91 direct function of pretraining. This overall functional relation, however, reflected the combined effects of pretraining on the immediate and delayed emergence of new equivalence classes (Sidman, 1994; Sidman et ai., 1985). Immediate emergence was defined as responding in a class consistent manner within the first two presentations of the 3SIM test block. Delayed emergence was defined as responding in a class consistent manner in the third to fifth presentation of the 3SIM test block. The pretraining of 3-member classes did not enhance immediate or delayed emergence of new classes under the simultaneous protocol. The pretraining of 4- or 5-member classes both produced the same modest increase in the percentage of subjects who showed the immediate emergence of new classes under the simultaneous protocol. In contrast, as the size of the pretrained classes increased from four to five members, the percentage of subjects who showed the delayed emergence of equivalence classes under the simultaneous protocol increased in an accelerated fashion. Thus, both immediate and delayed emergence of equivalence classes were direct functions of the pretraining of other equivalence classes. Effects of pretraining on behavioral processes. The test blocks included in the simultaneous protocol contained baseline, symmetry, and 1-node kernels. A detailed analysis of the performances occasioned by these kernels can be used to identify the effects of pretraining on each of these behavioral processes. When no pretraining was used, the introduction of the 3SIM emergent relations test block was correlated with a sudden disruption of relational responding. This decline occurred from the 100% level that had been maintained during the training. Such a disruption of baseline performances with the concurrent introduction of symmetry, transitivity, and equivalence probes appears to be a general phenomenon; a similar finding was reported by Fields et al. (1995) during study of the formation of 3-node 5-member equivalence classes using the SIM protocol. Amount of pretraining did not reduce the disruption of baseline performances in the initial 3SIM test blocks and did not facilitate the recovery of disrupted baseline performances. The reinforcement of baseline performances during emergent relations test blocks may have played a role in the disruption of conditional discriminative performances. Its effect will be investigated in subsequent research. When the performances in the initial test blocks are considered, pretraining of 3-member classes did not produce any changes in the relational responding occasioned by symmetry kernels. In contrast, the prior establishment of 4- or 5-member classes produced equal and modest increases in the relational responding evoked by new symmetry kernels. Pretraining of 3- and 4-member classes did not influence relational responding by 1-node kernels. In marked contrast, pretrained 5-member classes produced a very large increase in the relational responding evoked by new 1-node kernels. When delayed emergence is considered, pretraining with 4-member classes, and to a much greater

24 92 BUFFINGTON ET AL. extent with 5-member classes, increased the likelihood of relational responding occasioned by all emergent relations. Pretraining, then, influenced the formation of new equivalence classes under the simultaneous protocol by enhancing the performances occasioned by the symmetry and 1-node kernels. To summarize, pretraining does not influence the learning of new conditional discriminations, their resistance to disruption, or their susceptibility to resurgence. Thus, a constant proportion of the low yields observed under the simultaneous protocol can account for nonrecoverable disruptions of conditional discriminative responding occasioned by the baseline relations. Pretraining does, however, enhance the immediate emergence of relational control by new symmetry, transitivity, and equivalence kernels. In addition, the pretraining of the larger classes supported the emergence of relational responding by symmetry and 1- node kernels with repeated presentations of such trials. Pretraining, then, would appear to establish two stimulus control repertoires that generalized to the simultaneous protocol. One enhances the linking of remotely related stimuli, and the other enhances the emergence of bidirectional linkages between stimuli in a trained relation. Parameters that influence the enhancement effect. The prior establishment of one set of equivalence classes significantly increased the likelihood of learning new equivalence classes under the simultaneous protocol. That enhancement effect appeared to be a direct function of the size of the classes formed in pretraining. The number of stimuli in the pretrained classes, however, was correlated with three other parameters of the pretrained classes. As the size of the pretrained class increased from three to five members, the number of nodes in a pretrained class increased from 1 to 3, the number of conditional relations that were trained increased from 2 to 4 for each pretrained class, and the combined number of symmetry, transitivity, and equivalence probes in a pretrained class increased from 4 to 16. In addition, two procedures that were held constant across experimental groups may have also influenced overall outcome. These are the use of the simple-to-complex protocol itself and the use of differential feedback for responding on the baseline relations included in the test block in the simultaneous protocol. Additional research will be needed to isolate the effects of these variables on the enhancement of new equivalence classes formed using the simultaneous protocol. Summary. Relatively few college students can form equivalence classes when all baseline relations are trained concurrently and all emergent relations probes are presented thereafter and on a concurrent basis. The likelihood of equivalence class formation under such conditions increases after the prior establishment of other equivalence classes. Increasing the size of the pretrained classes (a) increased the speed of learning baseline relations, (b) decreased the intersubject variability in learning baseline relations, (c) increased the percentage of subjects who showed the immediate emergence of new classes, and (d)

25 PRETRAINING ENHANCES EQUIVALENCE 93 increased the percentage of subjects who showed the delayed emergence of new classes. Pretraining increased yield by enhancing the emergence of relations between remotely linked stimuli. These effects could have been a function of the size of the pretained classes, the number of nodes in the pretrained classes, and/or number of conditional relations that were established in pretraining. The identification of the reported effects was made possible by the use of a training and testing protocol that produced low yields when used alone. Such a preparation, then, is a valuable behavioral preparation for exploring the variables that influence equivalence class formation by normally functioning adults. References ADAMS, B. J., FIELDS, L., & VERHAVE, T. (1993). Effects of test order on intersubject variability during equivalence class formation. The Psychological Record, 43, BICKEL, W. K., & ETZEL, B. C. (1985). The quantal nature of controlling stimulusresponse relations as measured by tests of stimulus generalization. Journal of the Experimental Analysis of Behavior, 44, BUSH, K. M., SIDMAN, M., & DE ROSE, T. (1989). Contextual control of emergent equivalence relations. Journal of the Experimental Analysis of Behavior, 51, CATANIA, A. C. (1992). Learning (pp ). Englewood Cliffs, NJ: Prentice Hall. DEVANY, J. M., HAYES, S. C., & NELSON, R. O. (1986). Equivalence class formation in language-able and language-disabled children. Journal of the Experimental Analysis of Behavior, 46, DINSMOOR, J. A. (1995a) Stimulus control: Part I. The Behavior Analyst, 18, DINSMOOR, J. A. (1995b) Stimulus control: Part II. The Behavior Analyst, 18, DUBE, W. V., GREEN, G., & SERNA, R. W. (1993). Auditory successive conditional discrimination and auditory stimulus equivalence classes. Journal of the Experimental Analysis of Behavior, 59, DUBE, W. V., MCILVANE, W. J., & GREEN, G. (1992). An analysis of generalized matching-to-sample test procedures. The Psychological Record, 42, FIELDS, L., ADAMS, B. J., NEWMAN, S., & VERHAVE, T. (1992). Interactions among emergent relations during equivalence class formation. The Quarterly Journal of Experimental Psychology, 45, FIELDS, L., ADAMS, B. J., & VERHAVE, T (1993). The effects of equivalence class structure on test performances. The Psychological Record, 43, FIELDS, L., ADAMS, B. J., VERHAVE, T, & NEWMAN, S. (1990). The effects of nodality on the formation of equivalence classes. Journal of the Experimental Analysis of Behavior, 53, FIELDS, L., ADAMS, B. J., VERHAVE, T, & NEWMAN, S. (1993). Are stimuli in equivalence classes equally related to each other? The Psychological Record, 43,

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