PROBABILITY OF EQUIVALENCE FORMATION: FAMILIAR STIMULI AND TRAINING SEQUENCE. ERIK ARNTZEN Akershus University College

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1 The Psychological Record, 2004, 54, PROBABILITY OF EQUIVALENCE FORMATION: FAMILIAR STIMULI AND TRAINING SEQUENCE ERIK ARNTZEN Akershus University College The present study was conducted to show how responding in accord with equivalence relations changes as a function of position of familiar stimuli, pictures, and with the use of nonsense syllables in an MTO-training structure. Fifty college students were tested for responding in accord with equivalence in an AB, CB, DB, and EB training structure. The results showed that familiar stimuli presented as A-stimuli gave the highest yields (10 of 10 participants), whereas introducing the pictures at the end of the training (as E-stimuli) gave lower yields (5 of 10), and using nonsense syllables gave even lower yields (4 of 10). In addition, when all stimuli were Greek/Arabic letters only, 3 of 10 participants responded in accord with equivalence. When familiar stimuli were A-stimuli, but with a requirement of using keys on the keyboard, only 4 of 10 subjects responded in accord with equivalence. Furthermore, there was a high correlation between responding in accord with equivalence and reports of class consistent naming. Reaction time data also showed a typical pattern, in which there was an increase from training to test and a decrease during testing. Stimulus equivalence is defined as stimulus substitution (Green & Saunders, 1998) and stimulus equivalence has been seen as an important contribution in behavior analysis (e.g., Sidman, 1994) even if some researchers recently have been quite critical of its role (e.g., Barnes-Holmes, Hayes, & Roche, 2001; Tonneau, 2001). Furthermore, several authors have pointed to a relation between equivalence and verbal behavior (e.g., Catania, 1980, 1986; Pear, 2001) and to the "symbolic nature" of verbal behavior (Catania, 1986; Devany, Hayes, & Nelson, 1986). Thus, the emergence of equivalence classes has been found only in verbally competent organisms (Dugdale & Lowe, 2000) and Some results were presented in a paper at the ABA convention in Washington DC, May Thanks to Per Holth and Lanny Fields for comments on parts of an earlier draft and two anonymous reviewers for comments and suggestions during the reviewing process. I also thank Dag Erik Eilertsen for statistical assistance. Correspondence and reprint requests should be addressed to Erik Amtzen, Akershus University College, PO Box 372, 1301 Sandvika, Norway. ( erik.arntzen@equivalence.net).

2 276 ARNTZEN responding in accord with equivalence or symmetry has not been shown in nonhumans (e.g., Dugdale & Lowe, 2000; Hayes, 1989). In contrast, stimulus equivalence has been found consistently in human beings tested with a variety of stimulus materials (e.g., Arntzen & Holth, 2000a; Bentall, Jones, & Dickins, 1999; Devany, Hayes, & Nelson, 1986; Fields et ai., 2000; Randell & Remington, 1999; Roche, Barnes Holmes, Smeets, Barnes-Holmes, & McGeady, 2000; Sidman & Tailby, 1982) and in different modalities (e.g., Annett & Leslie, 1995; Belanich & Fields, 1999; Hayes, Tilley, & Hayes, 1988; O'Leary & Bush, 1996); it has been shown both in normal adults and children (e.g., Lipkins, Hayes, & Hayes, 1993; Pi lgrim, Chambers, & Galizio, 1995) and in persons with mental disabilities (e.g., Saunders & Spradlin, 1993). Some studies have shown that equivalence classes are not so easily formed as was first assumed, especially after a linear series training structure (Arntzen & Holth, 1997, 2000a, 2000b). The use of familiar stimulus material appears to affect the probability of equivalence outcome, as was shown in Haith and Arntzen (1998), where responding in accord with equivalence increased when the nodal stimulus was a nameable picture as opposed to a condition in which all stimuli were Greek letters. Furthermore, in another study (Arntzen & Holth, 2000b), the purpose was to investigate the likelihood that equivalence class formation would vary as a function of class size and number of classes. In Experiment 1, the equivalence outcome as a function of class size or class number was studied in a linear series training structure. Because class size and nodal number are confounded in a linear series training structure, a second experiment using a many-to-one structure (Experiment 2), in which pictures constituted the node, was included to separate these variables. The results from the experiments showed that the equivalence outcome decreased as a function of both number of classes and nodes, but that the decrease related to nodes was much more pronounced. The number of familiar stimuli should not be considered a critical factor in explaining the differences in equivalence outcome following either increasing number of classes or class size, as the equivalence outcome was about the same for the participants following the many-to-one training structure as for the participants following the linear series structure when number of classes was expanded. It is possible that the effects are due to familiar stimuli functioning as nodal stimuli or to the order in which the familiar stimuli are introduced. The use of nonsense syllables as stimuli in matching-to-sample tasks has been prominent in a number of studies (e.g., Cullinan, Barnes Holmes, & Smeets, 2000; Fields et ai., 2000; Fields, Verhave, & Fath, 1984). One could question whether the use of such stimuli facilitates naming to a greater extent than does the use of Greek, Cyrillic, or Arabic letters. The role of such stimuli (nonsense syllables) may be that the stimuli could facilitate responding in accord with equivalence. Sidman and co-workers raised the question of whether the establishment of equivalence classes requires verbal mediation. It was

3 FAMILIAR STIMULI AND TRAINING SEQUENCE 277 argued that if stimulus equivalence requires response mediation by naming, the organism should give a common name to all stimuli belonging to the same equivalence class (Sidman, Kirk, & Willson-Morris, 1985; Sidman & Tailby, 1982; Sidman, Willson-Morris, & Kirk, 1986). Sidman et al. (1986) administered oral naming tests and found that the participants did not give consistent names to the relevant visual or auditory stimuli. Several studies have shown that stimulus equivalence does not require mediation by vocal naming and suggested that the establishment of equivalent classes of stimuli does not depend on mediating responses (Lazar, Davis-Lang, & Sanchez, 1984; Sidman, Cresson, & Willson-Morris, 1974; Sidman & Tailby, 1982). However, as indicated by Sidman et al. (1986), homogeneous or common naming does not seem to occur regularly in human participants during tests of equivalence relations, and furthermore, even if naming has been shown to facilitate the emergence of equivalence (Eikeseth & Smith, 1992), there are still no conclusive data showing that naming is a necessary condition for the emergence of equivalence (e.g., Randell & Remington, 1999) and that reinforcement contingencies generate the equivalence relations (Sidman, 2000). However, forms of response mediation other than common vocal naming should be considered. Mcintire, Cleary, and Thompson (1987) argued that they had demonstrated equivalence performance in monkeys following the establishment of homogeneous "naming" in conditional discrimination tasks. The homogeneous "naming" consisted of a distinct pattern of responding under the control of each stimulus in a threemember class. Both Hayes (1989) and Saunders (1989) criticized the claim of Mcintire et al. (1987) that they had demonstrated equivalence in their monkeys, because all components of all tested relations were directly trained and, hence, no relations were derived. As suggested by Mcintire et al. (1987, 1989), heterogeneous verbal sequences may constitute another, equally plausible, mechanism for the apparent emergence of complex relations. If the establishment of stimulus equivalence were interpretable solely in terms of well-established operant principles, the equivalence could be based on bi-directional behavior chains, not necessarily verbal or overt. Some researchers have reported correlations between responding in accord with equivalence and verbal reports (Lane & Critchfield, 1996; Wulfert, Dougher, & Greenway, 1991). However, researchers specialized in the experimental analysis of human behavior have shown relatively little interest in data generated through self-reports (Lane & Critchfield, 1998), and the extent to which human operant performance is mediated verbally remains an important theoretical question (e.g., Horne & Lowe, 1996). The present study investigated differential probabilities of equivalence class formation across five conditions with different stimulus materials following an MTO or CaN training structure (AB, CB, DB, and EB) designed to produce three 5-member classes: (1) Only Greek and Arabic letters, (2) Greek, but A-stimuli replaced by pictures, (3) same as (2), but with the training sequence reversed so that the pictures were

4 278 ARNTZEN introduced at the end (as E-stimuli), (4) Greek stimuli, but with A-stimuli replaced by nonsense syllables, and (5) same as (2), but with presses on the keyboard rather than touches on the touch screen. Verbal reports were conducted in postexperimental interviews to investigate potential collateral classes of behavior, such as homogenous (common) or heteroge;lneous (individual) naming. In addition, the participants were also asked to categorize the stimuli. Furthermore, reaction time data were collected in order to study variables influencing the rapidity of the emergence of equivalence. Method Participants Fifty university or college students served as participants and were recruited from psychology and behavior analysis classes. All participants volunteered to take part in the experiment, and none were familiar with the equivalence paradigm. The participants were assigned to five experimental groups and exposed to a different set of stimuli, as shown in Tables 1 and 2. Apparatus The apparatus was the same as that described in Amtzen and Holth (1997). Procedure Stimulus material. Visual stimuli were displayed on the monitor. Greek and Arabic letters and nonsense syllables were used in the experiment (see Table 1). Furthermore, the pictures used as A-stimuli or E-stimuli are shown in Table 2. The presentation of the sample stimulus was always in the left-hand key (7 x 7 cm) of the monitor. Six comparison stimulus keys (4 x 4 cm) were arranged in two columns and three rows on the right-hand side of the monitor. Table 1 Stimuli Used in the Experiment Classes Class members A I!l ts Pictures LEO HUK POV B I) q> C 'l' S e o ~ cr E r ~ Pictures

5 FAMILIAR STIMULI AND TRAINING SEQUENCE 279 Table 2 Pictures Used as A- or E-stimuli ' -- :.-' ~~ #-~ ~-r'\ -1 ~. 'i...,t!. ~ t. "/I:_ 1 <. General information to the participants. When asked to join the experiment, the participants were told that the experiment was within the field of learning and involved tasks presented on a computer with a touch screen. 1 They were also told that the experiment would last approximately 60 min, depending on how rapidly and correctly they responded. Instruction. The experimenter gave the following instruction: "When you touch the left-hand stimulus, one or more stimuli will appear on the right. A touch on the correct stimulus will be followed by music from the cassette player, while incorrect responses will be followed by the blanking of the screen for 5 s before a stimulus in the left-hand key is presented again. Each part of the training requires a certain number of correct responses before proceeding to the next part. The training will be followed by tests, in which there will be no different consequences for correct and incorrect responses - no music and no blank screen." Training and test. Each trial started with the presentation of a sample stimulus. A touch on the sample stimulus was followed by the presentation of comparison stimuli in the keys on the right side of the monitor. The sample remained until a comparison stimulus was touched. To minimize the number of errors made during initial training, the conditional discrimination tasks were introduced step by step: When a sample stimulus appeared for the first time during training, a touch on the sample stimulus was followed by the presentation of the correct comparison stimulus only. Next, each correct comparison was presented together with one incorrect comparison, then with the second incorrect comparison, and this was gradually increased until all comparison stimuli were presented. The comparison stimuli were randomly positioned from trial to trial. The training was organized into different training parts: (1) AB, (2) CB, (3) mix AB and CB, (4) DB, (5) mix AB, CB, and DB, (6) EB, and (7) mix AB, CB, DB, and EB. The separate training blocks AB, BC, DB, and EB required the successive correct completion of the randomly intermixed seven trials of each type before mixing. The mixing parts included a total successive completion of 24 correct trials before testing. The equivalence tests were organized as two consecutive blocks with four of each trial type in each test block. 1 For 10 subjects, a response of pressing different numbers on the keyboard was required instead of a touching on the touch screen.

6 280 ARNTZEN The experimental conditions for the 10 groups are summarized in Table 3. For Group 1, all stimuli were Greek and Arabic letters. For Group 2, all stimuli were Greek letters, but with A-stimuli replaced by pictures. For Group 3, stimuli were the same as Group 2, but with E-stimuli replaced by pictures, so that the pictures were introduced at the end. For Group 4, all stimuli were Greek letters, but with A-stimuli replaced by nonsense syllables. For Group 5, due to an apparatus breakdown, 10 subjects were given the same stimulus material as subjects in Group 1, but instead of responses on the touch screen the subjects had to press different numbers on the keyboard. Table 3 Experimental Procedure Trained relations: A "Equivalence" tests: EA, ED, EC, DA, DC, and CA Group 1: All stimuli were Greek and Arabic letters Group 2: Pictures as A-stimuli Group 3: Pictures as E-stimuli Group 4: Consonant - vowel - consonant nonsense syllables as A-stimuli Group 5: All stimuli were Greek and Arabic letters, but the response required was a touch on the keyboard.

7 FAMILIAR STIMULI AND TRAINING SEQUENCE 281 Dependent measures. Key presses on the touch screen in front of the monitor or key presses on the keyboard, reaction times, and the number of trials to criterion were recorded. An index of equivalence was calculated for each subject on each test half by dividing the number of "correct" responses by the total number of trials during each test phase. Equivalence was defined as an index of 0.9 or 1.0. Postexperimental interview. After all matching tasks were completed, the oral-naming test was administrated to determine if participants could name the stimuli. All A-, B-, C-, D-, and E-stimuli were printed on two sheets of paper and the participants were asked to write down beside each stimulus the name that helped them solve the task. No feedback was given as to the adequacy of the label. At the end, the participants were given printouts of all the stimuli and asked to categorize the stimuli. No feedback was given. Statistical analyses. A ttest for differences in proportions was used to test for differences in responding according to equivalence for the five groups. For statistical analyses of reaction time, data were organized in six trial blocks-each block comprised one baseline measure and one test measure. Each measure was computed as a mean of five trials. Data were analyzed by a 2 x 6 x 5 repeated measures ANOVA with two repeated factors (test block and test condition) and one group factor (type of stimulus). For statistical analyses of equivalence and correspondence to verbal reports a chi-square test (Pearson) was used. Reliability check. All records on the postexperimental interview were also scored by another person. There was 100% agreement between the two raters. Results2 The results showed that when pictures served as A-stimuli, 10 of 10 participants responded in accord with equivalence, but when pictures were trained at the end (as E-stimuli), 5 of 10 participants responded in accord with equivalence (see Figure 1). Furthermore, when all stimuli were Greek and Arabic letters, only 3 of 10 participants responded in accord with equivalence. In addition, when nonsense syllables were A stimuli or when touches on the keyboard were required as responses, 4 of 10 participants responded in accord with equivalence. The group of subjects who were exposed to pictures as A-stimuli was significantly different from all other groups. Table 4 shows p-values from the test for differences in proportions. Reaction time to comparison stimuli during the five last training trials was between 0.9 and 2 seconds for all participants independent of groups (see Figure 2). For all participants there was an increase in reaction time in the first five test trials and a decrease during the test. This decrease in 2Summaries of responding in accord with equivalence, reaction times, and verbal reports for participants in each group are presented. A copy of the individual data may be obtained from the author upon request.

8 282 ARNTZEN ~ = :a ~ = u Q c:.~ = "'-... CIS ~ '".- - = = CIS ~ C'.s-.c :e u.~ - CIS'C c: Q Q U... U ~ CIS..c E!.- = Z = All Greek and Arabic Pictures as A-simuli Pictures as E-stimuli Nonsense Keyboard syllables as requirement A-stimuli Figure 1. The figure shows the percentage of subjects in each group responding in accord with equivalence. Table 4 Groups All t and p Values from Test for Differences in Proportions for Group with Pictures as A-StimUli Compared to Other Groups All Greek and Arabic letters Pictures as E-stimuli Nonsense syllables as A-stimUli Pictures as A-stimuli, but with keyboard as the response option tvalue 3,43 2, 45 2,94 2, 94 pvalue p < P < P < P < reaction time was reflected in a statistically significant main effect of test block, F(5, 205) = 17.93, P <.001. The main effect of test condition was statistically significant, F(1, 41) = , P <.001, indicating an overall effect of presenting a new stimulus. This effect gradually decreased during the experiment, and the test block by test condition interaction was significant, F(5, 205) = 38.02, P <.001. This interaction effect varied across stimulus type, resulting in a statistically significant block by condition by stimulus type interaction, F(20, 205) = 3.48, P <.001.There was no significant difference in reaction times between the subjects who responded in accord with equivalence and those who did not. Verbal reports for participants in the Greek/Arabic-letters group showed that only 3 participants both gave common class names and responded in accord with equivalence (see Table 5). Furthermore, the 7 other participants in the group either gave inconsistent common names or gave some common class names and some individual names, and they did not respond in accord with equivalence. For participants in the

9 FAMILIAR STIMULI AND TRAINING SEQUENCE 283 T, EA EC ED DA DC CA IGroup 1 I Trials Figure 2. The figure shows mean reaction times to comparison stimuli for subjects in the different groups. In each graph the last five training trials are followed by the first five test trials and the last five test trials. The uppermost panel shows mean reaction times to comparison stimuli for subjects with Greek and Arabic letters. The second panel from the top shows mean reaction times to comparison stimuli for subjects with Greek letters and pictures as A-stimuli. The third panel from the top shows mean reaction times to comparison stimuli for subjects with Greek letters and pictures as E-stimuli. The fourth panel from the top shows mean reaction times to comparison stimuli for subjects with Greek letters and nonsense syllables as A-stimuli. The lowermost panel shows mean reaction times to comparison stimuli for subjects with Greek letters and pictures as A-stimuli, but with a requirement of using the keyboard as the response option.

10 284 ARNTZEN pictures-as-a-stimuli group, 7 of 10 participants either gave common names or individual names to all stimuli, 2 participants gave individual names to some of the stimuli and a common name to some of the stimuli, 1 participant did not report any systematic naming, and all 10 participants responded in accord with equivalence. For participants in the group with pictures as E-stimuli, 5 of 10 participants reported individual names to all 15 stimuli and also responded in accord with equivalence. The remaining 5 participants gave some common names and some individual names, and none of them responded in accord with equivalence. For participants in the nonsense-syllables group, 3 of 10 participants reported common names to stimuli in the three groups and 1 participant reported individual names, and all 4 responded in accord with equivalence. The other 6 participants reported inconsistent class or individual names and responded in accord with equivalence. For participants in the group with the keyboard requirement, 4 of 10 participants reported common names according to the experimenter-defined classes and also responded in accord with equivalence. The 6 remaining participants reported inconsistent class or individual names and failed to respond in accord with equivalence. Statistical analyses showed a significant difference between reported naming for participants in Group 2 (pictures as A-stimuli) and Group 3 (pictures as E-stimuli) and reported naming for participants in the other three groups, X 2 (12, N = 50) = 29.47, P <.05. Furthermore, there was a statistically significant difference between participants responding in accord with equivalence and reporting naming and not reporting systematic use of names, X2 (1, N = 50) = 26.82, P <.001. As shown in Table 6, 25 participants who responded in accord with equ ivalence also categorized the stimuli in the three experimenterdefined groups, while 23 participants who did not respond in accord with equivalence did not categorize the stimuli in the three experimenterdefined groups. The chi-square test showed that there was a significant difference between participants responding in accord with equivalence and categorizing the stimuli in three experimenter-defined groups and those who made no such categorizations, X2 (1, N = 50) = 42.31, P <.001. Different forms of reported naming Table 5 Summary of Verbal Reports for Each Group Groups 2 3 No systematical naming reported 5 1 Common names reported 3 5 Individual names reported 2 5 Both common and individual names reported Note. Boldfaced numbers indicate how many participants responded in accord with equivalence in each group

11 FAMILIAR STIMULI AND TRAINING SEQUENCE 285 Table 6 Number of Participants Categorizing Stimuli in Three Experimenter-Defined Groups as Function of Responding in Accord with Equivalence Categorizing stimuli in the three experimenter-defined classes No Yes Not responding in accord with equivalence Discussion Responding in accord with equivalence The probability of equivalence class formation was higher when some of the stimuli were ''familiar,'' nameable pictures, than when all stimuli were Greek and Arabic letters, or nonsense syllables. Furthermore, the probability of equivalence class formation was higher when ''familiar'' stimuli were introduced in the first task, than when they were introduced later, and when a keyboard response as opposed to touch screen response was used, equivalence outcomes were lower. The lowest yield of equivalence outcome was found in the group with Greek letters and nonsense syllables as A stimuli. Because the results showed that the rate of responding in accord with equivalence was not influenced by introducing pictures early in the training (as A-stimuli)-which is in agreement with an earlier study in which pictures were the nodal stimulus (B-stimuli) (Arntzen & Holth, 2000b), whereas introducing pictures or nameable stimuli later in the conditional discrimination training (E-stimuli) produced significant lower yields-the critical variable seems to be when the picture is introduced and not whether the picture or namable stimulus is the node. The markedly higher probability of equivalence class formation when stimuli were nameable pictures may indicate that differential responding to different samples and comparison stimuli facilitates partitioning of the all-inclusive class. According to Sidman's analysis (e.g., Sidman, 1994, 2000), then, only the common reinforcer has to drop out of the allinclusive class to allow partitioning of the stimulus set into the three defined equivalence classes. It may be easier to merge stimuli into existing equivalence classes than to establish new classes, and it can be argued that nameable stimuli have already entered into at least one equivalence class based on their respective names (Saunders, Saunders, Kirkby, & Spradlin, 1988). Thus, when the pictures are introduced at the end in the training, the rate of responding in accord with equivalence is reduced. This may be because other forms of stimulus control have been established that are not compatible with picture naming. Furthermore, all 4 participants in the group with nonsense syllables who did not respond in accord with equivalence failed on the tests in which both sample and comparison stimuli were Greek letters. This may be an effect of blocking. According to Randell and Remington (1999), findings indicate that participants' verbal behavior can either facilitate or hinder class formation, depending

12 286 ARNTZEN on how congruent employed naming strategies are with the experimenter-designed classes, which govern positive test outcomes. Another type of argument may be that the different yields in the group pictures-as-a-stimuli vs. the group pictures-as-e-stimuli are correlated both with the early and late introduction of the familiar stimuli and with the number of reinforcers occasioned by them. According to this, in the present procedure the minimum number of separate AB, CB, DB, and EB training trials required was identical. However, because the training was organized into different training parts: (1) AB, (2) CB, (3) mix AB and CB, (4) DB, (5) mix AB, CB, and DB, (6) EB, and (7) mix AB, CB, DB, and EB, the minimum number of AB trials could be 18 more trials than the minimum number of EB trials. On balance, the results showed no difference in the number of trials needed to reach criterion during mixing of AB, CB, DB, and EB trials for participants in the two groups. Moreover, the participants in the pictures-as-e-stimuli group did not fail more often on EA-test trials than on the other types of test trials. Therefore, it is more probable that the differences in equivalence outcome in the group pictures-as-a-stimuli vs. the group pictures-as-e-stimuli are correlated with the early and late introduction of the familiar stimuli and not with the number of reinforcers occasioned by them. As Sidman (1994) has argued the stimuli used in the matching-tosample tasks to test for equivalence relations have been arbitrary stimuli that clearly have no meaning to the participants. One study used sample stimuli that the participants could pronounce and found that responding in accord with equivalence varied as function of pronounceability (Mandell & Sheen, 1994). However, nonsense syllables could function as familiar or nameable stimuli, as they are relatively easy to pronounce. The results from the present experiment with nonsense syllables as A-stimuli showed that there was no difference compared to conditions in which all stimuli were Greek or Arabic letters. In the present study, when keyboard presses were used as the response option the number of participants responding in accord with equivalence was significantly lower than when presses on the touch screen were used. Accordingly, de Rose (1996) referred to a study with college students who were trained in a series of two-choice conditional discriminations. They used two response topographies; response selections by touching keys on a keyboard or clicking on a mouse. They found that the participants in the group using a keyboard gave lower yields of equivalence than did participants in the group using a mouse. They argued that procedural variations could affect the probability of select or reject relations during the baseline conditions. Furthermore, they argued that a response topography involving the participant moving the cursor via the mouse increases the probability of observing the S+, and therefore increases the likelihood of a select relation. This is quite similar to the present experiment in which the participants responded by touching the stimuli directly, therefore increasing the probability of observing the correct comparison. This sort of stimulus control selection

13 FAMILIAR STIMULI AND TRAINING SEQUENCE 287 behavior will be decreased for the participants using the keyboard. Another explanation could be connected to verbal behavior. The participants in the group with the keyboard option who did not respond in accord with equivalence reported either common names that were inconsistent class names or very few names. It could be that the numeric keys used on the keyboard interrupted the naming of stimuli. In his 1996 study, de Rose argued that "When baseline conditional discriminations are visual-visual, and the stimuli are arbitrary, baseline relations do not provide a 'name' for the stimuli" (p. 269). It is not clear why this should be an argument for participants not generating their own stimulus names. Naming may occur when stimuli are familiar (Stromer & Mackay, 1996). The results in the present experiment showed that participants reported a less consistent number of names when all stimuli were Greek/Arabic, or Greek/Arabic and nonsense syllables. Sidman (1994) has argued that spontaneous naming could be related to the length of the intertrial interval used in the experiment, and that longer intertrial intervals (above sec) would encourage talking. In the present experiment the intertrial interval was 2 sec. Some papers reported a longer intertrial interval (20 sec) (Pilgrim, Chambers, & Galizio, 1995), but more research should be done using different intervals. The results also showed that participants reported naming the experimental stimuli, and there was a high correspondence between responding in accord with equivalence and reporting of naming (common or intraverbal). In spite of a high correspondence between test performance and reporting of verbal behavior during the test, there is no way to prove that the two classes of behavior correlate. One is a relevant variable in the production of the second, that is, the two classes do not derive from a common set of variables. Repeated naming of the sample and the correct comparison stimulus could serve the function of mediating behavior in symmetrical responding. Horne and Lowe (1996) described this kind of bidirectional responding as intraverbal naming, in which naming is a bidirectional stimulus-classifying behavior and describes the function of speaker and listener behavior resulting from an individual's history of reinforcement within a behavioral community. Thus, success on equivalence tests is proposed to result from participants' common naming of individual stimuli or by individual stimulus names or intraverbal rules. This is in accord with the results from the current experiment in which the data obtained from postexperimental interviews showed a high correspondence between stimulus naming (common or individual) and responding in accord with equivalence. All participants and only those participants who categorized the stimuli correctly in three classes after the experiment also responded in accord with equivalence. This is in accord with a naming account arguing that naming may be critical for the establishment of arbitrary stimulus classes (Lowe, Horne, Harris, & Randle, 2002). Reaction time data are similar to earlier findings from other papers in which reaction time increases from the last training trials to the first test

14 288 ARNTZEN trials and decreases throughout testing (Arntzen & Holth, 1997, 2000a, 2000b; Holth & Arntzen, 1998, 2000). With regard to testing following a linear series training structure, Fields and Verhave (1987) argued that there is an inverted correlation between nodal number and accuracy, but others have argued that reaction time is sensitive to different variables even when the accuracy of responding is not (Holth & Arntzen, 2000; Spencer & Chase, 1996). An inverted correlation between nodal number and reaction times has been found (e.g., Arntzen & Holth, 2000b; Spencer & Chase, 1996), but in Arntzen and Holth (2000b), tests were organized in separate blocks and the decreasing effect could have been an effect of repeated testing and not of nodal number. However, a recent study by Imam (2001) did not provide support for an effect of nodal number. Concerning the present experiment, which had an MTO training structure, one may ask whether there was an effect of "nodal density," the number of singles linked to a node, and reaction times. The results from the present experiment showed that there was a decrease over repeated testing, except for participants with the keyboard option. As argued elsewhere (e.g., Holth & Arntzen, 1998), the initial increase in reaction times during testing may indicate that stimulus equivalence does not emerge as immediately as suggested by Sidman (1992). Higher reaction times during initial testing may indicate precurrent problem-solving behavior prior to the selection of a comparison stimulus, not as intervening variables,.but as precurrent responses to a problem situation. One could argue that the first appearance of a sample in the test requires a "precurrent" response (Skinner, 1968) as in naming (Horne & Lowe, 1996). In sum, the probability of class formation when A-stimuli were pictures matched that of previous studies with B-stimuli (nodes) as pictures. The likelihood of equivalence was influenced differentially by training sequences: Reversing the training sequence, so that pictures were introduced later, produced lower yields. Replacing the A-stimuli with nonsense syllables instead of pictures produced the lowest likelihood of class formation. Data obtained from postexperimental interviews showed a high correspondence between stimulus naming (common or individual) and responding in accord with equivalence. All participants who categorized the stimuli correctly in three classes after the experiment also responded in accord with equivalence. References ANNEn, J. M., & LESLIE, J. C. (1995). Stimulus classes involving olfactory stimuli. The Psychological Record, 45, ARNTZEN, E., & HOLTH, P. (1997). Probability of stimulus equivalence as a function of training design. The Psychological Record, 47,

15 FAMILIAR STIMULI AND TRAINING SEQUENCE 289 ARNTZEN, E., & HOLTH, P. (2000a). Differential equivalence test outcomes as a function of training structure and class number. The Psychological Record, 50, ARNTZEN, E., & HOLTH, P. (2000b). Probability of stimulus equivalence as a function of class size vs. number of classes. The Psychological Record, 50, BARNES-HOLMES, D., HAYES, S. C., & ROCHE, B. (2001). The (not so) strange death of stimulus equivalence. European Journal of Behavior Analysis, 2, BELANICH, J., & FIELDS, L. (1999). Tactual equivalence class formation and tactual-to-visual cross-modal transfer. The Psychological Record, 49, BENTALL, R. P., JONES, R. M., & DICKINS, D. W. (1999). Errors and response latencies as a function of nodal distance in 5-member equivalence classes. The Psychological Record, 49, CATANIA, A. C. (1980). Autoclitic processes and the structure of behavior. Behaviorism, 8, CATANIA, A. C. (1986). On the difference between verbal and nonverbal behavior. The Analysis of Verbal Behavior, 4, 2-9. CULLINAN, V. A., BARNES-HOLMES, D., & SMEETS, P. M. (2000). A precursor to the relational evaluation procedure: Analyzing stimulus equivalence II. The Psychological Record, 50, DE ROSE, J. C. (1996). Controlling factors in conditional discriminations and tests of equivalence. In 1. R. Zentall & P. M. Smeets (Eds.), Stimulus class formation in humans and animals (pp ). Amsterdam: Elsevier. 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, DUGDALE, N., & LOWE, C. F. (2000). Testing for symmetry in the conditional discriminations of language-trained chimpanzees. Journal of the Experimental Analysis of Behavior, 73, EIKESETH, S., & SMITH, T. (1992). The development of functional and equivalence classes in high-functioning autistic children: The role of naming. Journal of the Experimental Analysis of Behavior, 58, FIELDS, L., VARELAS, A., REEVE, K. F., BELANICH, J., WADHWA, P., DEROSSE, P., & ROSEN, D. (2000). Effects of prior conditional discrimination training, symmetry, transitivity, and equivalence testing on the emergence of new equivalence classes. The Psychological Record, 50, FIELDS, L., & VERHAVE, 1. (1987). The structure of equivalence classes. Journal of the Experimental Analysis of Behavior, 48, FIELDS, L., VERHAVE, 1., & FATH, S. (1984). Stimulus equivalence and transitive associations: A methodological analysis. Journal of the Experimental Analysis of Behavior, 42, GREEN, G., & SAUNDERS, R. R. (1998). Stimulus equivalence. In K. A.Lattal & M. Perone (Eds.), Handbook of research methods in human operant behavior (pp ). New York: Plenum Press. HAYES, L. J., TILLEY, K. L., & HAYES, S. C. (1988). Extending equivalence and membership to gustatory stimuli. The Psychological Record, 38, HAYES, S. C. (1989). Nonhumans have not yet shown stimulus equivalence. Journal of the Experimental Analysis of Behavior, 51, HOLTH, P., & ARNTZEN, E. (1998). Stimulus familiarity and the delayed emergence of stimulus equivalence or consistent nonequivalence. The Psychological Record, 48, HOLTH, P., & ARNTZEN, E. (2000). Reaction times and the emergence of class consistent responding: A case for precurrent responding? The Psychological Record, 50,

16 290 ARNTZEN HORNE, P. J., & LOWE, C. F. (1996). On the origins of naming and other symbolic behavior. Joumal of the Experimental Analysis of Behavior, 65, IMAM, A. A (2001). Speed contingencies, number of stimulus presentations, and the nodality effect in equivalence formation. Joumal of the Experimental Analysis of Behavior, 76, LANE, S. D., & CRITCHFIELD, T. S. (1996). Verbal self-reports of emergent relations in a stimulus equivalence procedure. Joumal of the Experimental Analysis of Behavior, 65, LANE, S. D., & CRITCHFIELD, T. S. (1998). Classifications of vowels and consonants by individuals with moderate and mental retardation: Development of arbitrary relations via matching-to-sample training with compound stimuli. Joumal of Applied Behavior Analysis, 31, LAZAR, R., DAVIS-LANG, D., & SANCHEZ, L. (1984). The formation of visual stimulus equivalence in children. Journal of the Experimental Analysis of Behavior, 41, LlPKINS, R., HAYES, S. C., & HAYES, L. J. (1993). Longitudinal study of the development of derived relations in an infant. Journal of Experimental Child Psychology, 56, LOWE, C. F., HORNE, P. J., HARRIS, F. D. A, & RANDLE, V. R. L. (2002). Naming and categorization in young children: vocal tact training. Journal of the Experimental Analysis of Behavior, 78, MANDELL, C., & SHEEN, V. (1994). Equivalence class formation as a function of the pronounceability of the sample stimulus. Behavioural Processes, 32, MCINTIRE, K. D., CLEARY, J., & THOMPSON, T. (1987). Conditional relations by monkeys: Reflexivity, symmetry, and transitivity. Journal of the Experimental Analysis of Behavior, 47, MCINTIRE, K. D., CLEARY, J., & THOMPSON, T. (1989). Reply to Saunders and to Hayes. Journal of the Experimental Analysis of Behavior, 51, O'LEARY, C. A, & BUSH, K. M. (1996). Stimulus equivalence in the tactile modality. The Psychological Record, 46, PEAR, J. J. (2001). The science of learning. Philadelphia, PA: Psychology Press. PILGRIM, C., CHAMBERS, L., & GALIZIO, M. (1995). Reversal of baseline relations and stimulus equivalence: II. Children. Journal of the Experimental Analysis of Behavior, 63, RANDELL, T., & REMINGTON, B. (1999). Equivalence relations between visual stimuli: The functional role of naming. Journal of the Experimental Analysis of Behavior, 71, ROCHE, B., BARNES-HOLMES, D., SMEETS, P. M., BARNES-HOLMES, Y., & MCGEADY, S. (2000). Contextual control over derived transformation of discriminative and sexual arousal functions. The Psychological Record, 50, SAUNDERS, K. J. (1989). Naming in conditional discrimination and stimulus equivalence. Journal of the Experimental Analysis of Behavior, 51, SAUNDERS, K. J., & SPRADLIN, J. E. (1993). Conditional discrimination in mentally retarded subjects: Programming acquisition and learning set. Journal of the Experimental Analysis of Behavior, 60, SAUNDERS, R. R., SAUNDERS, K. J., KIRKBY, K. C., & SPRADLIN, J. E. (1988). The merger and development of equivalence classes by unreinforced conditional selection of comparison stimuli. Journal of the Experimental Analysis of Behavior, 50, SIDMAN, M. (1992). Equivalence relations: Some basic considerations. In S. C. Hayes & L. J. Hayes (Eds.), Understanding verbal relations (pp ). Reno, NV: Context Press.

17 FAMILIAR STIMULI AND TRAINING SEQUENCE 291 SIDMAN, M. (1994). Equivalence relations and behavior: A research story. Boston: Authors Cooperative. SIDMAN, M. (2000). Equivalence relations and the reinforcement contingency. Journal of the Experimental Analysis of Behavior, 74, SIDMAN, M., CRESSON, 0., & WILLSON-MORRIS, M. (1974). Acquisition of matching to sample via mediated transfer. Journal of the Experimental Analysis of Behavior, 22, SIDMAN, M., KIRK, B., & WILLSON-MORRIS, M. (1985). Six members stimulus classes generated by conditional-discrimination procedures. Journal of the Experimental Analysis of Behavior, 43, SIDMAN, M., & TAILBY, W. (1982). Conditional discrimination vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37, SIDMAN, M., WILLSON-MORRIS, M., & KIRK, B. (1986). Matching-to-sample procedures and the development of equivalence relations: The role of naming. Analysis and Intervention in Developmental Disabilities, 6, SKINNER, B. F. (1968). The technology of teaching. New York: Prentice-Hall, Inc. SPENCER, T. J., & CHASE, P. N. (1996). Speed analysis of stimulus equivalence. Journal of the Experimental Analysis of Behavior, 65, STROMER, R., & MACKAY, H. A. (1996). Naming and the formation of stimulus classes. In T. R. Zentall & P. M. Smeets (Eds.), Stimulus class formation in humans and animals (pp ). Amsterdam: Elsevier. TONNEAU, F. (2001). Equivalence relations: A critical analysis. European Journal of Behavior Analysis, 2, WULFERT, E., DOUGHER, M. J., & GREENWAY, D. E. (1991). Protocol analysis of the correspondence of verbal behavior and equivalence class formation. Journal of the Experimental Analysis of Behavior, 56,

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