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The generalization of emergent relations in equivalence classes: stimulus substitutability.

An equivalence class is a group of stimuli that become related to each other even though they do not resemble one another (Sidman, 1971). The written words CHIEN, DOG, and PERRO and the "picture of a dalmatian" can be established as a 4-member equivalence class by training three pairs, such as CHIEN-DOG, DOG-PERRO, and PERRO-"picture of a dalmatian." A 4-member equivalence class contains 16 stimulus-stimulus relations, three of which are established by training; the remaining 13 stimulus-stimulus pairs are presented as emergent relations tests to assess class formation (Fields, Adams, Newman, & Verhave, 1992; Fields & Verhave, 1987). If a person identifies the relatedness of the stimuli in each test pair, all of the stimuli are related to each other and an equivalence class has been formed (Fields & Verhave, 1987; Fields, Verhave, & Fath, 1984; Sidman & Tailby, 1982). Different test pairs assess reflexivity (e.g., CHIEN-CHIEN), symmetry (e.g., DOG-CHIEN), transitivity (e.g., DOG-"picture of a dalmatian"), and equivalence or symmetry and transitivity in combination (e.g.,"picture of a dalmatian"-CHIEN) (Bush, Sidman, & de Rose, 1989; Fields & Verhave, 1987; Fields et al., 1992). When all of the emergent relations tests are passed, the stimuli function as an equivalence class.

In natural settings, stimuli have a range of variation. Thus, because the picture of a dalmatian is a member of the class of dog-words, would a picture of a beagle become related to DOG, CHIEN, and PERRO? This possibility can be assessed by conducting generalization tests for all emergent relations. For example, a generalization test of equivalence would include the "picture of a beagie" as a sample with CHIEN as a comparison. The likelihood of choosing CHIEN would index the relatedness of the new picture to the class member.

Fields, Reeve, Adams, and Verhave (1991) demonstrated the generalization of the equivalence relation in a 3-member class. In the present study we assessed whether novel stimuli that resemble one member of a class became related to all of the members of a 4-member equivalence class. In addition, the similarity of the different generalization gradients were used to evaluate the substitutability of the stimuli in the equivalence class.

Experiment 1

Method

Subjects

Six undergraduate students at Queens College/CUNY were recruited from an introductory psychology class. No subject had any prior familiarity with the research. Each subject received partial course credit for completing the experiment. Credit did not depend on performance. Completion of the experiment required five or six sessions scheduled over a 3-week period. Each session lasted for 1-1.5 hr.

Apparatus and Stimuli

Experimental stimuli were presented on a monochrome computer monitor. Subjects were seated in a cubicle at a table facing the microcomputer. Responses consisted of touching specific keys on the computer keyboard and were recorded by the computer. The experiment was conducted using software specifically developed for the study equivalence classes.

Each of the two classes was composed of three nonsense syllables and a group of lines. In Class 1, the nonsense syllables were LEQ (A1), HUK (B1), and POV (C1); in Class 2, the nonsense syllables were MEV (A2), GUQ (B2), and ZOJ (C2). The lines were composed of contiguous horizontal strings of ASCII Character 177 ([176]) and were identified according to the number of ASCII characters in the line. Each ([176]) was 3 mm wide and 5 mm high on the computer screen. The D stimuli used for training were designated by class and length. For example, the D stimulus in Class 1 was 1 unit long and was designated D1(1) where the numeral after D identified class membership and the numeral between the parentheses refers to line length. Likewise, the D stimulus in Class 2 was 25 units long and was designated D2(25). The intermediate line lengths between Class 1 and Class 2 were reserved for tests of the generalization of emergent relations; they were designated D(x) where the value of x referred to the length of the line. Class membership was not assigned to these test stimuli.

Procedure

Trial structure, contingencies, and responses within a trial Each trial began when "Press ENTER" appeared on the screen. Pressing the ENTER key removed the message and displayed the sample. Pressing the space bar in the presence of a sample added two comparisons in an isoceles triangular array on the monitor with the sample at the vertex and the comparisons at the corners of the base. Subjects pressed the number "I" key on the top row of the keyboard to choose the comparison on the left or the number "2" key to choose the comparison on the right. Either choice cleared all stimuli from the screen and produced a feedback message. On each trial, the sample (Sa) and positive comparison (Co+) from one class were presented along with a negative comparison (Co-) from the other class. If the Co+ was chosen, "RIGHT" appeared on the screen and remained there until the subject pressed the "R" key. If the Co- was chosen, the message "WRONG" appeared on the screen and remained there until the subject pressed the "W" key. When noninformative feedback was scheduled, the letter "E" appeared as soon as the subject chose either of the comparisons and remained there until the subject pressed the "E" key. After the appropriate response (R, W, or E) the screen was cleared, and the next trial began (see Fields, Adams, Verhave, & Newman, 1990, for further details).

Trial block structure. Each stage of training and testing was conducted in blocks; all trials in a block were presented in a random order without replacement. In training, each block was repeated until all trials occasioned correct responding (100% mastery criterion). Informative feedback was provided after each trial. Thereafter, the percentage of trials that occasioned informative feedback was reduced to 75%, then to 25%, and finally to 0% over successive trial blocks as long as performance within a block was maintained at 1 00% accuracy. In all testing stages, with the exception of Stages 1 1 and 14, test trials were presented along with training trials in a 1:1 ratio of training trials to test trials. In Stages 11 and 14, no training trials were presented. In all testing stages, all choice responses were followed by noninformative feedback.

Pretraining. In Stage 1, subjects were trained to make the appropriate keyboard responses in the presence of each cue used within each trial. This was accomplished by the serial deletion of instructional prompts (Fields, 1980). Stage 1 ended once the stimuli were presented with no prompts and performance exceeded 85% accuracy (14/16 correct trials) during a single block. For the remainder of the experiment, if a keyboard error was made, the instruction relevant to that error reappeared on the screen for that, and the next two trials (see Fields et al., 1990; Fields et al., 1992, for additional details).

In Stages 2-9, different trial blocks were presented to establish two 3-member equivalence classes. The symbolic representation of the stimuli used in each block and the number of trials in each block are listed in Table 1. After training AB, BA symmetry was tested. After training BC, CB symmetry was assessed. Following a maintenance test of BA and CB, AC transitivity was assessed and was followed by a CA equivalence test. Maintenance of the emergent and the trained relations was assessed with AB, BC, BA, CB, AC, and CA tests, demonstrating the formation of 3-member classes. Class size was expanded by training CD. Thereafter, the new emergent relations were assessed on a mixed basis with DC, BD, AD, DB, and DA tests for both classes. In the same block, maintenance of the previously established emergent relations was assessed with BA, CB, AC, and CA tests for both classes. No baseline trials were presented. The mastery criterion in Stages 2-11 was 100% correct for a block.

Generalization Test 1. After two 4-member equivalence classes were established, the generalization of four types of emergent relations was assessed in Stage 12. Each relation was tested in its own block of trials. The trials presented in each block are represented symbolically in Table 2. In all generalization blocks, the samples were line lengths, D(x). The generalization of DD reflexivity contained D1 and D2 as comparisons. The generalization of DC symmetry contained C1 and C2 as comparisons. The generalization of DB equivalence contained B1 and B2 as comparisons. The generalization of DA equivalence contained Al and A2 as comparisons.

In each test block, the samples in four trials (two from each class) were the D stimuli used in training. In the remaining 46 trials, the samples were the intermediate lines D(2) through D(24). Thus, each block contained 50 trials. Each of the intermediate line lengths appeared twice per block as a sample. Each of the four test blocks was presented five times in the order DB, DC, DA, DD, DC, DB, DD, DA, DD, DA, DC, DB, DA, DD, DB, DC, DB, DA, DC, and DD. In total, 20 blocks were presented regardless of performance on any block.

Retraining of CD with five variants of D2. In Stage 13, CD was retrained with D1(1) and five lines in Class 2, D2(21) through D2(25). In Stage 14, control by the emergent relations was assessed with D1(1)-C, D2(x)-C, D1(1)-B, D2(x)-B, D1(1)-A, D2(x)-A, B1-D1(1), B2-D2(x), A1-D1(1), and A2-D2(x) tests, where x corresponds to the values of D used during retraining. Five 20-trial test blocks were used. One variant of D2 appeared in each block. These variants were D2(22), D2(21), D2(25), D2(23), and D2(24) in the first through fifth block, respectively. This order was randomly selected. The mastery criterion in Stages 13 and 14 was 100% correct for a block.

Generalization Test 2. In Stage 15, the generalization of emergent relations was assessed with the presentation of the blocks of trials represented symbolically in Table 2. The generalization test blocks for DC symmetry, and DB equivalence and DA equivalence were identical to those used in Stage 12 with the following changes. These test blocks contained only 42 trials. Each line length from D1(1) through D(20) and one of the five D2 training variants appeared twice per block as a sample. The block for testing the generalization of reflexivity was identical to the one used in Stage 12 except that a different training variant of D2 was used as a comparison in each block. The stimulus D(21) was used in Test Blocks 4, 9, 10, and 18; D2(22) was used in Blocks 5, 12, 14, and 17; D2(23) was used in Blocks 2, 7, 8, and 16; D2(24) was used in Blocks 6, 11, 13, and 20; and D2(25) was used in Blocks 1, 3, 15, and 19. Each of the four test blocks was presented five times in the order DA, DD, DB, DC, DD, DB, DA, DC, DB, DD, DC, DA, DA, DC, DD, DB, DB, DA, DC, and DD. In total, 20 blocks were presented regardless of performance on any block.

Results

Table 3 lists the number of blocks needed to meet criterion for each trained and emergent relation. For most subjects, each trained relation was established quickly. In addition, very few blocks were needed to pass each emergent relations test. Thus, 4-member equivalence classes were established rather quickly for all subjects.

Figure 1 shows the generalization gradients obtained after training with one variant in Class 2, and after retraining with five variants in Class 2. Each graph contains the generalization gradients of reflexivity, symmetry, DB and DA equivalence obtained for one subject after each training condition. On each graph, the vertical lines separate the D stimuli that are class members from the test lines. Each gradient shows the percentage of choice of the Class 2 comparison for each line variant used as a sample. The gradients for choice of the Class-1 comparisons are not shown because they are mirror images of the Class 2 gradients. Gradients obtained after the 1-variant training condition appear in the first and third rows, and those obtained after 5-variant training appear in the second and fourth rows.

For all subjects, when a given variant of D was presented, the D2, C2, B2, and A2 comparisons were chosen with similar likelihoods. Thus, differences in the amount of generalization occasioned by a given variant was not a function of the type of generalization test. All four gradients (reflexivity, symmetry, DB equivalence, and DA equivalence) were tightly clustered. This occurred after training with both one and five Class-2 variants. There were no systematic shifts in the gradients obtained after 1-variant and 5-variant training.

The D stimuli that were members of Class 2 in training almost always occasioned choice of the Class-2 comparisons for all tests. In addition, the test variants that were most similar in length to the D2 class members almost always occasioned choice of the Class-2 comparisons. When line length became increasingly dissimilar to the D stimuli which were members of Class 2 in training, choice of Class-2 comparisons declined systematically to zero.

Discussion

After establishing two 4-member equivalence classes, generalization gradients of reflexivity, symmetry, and equivalence were obtained. Emergent relations tests were interspersed among the generalization test trials.

The emergent relations tests always occasioned the choice of class-related comparisons during the 2,000 generalization test trials. In addition, the gradients were stable throughout testing. These data demonstrate the cohesiveness of the equivalence classes and the generalization of emergent relations in the absence of reinforcement.

During the generalization tests, the variants closest to the Class-2 line occasioned the choice of Class-2 comparisons on almost all test trials. These variants functioned as class members even though they were not used during class formation training. Thus, the range of stimuli that act as class members exceeds the number of stimuli used to establish an equivalence class.

As the disparity between the variant and the D stimuli that were members of Class 2 became even greater, the choice of the Class-2 comparisons declined systematically to zero. The same mechanisms that account for primary generalization gradients (Blough, 1983; Chase, 1983) probably account for the gradients obtained in the present experiment.

All generalization gradients of emergent relations overlapped. For each variant, the D2, C2, B2, and A2 comparisons were chosen with similar likelihoods. The likelihood, however, differed across variants. Thus, all class members were equally related to a given variant, and by implication equally related to each other.

When the number of training variants increased from one to five, the gradients did not become broader. Studies of the formation of classical and probabilistic classes show that the use of multiple positive exemplars in training increases generalization to novel exemplars (Delius & Habers, 1978; Herrnstein, 1984; Wright, Cook, Rivera, Sands, & Delius, 1988). Although the results of the current experiment appear to contradict these findings, the inconsistency can be explained in the following manner. After 1-variant training, Test Line Variants 20-24 occasioned 100% choice of Class-2 comparisons. When these stimuli were used in 5-variant training, the training could not increase performance. Hence, the generalization gradients did not shift. Broader generalization gradients might have been induced by training with line variants that occasioned lower levels of generalization in the 1-variant training condition. Future research will be needed to assess this possibility.

To summarize, stimuli that resemble one member of a 4-member equivalence class become equally related to all class members. Individual differences were seen in the range of variants that occasioned 100% choice of the Class-2 comparison, the slopes of the gradients, and the smoothness of the gradients. These results systematically replicate and extend the findings reported by Fields et al. (1991).

Experiment 2

Experiment 1 showed the essential stability of the generalization gradients of emergent relations. In the present experiment we showed that gradients can be shifted if a subject is provided with a third comparison, the choice of which would indicate that a sample was not related to either class. This third comparison was called the neither comparison.

Method

Subjects

The six subjects in Experiment 1 served as subjects in this experiment.

Apparatus and Stimuli

The apparatus and stimuli from Experiment 1 were again used.

Procedure

Trial block structure. In training, the trial block was repeated with the presentation of informative feedback after each trial until all trials occasioned correct responding (100% mastery criterion). Thereafter, the percentage of trials that occasioned informative feedback was reduced to 75%, then to 25%, and finally to 0% over successive trial blocks as long as performance within a block was 100% accurate. In the testing block, all choice responses were followed by noninformative feedback. All trials differed from the trials in Experiment 1 by the addition of a third comparison, If NEITHER Press 4, which appeared in the center position, slightly below the other two comparisons. It was called the neither comparison.

Training. Stage 16 began with the presentation of the following instructions on the monitor: "You will learn how to use the number 4 key to select a third choice. Please select the comparison stimulus that is related to the sample. If neither comparison is related to the sample, press the number 4 key. Thank you for your cooperation." Two types of AB training trials were used. In all trials, either Al or A2 was the sample. In some of the trials, one B stimulus came from the same class as the sample and the other came from the other class. In these trials, the B stimulus that came from the same class as the sample was the Co+. The other B stimulus and the neither comparison were both Co-s. In the remaining trials, neither of the B stimuli came from the same class as the sample. In these trials, the neither comparison was the Co+ and the B stimuli were Co-s. Thus, the neither comparison served both as Co+ and Co- across trials. The trials used in Stage 16 are listed in Table 4. In Stage 17, the use of the neither comparison by another group of stimuli was tested. Here, two types of BC trials were used. In some trials, the neither comparison was correct; in the other trials, it was incorrect. The trials used in Stage 17 are listed in Table 4. The mastery criterion in Stages 16 and 17 was 100% correct for a block.
Table 4
Symbolic Representation of Stimulus Triads in Stages 16-17
Sa Co+ Co- Co- Presented
Stage 16. Training
A1 B1 B2 NC 4
A2 B2 B1 NC 4
Al NC B2 B2 2
A2 NC B1 B1 2
Stage 17. Testing
B1 C1 C2 NC 4
B2 C2 C1 NC 4
B1 NC C2 C2 2
B2 NC C1 C1 2
Notes. The neither comparison always appeared in the center position, and was
represented by NC. The other comparisons appeared equally often on the left as o
n the
right.


Generalization Test 3. In Stage 18, the generalization test blocks for the four types of emergent relations were identical to those used in Stage 15 of Experiment 1 (Table 2) with the following changes. On each test trial, the third comparison If NEITHER Press 4 appeared on the screen. The stimulus D(21) was used in Test Blocks 4, 5, 8, and 19; D2(22) was used in Blocks 9, 11, 15, and 20, D2(23) was used in Blocks 6,13, 16, and 17; D2(24) was used in Blocks 2, 3, 7, and 18; and D2(25) was used in Blocks 1, 10, 12, and 14. Each of the four test blocks was presented five times in the order DD, DC, DA, DB, DC, DB, DD, DA, DD, DC, DB, DA, DD, DB, DA, DC, DA, DB, DD, and DC. In total, 20 blocks were presented regardless of the performance on any block.

Results

Subjects required four or five blocks to reach the criterion during neither comparison training. Five subjects needed one block to pass the transfer test for the use of the neither comparison. This demonstrated that the choice of the neither comparison was not restricted to the context of the stimuli used in training. One subject (220) was not exposed to the neither comparison transfer test because of experimenter error.

The first and third rows of Figure 2 depict the generalization of emergent relations after training with the neither comparison. These graphs have the same format as the graphs in Figure 1. Each graph is for one subject. The results are similar to those reported in Experiment 1. For each subject, all of the generalization gradients overlapped. The tests which contained the Class-2 line lengths used in training occasioned 100% choice of Class-2 comparisons. A range of test stimuli also occasioned 100% choice of the Class-2 comparisons. With further increases in the disparity between the lengths of the test lines and the Class-2 training lines, the likelihood of choosing the Class-2 comparisons decreased systematically to zero.

The second and fourth rows of Figure 2 contain graphs that show the choice of the neither comparison during the generalization tests. Each neither comparison graph is presented immediately beneath the graph that shows the likelihood of choosing the Class-2 comparison during the corresponding emergent relations test.

The graphs in the top two rows are for the three subjects who used the neither comparison during the generalization test blocks. When a variant always occasioned the choice of the Class-2 comparisons, the neither comparison was not chosen. As the length of the variants decreased even more, the choice of the Class-2 comparisons declined systematically to zero. For that range of variants, the likelihood of choosing the neither comparison increased to a maximum and then declined to zero. This pattern of choosing the neither comparison occurred for all of the generalization tests for these subjects. The graphs on the bottom two rows illustrate the data for the three subjects who rarely chose the neither comparison on the generalization test trials.

Figure 3 compares the generalization gradients for each emergent relation before and after introduction of the neither comparison. Data for each subject are presented in a separate column. The generalization gradients for each type of emergent relation are presented on a separate graph. From top to bottom the graphs show generalization of reflexivity, symmetry, DB equivalence, and DA equivalence, respectively.

Three subjects (219, 220, and 2Z5) used the neither comparison. Their data are presented in columns on the left half of Figure 3. For these subjects, the generalization gradients shifted to the right after the introduction of the neither comparison. This occurred for each type of emergent relations test. This shift shows a decrease in generalization. To illustrate with Subject 220, in the DB equivalence test the sample line length of 14 occasioned the Class-2 comparison 90% of the time when the neither was not available and 10% of the time when the neither was available. The shapes and slopes of the gradients, however, did not change. Three other subjects (221, 223, and 226) did not use the neither comparison. Their data are presented in the three columns on the right half of Figure 3. For most tests, there was no consistent shift in the generalization gradient after the introduction of the neither comparison.

Discussion

Experiment 2 determined whether the availability of an option that enabled a subject to assign a variant to neither of the specified equivalence classes would influence the generalization gradients of emergent relations. For the three subjects who used the neither comparison during the generalization tests, fewer variants occasioned 100% choice of the Class-2 comparisons, and other variants occasioned less frequent choice of the Class-2 comparison. Thus, when the neither comparison was available and chosen, the generalization gradients of emergent relations were narrowed. For each of these subjects, the gradients overlapped, replicating the main effect reported in Experiment 1. The variants that were closest in length to a class member functioned as members of that class. Because the use of the neither comparison reduced the number of such variants, the extension of equivalence classes by generalization was modulated by the use of the neither comparison.

The remaining three subjects did not use the neither comparison during the generalization tests, and the gradients did not shift from those obtained in Experiment 1. These results further illustrate the stability of equivalence classes and their extensions in the absence of maintaining consequences over the course of an additional 2,000 trials.

The use of the neither comparison in the generalization tests by only three of six subjects may be accounted for in the following manner. In the training trials, reinforcement for choosing the neither comparison was predicted by the absence of a relation between the sample and the comparisons, or by the presence of identical comparisons regardless of sample. If the use of the neither comparison came under the control of the identical comparisons, it would not be used in the generalization tests, because identical comparisons do not appear there. This probably occurred with three subjects. If the use of the neither comparison came under the control of a null relation between sample and comparison, it would be used in the generalization tests in which similar stimulus conditions could occur in the test trials. This probably occurred for the other three subjects. Further experimental analysis is needed to evaluate this interpretation.

In summary, Experiment 2 replicated the results observed in Experiment 1 and demonstrated that the generalization gradients of emergent relations can be changed by the use of the neither comparison. The data also demonstrated the stability of equivalence classes in the absence of maintaining operations.

General Discussion

Stimulus substitutability. The stimuli in equivalence classes are assumed to be substitutable or interchangeable (Hayes, 1991; Sidman & Tailby, 1982). Empirical confirmation is inferred from the performances occasioned by the emergent relations tests also used to demonstrate the existence of the classes themselves. The status of substitutability would be substantially strengthened through assessment with tests other than those used to demonstrate class formation.

Post-class-formation transfer tests provide that option. The generalization tests of emergent relations observed in Experiments 1 and 2 provide such a post-class-formation test of substitutability. Because all of the gradients overlapped, the likelihood of choosing all four Class-2 comparisons was equal for a given variant, whereas the degree of generalization differed across variants. These data showed that a variant was equally related to all class members, regardless of gradient breadth or use of the neither comparison. All of the stimuli in the class were substitutable for each other.

Other post-class-formation tests have been used to assess substitutability. For example, de Rose, McIIvane, Dube, Galpin, and Stoddard (1988) measured transfer of discriminative function. Hayes, Kohlenberg, and Hayes (1991) measured transfer of consequential function. Mackay and Sidman (1984), Wulfert and Hayes (1988), and Fields, Adams, Verhave, and Newman (1993) measured the transfer of responding. Finally, Sidman, Wynne, Maguire, and Barnes (1989) measured transfer of contingency reversal. The results of these experiments, however, provided only partial support for substitutability.

Naturally occurring categories. The set of stimuli used in the present experiment are akin to the stimuli that constitute natural categories. Natural categories contain a very wide range of exemplars, some of which do not resemble each other, and others that do resemble each other. For example the natural category (DOG) contains the written words DOG, CHIEN and PERRO, and the pictures of dogs from different breeds. In natural categories, all of the stimuli are related to each other, regardless of physical resemblance. All of the dog-pictures are related to the other dog-pictures, all of the dog-words are related to the other dog-words, and all of the dog-pictures are related to all of the dog-words. This description also characterizes natural kind categories (Gelman, 1988a; 1988b; Gelman & Markman, 1986; 1987). A plausible case can be made that such categories reflect the joint operation of stimulus equivalence and primary generalization (Fields et al., 1991). The stimuli that do not resemble each other and one picture of a dog can become members of an equivalence class by training DOG-CHIEN, CHIEN-PERRO, and Perro-"picture of a dalmatian." The picture thus becomes related to all three words and all three words become related to each other and to the picture. The physical similarities of the pictures account for their relatedness to each other (Herrnstein, 1984; Honig & Stewart, 1988; Hrycenko & Harwood, 1980; Hull, 1920; Medin & Smith, 1984; Neisser & Weene, 1962; Rosch & Mervis, 1975; Smoke, 1932). Finally, the relatedness of all pictures to all words reflects the participation of the "picture of a dalmatian" in both processes. The results of the present experiments, then, support the notion that natural categories, and natural kind categories can be accounted for by the procedures used to establish equivalence classes operating in conjunction with primary generalization. Whether these processes function in an additive manner will have to be evaluated with additional research.

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This research was supported partly by ARI Contract MDA903-90-C-0132, NIBHHD Grant R01-HD21110, and PSC/CUNY Grant 661287. Portions of these data were reported by Barbara J. Adams, Lanny Fields, John Brown, and Thom Verhave in a paper titled, "The relationship between primary generalization and the generalization of equivalence," and Lanny Fields, John Brown, Barbara J. Adams, and Thom Verhave in a paper titled, "The effects of a neither option on the generalization of emergent relations" both of which were presented at the 1991 Annual Conference of the Association for Behavior Analysis, in Atlanta, GA. Reprints can be obtained from Lanny Fields at the College of Staten Island/CUNY, 130 Stuyvesant Place, Staten Island, NY 10301, or from Thom Verhave at Queens College/CUNY, Department of Psychology, Kissena Boulevard, Flushing, NY 11367.
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Author:Fields, Lanny; Adams, Barbara J.; Brown, John L.; Verhave, Thom
Publication:The Psychological Record
Date:Mar 22, 1993
Words:5699
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