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Mutual selection and membership in open-ended classes: variant-to-base and base-to-variant testing.

Behavior that is controlled by categories or classes of stimuli is of great adaptive utility because it enables an individual to respond effectively to the new stimuli that are inevitably encountered in real world settings (Bruner, Goodnow, & Austin, 1965; Medin & Smith, 1984; Rosch & Mervis, 1975; Smith, 1989). Some categories or stimulus classes are said to be open-ended because they contain an infinite number of exemplars that resemble each other (Herrnstein, 1990). Open-ended classes have also been called dimensional, perceptual (Fields & Reeve, 2000), feature-based (Stromer & Mackay, 1997), similarity-based (Wasserman, Keidinger, & Bhatt, 1988), fuzzy (Rosch & Mervis, 1975), ill-defined (Homa & Chambliss, 1985; Homa & Little, 1985), and probabilistic (Medin & Smith, 1984). Because open-ended classes are ubiquitous, it is important to understand the properties that characterize class members. The present experiment investigated an unexplored property of open-ended classes: mutual selectivity.

An open-ended class consists of contiguous stimuli along some continuum, all of which occasion the same response that has been trained to one or a few of the stimuli in that range (Cook, Wright, & Krendrick, 1990; Fields & Reeve, 2001; Goldiamond, 1966; Hull, 1920; Keller & Schoenfeld, 1950; Lea, 1984; Reeve & Fields, 2001; Wasserman et al., 1988; Wright, Cook, Rivera, Sands, & Delius, 1988). This definition implies that all of the stimuli in a class should be substitutable or interchangeable with each other (Goldiamond, 1962; Sidman, 1994). In tests conducted in a conditional discrimination format, interchangeability would be demonstrated by the selection of any class member used as a comparison stimulus in the presence of any member of the same class presented as a sample. That is, all of the stimuli in a class should result in the mutual selection of each other. Mutual selection, then, might be viewed as a defining property of stimuli that are members of open-ended classes. Indeed, mutual selection of phys ically disparate stimuli is the basis for demonstrating the formation of another type of category called an equivalence class (Fields & Verhave, 1987; Sidman, 1994; Sidman & Tailby, 1982).

Of necessity, the evaluation of mutual selectivity requires the presentation of tests conducted in variant-to-base and base-to-variant formats (Reeve & Fields, 2001). These can be illustrated by considering straight lines that vary in length, with the shortest and longest lines serving as the base stimuli for the classes of short and long lines, respectively. When tests are conducted in the variant-to-base format, intermediate length lines called variants are presented as sample stimuli along with the longest and shortest lines (base stimuli) as comparisons. With these tests, the class of long lines would include all variants that occasioned the selection of the long line comparison with the same high likelihood. When the base-to-variant tests are conducted, either the longest or shortest lines (the base stimuli) are presented as samples with the variants as comparisons. In these tests, the class of long lines would include all variants selected with the same high likelihood in the presence of the long line p resented as a sample (Fields & Reeve, 2000).

According to mutual selection, the variants that are members of an open-ended class would be those that occasion the selection of the base stimulus during the variant-to-base tests and are also selected in the presence of the same base stimulus during the base-to-variant tests. In addition, the variants that are not class members would include those variants that were selected in the presence of a given base stimulus in base-to-variant tests but did not occasion the selection of the same base stimulus in variant-to-base tests, or vice versa. Notwithstanding the plausibility of assuming that the stimuli in an open-ended class should have the functional property of mutual selection, data obtained from many studies of stimulus generalization and psychophysics suggest otherwise.

With respect to generalization, generalization among similar stimuli is influenced by variables such as the frequency (Thomas & Vogt, 1983; Thomas, Windell, Williams, & White, 1985), range (Cro11, 1972; Hansen, Tomie, Thomas, & Thomas, 1974; Thomas & Bistey, 1964; Thomas, Strub, & Dickson, 1974), number (Thomas & Bistey, 1964), separation (Thomas, Mood, Morrison, & Wiertelak, 1991), assymetry (Thomas, 1993), frame or reference (Thomas, Lusky, & Morrison, 1992), and stimulus labeling (Galizio & Baron, 1976, 1979) in generalization tests. Because generalization tests are used to assess class width, and test format is a parameter of generalization testing, test format, then, might influence the width of the same nominal open-ended stimulus class. With regard to thresholds, many studies have shown that the quantitative value of a difference threshold is influenced by the psychophysical method used for its determination (Gescheider, 1997; Woodworth, 1938; Woodworth & Schlosberg, 1954). A difference threshold is th e narrowest range of stimuli that occasion the same response. An open-ended class is the broadest range of stimuli that occasion the same response. Thus, the determination of difference thresholds and open-ended class width both involve the measurement of stimulus ranges that occasion common responses. Because procedural variables influence difference thresholds, procedural variables such as test format might influence the range of stimuli that function as members of the same nominal open-ended class. To summarize, the generalization and threshold experiments suggest that the ranges of stimuli that function as members of the same nominal class might vary with test format. If so, not all of the stimuli in the same nominal class would result in the mutual selection of each other. Mutual selection, then, would not be a functional property of the stimuli in open-ended classes.

To date, only variant-to-base tests have been used to identify stimuli that are members of open-ended classes (Fields & Reeve, 2001; Wasserman et al., 1988; Wright et al., 1988;). To our knowledge, base-to-variant tests have never been used to identify the variants that function as members of open-ended classes. Thus, no data are available to determine whether all of the stimuli in an open-ended class actually occasion the mutual selection of each other. In the present experiment, open-ended classes were formed by students with prior exposure to forced choice primary generalization test trials that were conducted in the absence of reinforcement (Reeve & Fields, 2001). This new method for the establishment of open-ended classes differs from traditional induction procedures that involve differential reinforcement of responding in the presence of multiple exemplars (Homa & Little, 1985; Honig & Stewart, 1988; Jitsumori, 1996; Malott & Siddall, 1972; Markle, 1990; Rosch & Mervis, 1975; Tiemann & Markle, 1990; Was serman et al., 1988; Wright et al., 1988). After the induction of open-ended classes, we measured the range of stimuli that functioned as members of the same nominal class using generalization tests conducted in the traditional variant-to-base format and a newly developed base-to-variant format. In a second experiment we measured the discriminability of the stimuli along the domain to determine whether the class consisted of stimuli that were discriminable from each other.

Experiment 1

Method

Subjects

Three undergraduate students at Queens College participated in the study. They were recruited from advanced psychology classes and were not familiar with the research area. Students received partial course credit upon completion of the experiment but credit did not depend upon performance. All participants were required to read and sign an informed consent statement prior to participation in the experiment. The entire experiment lasted about 3 hours. Each experimental session lasted approximately 1.5 hr.

Apparatus

Hardware. The experiment was conducted with IBM-compatible personal computers that displayed all stimuli on 15-in. SVGA color monitors. Responses consisted of touching specific keys on a standard keyboard. The experiment was controlled by customized software developed to conduct stimulus control experiments.

Stimuli. During Phase 2, horizontal lines of varying length were used to train subjects to use a neither comparison. The lines were produced with a string of ASCII character Alternate 196, each of which will be called a unit. Each unit was 3 mm wide by 5 mm high on the monitor. The lines varied in length from 1 to 24 units. The neither comparison and its use are described below.

During Phases 3-5, 19 stimuli were presented to the subjects. Each was a 2- x 2-in. borderless square that contained a different percentage of dark pixels on a white background. The pixels were large enough that the squares did not appear as different shades of gray. A stimulus dimension was produced by varying the percentage of darkened pixels in the square. The percentage of dark pixels defined each square's "fill" value and ranged from 23% (Fill23) to 77% (Fill77) in 3% increments. For each fill value, the pattern of pixels was randomly generated preexperimentally and remained fixed throughout the experiment. Fill23 and Fill77 defined the endpoints of the fill dimension. Fill50 was the physical midpoint of the dimension, while Fill35 and Fill62 were two intermediate values on either side of the midpoint. The remaining 12 stimuli are not illustrated. Prior research has shown that the adjacent stimuli along the fill continuum are discriminable from each other (Reeve & Fields, 2001).

Procedure

Trial format and responses within a trial. All trials used a matching-to-sample format. A trial began when "Press ENTER" appeared on the screen. Pressing the enter key cleared the screen and displayed a sample stimulus at the top center of the monitor. Pressing the space bar displayed two comparison stimuli at the bottom left and right corners while the sample remained on the screen. During trials in which the third comparison was programmed, the words "If NEITHER press 4" appeared between the two other comparisons.

During a trial, the left or right comparison was selected by pressing the number 1 or 2 key, respectively. Pressing the number 4 key selected the neither comparison, when available. A comparison selection cleared the screen and concurrently displayed a feedback message centered on the screen. When informative feedback was scheduled, the messages "RIGHT" or "WRONG" appeared, depending on the accuracy of the comparison selection. The message remained on the screen until the R (for "RIGHT") or W (for "WRONG") key was pressed. During some training and all test trials, noninformative feedback was scheduled following a comparison selection. This consisted of a dashed line surrounding the letter E (- - E - -) that signaled the end of a trial. The dashed line remained on screen until the student pressed the "E" key which was used as an observing response (Dinsmoor, 1985) to the noninformative feedback. After an appropriate observing response was made, the screen was cleared and the next trial began (Fields, Landon-Ji menez, Buffington, & Adams, 1995).

Trial block structure and feedback contingencies. Each phase of training and testing was conducted with blocks of trials. Within each block in all experimental phases, the trials were presented in a random order without replacement. At the start of training, a block was presented repeatedly with informative feedback after each comparison selection until all trials within the block occasioned 100% correct responding. Thereafter, the percentage of trials that occasioned informative feedback was reduced to 75%, 25%, and finally to 0% over successive blocks as long as 100% accuracy within a block was maintained. During feedback reduction, the trials that were followed by informative feedback were randomly determined. If 100% correct responding was not achieved within three blocks at a given feedback level during training, the student was returned to the previous feedback level for that particular block.

Phase 1: Instructions and keyboard familiarization. Prior to the experiment, students were presented with the following instructions on the screen:

Thank you for volunteering to participate. PLEASE DO NOT TOUCH ANY KEYS ON THE KEYBOARD YET! You will be presented with many trials. Each trial contains three or four CUES that are shapes, symbols, or common words. YOUR TASK IS TO DISCOVER HOW TO RESPOND CORRECTLY TO THE CUES BY PRESSING CERTAIN KEYS ON THE COMPUTER'S KEYBOARD. Initially, INSTRUCTIONS will tell you how to respond to the cues, and LABELS will help you identify the cues on the screen. The labels and instructions will slowly disappear. The experiment is conducted in phases. When each phase ends, the computer will sometimes tell you how you did. If you want to take a break at any time, call the experimenter. Thank you for your cooperation!

Press the space bar to continue.

After pressing the space bar, students learned to emit the appropriate keyboard responses to complete a trial. To accomplish this, 16 trials, each containing three English words such as KING, QUEEN, and CAMEL, were presented. The semantic relatedness between the sample word (e.g., KING) and one of the comparisons (e.g., QUEEN) was used to prompt the selection of the correct comparison. Informative feedback followed each comparison selection (refer to Fields, Reeve, Adams, Brown, & Verhave, 1997, for further details).

Correct responding to the stimuli in a trial during Phase 1 was also facilitated by instructional prompts (e.g., "Make your choice by pressing 1 or 2") that were deleted in a serial manner across trials (refer to Fields et al., 1997, or Fields, Adams, Verhave, & Newman, 1990, for further details). Phase 1 ended once the stimuli were presented without prompts and performance exceeded 85% accuracy (14/16 correct trials) during a single block. For the remainder of the experiment, if a nonexperimentally defined key was pressed during a trial, the instruction used to prompt the appropriate key press during Keyboard Familiarization (Phase 1) reappeared on the screen for three subsequent trials.

Phase 2: Neither-comparison training. The goal of the experiment was to measure the range of variants that function as members of higher-and lower-value fill-based classes. It was considered likely, however, that some intermediate value fill-variants would not be functioning as a member of either the high- or the low-fill class. Thus, it was necessary to provide a subject with a response (selection of the neither comparison) that could be used to indicate that a particular fill variant was not functioning as a member of either the high- or low-fill-based class. This response has also been called a default option (Innis, Lane, Miller, & Critchfield, 1998; Lane, Clow, Innis, & Critchfield, 1998).

The use of the neither comparison was trained with stimuli that were horizontal lines which varied from 1 to 24 units in length. Because each unit was 3 mm wide, the lines varied from 3 to 72 mm in length in 3-mm steps. All trials included three comparison stimuli: a 1- and a 24-unit line along with a neither option. The presentation of the 1- to 6-unit lines as samples occasioned reinforcement for the selection of the 1-unit comparison. The presentation of the 19- to 24-unit lines occasioned reinforcement for the selection of the 24-unit comparison. The presentation of the 11- to 14-unit lines occasioned reinforcement for the selection of the neither comparison. The remaining line lengths were used in testing only and never occasioned reinforcement. All training and testing consisted of blocks of trials. All trials in a block produced differential feedback until responding in a block reached 100% accuracy. Thereafter, feedback was reduced as previously described. Once performance was maintained in the absenc e of feedback, generalization tests were conducted using all line lengths. Some tests were conducted in the variant-to-base format in which all of the line lengths were presented as samples. Each trial contained the same three comparisons used for training. Other tests were conducted in the base-to-variant format. In some trials, the 1-unit line was presented as the sample along with a variant, the neither option, and the 24-unit line as the comparisons. On the remaining trials, the 24-unit line was presented as the sample. The comparisons consisted of a variant, the neither option, and the 1-unit line. In all of the base-to-variant tests, the variant changed from trial to trial in a random order.

Phase 3: Identity conditional discrimination training. Next, students received identity conditional discrimination training with fill-based stimuli. Fill23 and Fill77 were randomly alternated as samples. The two comparisons were Fill23 and Fill77. Each comparison appeared equally often on the left and right of the screen. A correct response was the selection of the comparison that was identical to the sample. When 100% informative feedback was scheduled, each block contained 32 trials. When 75, 25, or 0% feedback was scheduled, each block contained 16 trials. Feedback was reduced as previously described. Phase 3 was completed when a student made no errors during a block with 0% informative feedback.

Phase 4: Class formation through two-choice generalization testing. Once the identity conditional discriminations were established, two broad fill-based stimulus classes were induced by conducting a two-choice generalization test in a variant-to-base format (Reeve & Fields, 2001). Within a test block, each of the 17 fill values was presented as a sample twice for a total of 34 trials. Fill23 and Fill77 were the two comparisons. For each sample, a given comparison appeared once on the left and once on the right in random order. All comparison selections were followed by noninformative feedback. Students received 38 two-choice generalization trials in each of 20 test blocks. Thus, each variant was presented 40 times, a value that maximized the range of variants that came to function as members of perceptual classes (Reeve & Fields, 2001). The trial format, block structure, response contingencies, and responses within a trial were the same as those used in Phase 2.

Phase 5: Measurement of class width with three-choice generalization tests. As mentioned in the introduction, the widths of functionally independent classes can be determined using generalization tests that contain stimuli from from one of two classes and a neither comparison (Belanich, 2002; Reeve & Fields, 2001). That procedure was used in the current experiment to measure the widths of fill-based classes at each end of the fill continuum. These generalization tests were conducted using the same fill stimuli with three comparison selections available on all trials. Half of the trials were conducted in the variant-to-base format and the other in the base-to-variant format, each of which will be described below. The stimuli used in all trials are listed in Table 1.

In the variant-to-base tests, the variants of the fill stimuli were presented as samples with the Fill23, Fill77, and the neither option presented as comparisons. For each fill variant presented as a sample, we measured the likelihood of selecting each of the three comparisons. On all trials, subjects could also select the neither comparison. Thus, the inclusion of the neither comparison allowed for a functional separation of the range of low- and high-fill stimuli that occasioned the selection of the Fill23 or Fill77. This test was conducted in a block of 38 trials. Each variant was presented in 2 trials in the block. Variant values were presented in randomized order without replacement.

In all base-to-variant tests, one of the endpoint stimuli on the fill dimension was presented as a sample, the other endpoint stimulus was presented as the nominal negative comparison, and all trials contained the neither comparison. The variants of the fill patterns were presented as the other comparison. Half of the trials contained Fill23 as the sample with Fill77 and the neither option as constant comparisons, and fill values 23 to 68 as the other comparisons. The other trials contained Fill77 as the sample with Fill23 and the neither option as constant comparisons, and fill values 77 to 32 as the other comparisons. Pilot work suggested that the ranges of variants that functioned as class members could be identified with the use of the aforementioned ranges of variants. The inclusion of the neither comparison on all trials permitted the functional separation of the ranges of fill variants that were selected exclusively in the presence of the Fill23 and Fill77 samples. All of these tests were conducted in a block of 56 trials. Each variant in a block was presented in 2 trials. Variant values were presented in randomized order without replacement.

Definition of class membership and order of presenting test blocks. The variant-to-base and base-to-variant test blocks were presented four times each, in simple alternation. Each variant was presented eight times in each test format, allowing for a 12% variation in selection probability. In the variant-to-base tests, the variants that occasioned the selection of a given comparison on at least 88% of the trials were functioning as potential members of the same class as the selected comparison. In the base-to-variant tests, the variants that were selected in the presence of a given sample on at least 88% of the trials were functioning as members of the same class as that sample.

Results and Discussion

Two-choice variant-to-base generalization tests. Figure 1 contains the results of the two-choice generalization tests conducted with the fill variants in the variant-to-base format. During this test, a broad range of contiguous lower fill variants almost always occasioned the selection of the Fill23 comparison. In addition, a different range of contiguous higher fill variants almost always occasioned the selection of the Fill77 comparison. These ranges of stimuli will be called the "plateaus" of the gradients. The likelihood of selecting either comparison decreased rapidly and systematically for the intermediate range of fill variants that were between the plateaus. For Subjects 1692 and 1707, similar ranges of variants occasioned the selection of the Fill23 and Fill77 comparisons. For Subject 1732, however, a much larger range of variants occasioned the selection of the Fill23 rather than the Fill77 comparison. Finally, the variants that defined the plateaus for Subjects 1692 and 1707 occasioned somewhat hig her levels of comparison selection than they did for Subject 1732.

The variants that occasioned the selection of the low-fill comparison could have been functioning as members of a low-fill class, the variants that occasioned the selection of the high-fill comparison could have been functioning as members of a high-fill class. That conclusion, however, is questionable because of the availability of only two comparisons. In a two-choice generalization test, the selection of one comparison is the arithmetic complement of the selection of the other comparison. Thus, if we assume that the low-fill stimuli were functioning as members of the low-fill class, the other fill variants might have occasioned the selection of the other comparison as a default and might not be functioning as a class. Further, because only two comparisons were available, the selection of one comparison in the presence of intermediate fill variants might have been driven by the responses available rather than by the class functionality of the stimuli. Thus, particular variants might not have been functionin g as members of a class even though they were occasioning responses that would appear to index class membership. For these reasons, the data obtained in the two-choice generaization tests could not be used to determine the range of fill variants that were functioning as members of low-fill or high-fill classes (Fields et al., 1997; Reeve & Fields, 2001; Wasserman et al., 1988).

Three-choice variant-to-base tests. The results of the 3-choice variant-to-base generalization tests are shown in Figure 2. The variants closest to Fill23 almost always occasioned the selection of the Fill23 comparison. As the value of the variants became larger, the likelihood of selecting the Fill23 comparison declined and was accompanied by a complementary increase in the selection of the neither comparison. These variants, however, rarely occasioned the selection of the Fill77 comparison. Finally, Subjects 1692 and 1707 used the neither comparison more frequently than did Subject 1732.

A similar pattern of responding was observed in the presence of the lower values of the fill variants. The variants that were most similar to Fill77 almost always occasioned the selection of the Fill77 comparison. As the value of a variant became lower, the likelihood of selecting the Fill77 comparison declined and was accompanied by a complementary increase in the selection of the neither comparison. These variants, however, rarely occasioned the selection of the Fill23 comparison. The intermediate values of the fill variants typically occasioned the selection of the neither comparison more than either of the fill comparisons for Subjects 1692 and 1707. This occurred to a lesser degree for Subject 1732.

Stimuli along a continuum are functioning as members of a class if they all occasion the selection of the same comparison stimulus with a high and equivalent likelihood. The outcomes of the generalization tests conducted in the variant-to-base format showed the formation of two classes: a low-fill class consisting of fill-based variants that occasioned the selection of the lowest fill value on the dimension and a high-fill class consisting of another nonoverlapping range of fill variants that occasioned the selection of the highest fill value. Finally, the complementary relation between the selection of one comparison and the selection of the neither comparison showed that two functionally independent stimulus classes were formed, one at each end of the fill-based continuum.

Three-choice base-to-variant tests. Figure 3 illustrates the outcome of the three-choice base-to-variant tests conducted with Fill23 as the sample. The variants most similar to Fill23 were almost always selected in the presence of the Fill23 sample. Variants of greater value were selected with decreasing likelihood and were accompanied by a complementary increase in the selection of the neither comparison. The Fill77 comparison was rarely selected in the presence of Fill23 and the variants used as comparisons. Similar results were obtained for all subjects. For Subjects 1692 or 1707, the higher value fill comparisons were rarely selected in the presence of the Fill23 sample. For Subject 1732, however, the higher value fill comparisons were selected with somewhat greater likelihood in the presence of the Fill23 sample.

Figure 4 illustrates the results of the base-to-variant tests that used the Fill77 stimulus as a sample. The variants most similar to Fill77 were almost always selected in the presence of the Fill77 sample stimulus. Variants of lesser value were selected with decreasing likelihood and were accompanied by a complementary increase in the selection of the neither comparison. The Fill23 comparison was rarely selected in the presence of Fill77 and the variants used as comparisons. Similar results were obtained for all subjects. One notable difference can be seen across subjects, however. For Subjects 1692 and 1707, the lower value fill comparisons were rarely selected in the presence of the Fill77 sample. For Subject 1732, however, the lower value fill comparisons were selected with somewhat greater likelihood in the presence of the Fill77 sample.

Stimuli along a continuum function as members of a class if they are selected with high and equivalent likelihoods in the presence of a given stimulus. The outcomes of the generalization tests conducted in the base-to-variant format, which were presented in Figures 3 and 4, showed the formation of two classes: a low-fill class consisting of fill-based variants that were selected in the presence of the lowest fill value and a high-fill class consisting of another nonoverlapping range of fill variants that were selected in the presence of the highest fill value. Finally, the complementary relation between the selection of the variant comparisons and the selection of the neither comparison showed that two functionally independent stimulus classes were formed, one at each end of the fill-based continuum.

Test format effects on class width. Figure 5 depicts the generalization gradients obtained in both test formats for the high- and low-fill classes for each subject. Class width was defined by the variant-to-base test as the range of stimuli that occasioned the selection of the endpoint stimuli. Class width was also defined by the base-to-variant test as the range of variants that were selected in the presence of a given endpoint stimulus. These class widths are reflected by the plateaus of the relevant gradients and are also listed quantitatively in Table 2. A comparison of these gradients show how test format influenced the widths of the classes at each end of the fill-based continuum.

When the low-fill stimuli were considered, the range of variants that occasioned the selection of the Fill23 comparison during the variant-to-base test was larger than the range of variants that were selected in the presence of the Fill23 sample during the base-to-variant test. That is, the width of the low-fill class as measured by the variant-to-base test was greater than class width as measured by the base-to-variant test. In contrast, when the high-f ill stimuli were considered, the range of variants that occasioned the selection of the Fill77 comparison during the variant-to-base test was smaller than the range of variants that were selected in the presence of the Fill77 sample during the base-to-variant test. That is, the width of the high-fill class as measured by the variant-to-base test was smaller than class width measured with the base-to-variant test. A 2 x 2 ANOVA confirmed the significance of the interaction between test format and class location on class width, F(3, 8) = 45.02, p = .0026. Tukey -Kramer post hoc paired comparison tests showed that the difference in class width measured in each test fomat was significant for the low-fill class (p < .01) and high-fill class (p < .01). Finally, the absolute magnitude of the differences in class width measured in the two test formats were not significantly different for the two classes (p = .57).

The extent to which the differences in class width can be attributed to test format can be evaluated with a correlational analysis that uses adjusted values of [r.sup.2]. This analysis showed that test format accounted for 93% of the difference in the range of variants that functioned as members of the low-fill class, and 99% of the difference in the range of variants that functioned as members of the high-fill class. A correlational analysis also showed that the absolute value of the variants in each class accounted for 96% of the difference in the directionality effect of the test format. To summarize, test format influenced the widths of two open-ended classes, and the differences in class width obtained with each test format reversed for the classes at each end of the fill dimension.

Possible determinants of the test format effect on class width. Test format appears to be a nonsensory determinant of the stimuli that function as members of an open-ended class. It is also possible that the observed differences in class width might have been driven by a confound that differentiated the trials presented in each format. One such variable is the negative comparison used in each test format. The variant-to-base tests contained the same two comparisons on all trials. In contrast, the base-to-variant tests contained variants as one comparison and a constant negative comparison. In the base-to-variant tests, then, the selection of the variable comparison might have been driven by responding away from the constant negative comparison (Carrigan & Sidman, 1992; Johnson & Sidman, 1993; Strikeleather & Sidman, 1990; Stromer, 1986; Stromer & Osborne, 1982; Tomonaga, 1993). According to this argument, the difference in class width observed in the current experiment would reflect the effect of a methodolog ical confound rather than a true difference in class width produced by test format. Two points, however, raise questions regarding the plausibility of this hypothesis.

First, if the argument is to be accepted, the constancy of the negative comparison should have had the same effect on the direction of the test format effect regardless of the absolute values of the stimuli in a class. In the current experiment, the differences in class width reversed for the high-fill and low-fill classes. Therefore, the constant negative comparison hypothesis does not account for at least 50% of the findings reported in this experiment.

Second, when a specific variant is used in both test formats, once all of the stimuli on a trial are present, the trials in both formats contain the same three stimuli, albeit in different positions during a trial. Thus, if membership in Class 1 is being evaluated, a variant-to-base trial would have X' presented as the sample with X1 and X2 as comparisons, while the companion base-to-variant trial would have X1 presented as the sample with X' and X2 as comparisons. If it is assumed that a subject scans all of the stimuli on a trial many times before selecting a comparison, it does not seem plausible that the nominal negative comparison can be considered as a constant in the base-to-variant trial any more than in a variant-to-base trial. These considerations suggest that the presence or absence of a constant negative comparison does not provide a plausible account for the differences in class width measured with the different test formats.

The difference in the effect of test format on class width would appear to be governed by some as yet unspecified parameters that characterize the stimulus displays presented under each format. Some possible parameters might be the order of introducing the stimuli in a trial, and the relative positions of sample and comparison stimuli in a trial.

Experiment 2

At least two demonstrations are needed to conclude that the stimuli arrayed along a continuum are functioning as members of a class (Fields & Reeve, 2001; Lea, 1984; Reeve & Fields, 2001; Wasserman et al., 1988). First, many variants must occasion a given response (such as comparison selection) even though that response has been established in the presence of only one or a few stimuli in the dimension (Keller & Schoenfeld, 1950; Wright et al., 1988). The importance of the first requirement can be appreciated by considering that appropriate and novel stimulus relations will control responding even though those relations had not been directly trained (Bruner et al., 1956; Fields & Reeve, 2001; Hull, 1920; Keller & Schoenfeld, 1950). Thus, with minimal training, a subject can respond appropriately to new stimuli. Such performances are of major adaptive value for an organism's survival.

Second, those stimuli must be discriminable from each other (Honig & Stewart, 1988; Wasserman et al., 1988). The importance of the second requirement can be understood by considering the implications of not satisfying that requirement. Specifically, stimuli can be measurably different from each other but are not discriminable from each other (can not or do not occasion differential responding). When that occurs, the stimuli that differ physically, would be functioning as one, from a psychological point of view (Bhatt, Wasserman, Reynolds, & Knauss, 1988; Cook et al., 1990; Fields et al., 1997; Wasserman et al., 1988). If the stimuli in a putative class were not discriminable from each other, it would be trivial to say that they were functioning as members of a conceptual class or category. Thus, the generalization of responding among such stimuli would not be of adaptive significance. A demonstration of discriminability among the stimuli in a putative class, then, is needed to conclude that the stimuli in a s et are actually functioning as members of a class (Bruner et al., 1956; Cook et al., 1990; Fields et al., 1997; Lea, 1984; Wasserman et al., 1988).

In Experiment 1, many contiguous variants occasioned the selection of the same comparison stimuli. Thus, those stimuli might have been functioning as members of open-ended classes. Experiment 1, however, did not provide measures of the discriminability of adjacent stimuli along the fill dimension. Experiment 2 determined whether many of adjacent fill patterns in each putative class were discriminable from each other.

Method

Subjects and Apparatus

The subjects were the same as those who participated in Experiment 1. Experiment 2 was conducted immediately after Experiment 1. The apparatus, trial contingencies, and fill stimuli were the same as those used in Experiment 1.

Procedure

Discriminability of adjacent fill patterns was assessed in a procedure that involved five phases. In Phase 1, Fill values 23, 26, 29, 32, as well as 65, 68, 71, 74, and 77 were used as samples along with Fill23, Fill77, and neither as comparisons. In Phase 2, Fill values 26, 29, 32, 38, as well as 62, 65, 68, 71, and 74 were used as samples along with Fill26, Fill74, and neither as comparisons. In Phase 3, Fill values 32, 35, 38, as well as 59, 62, 65 and 68 were used as samples along with Fill32, Fill68, and neither as comparisons. In Phase 4, Fill values 38, 41, 44, as well as 56, 59, and 62 were used as samples along with Fill38, Fill62, and neither as comparisons. In Phase 5, Fill values 44, 47, 50, 53, and 56 were used as samples along with Fill44, Fill56, and neither as comparisons.

In each phase, selection of a given fill comparison was reinforced only if it was identical to the sample. Selection of the neither comparison was reinforced only when the sample presented was not identical to either of the comparison fill values. These contingencies maximized the discrimination between the intermediate fill values and the fill values at the endpoints of the dimension (Blough & Blough, 1977; Hamilton & Coleman, 1933; Reeve & Fields, 2001; Wright, 1972; Wright & Cumming, 1971). In each phase, the training block was repeated with 100% informative feedback until 100% correct responding was obtained. Feedback was then reduced as indicated in trial block structure and feedback contingencies described in Experiment 1. No informative feedback was presented for the last four blocks of each phase.

Results and Discussion

In Phase 1, there was substantial intersubject variation both in the accuracy of comparison selection during the first training block (30, 60, and 90%) and the number of blocks required to reach the mastery criterion (2, 3, and 25). Two subjects learned the conditional discriminations with relatively little training. For them, the reinforcement contingencies in Experiment 2 probably sharpened preexisting discriminations between adjacent fill patterns. The third subject (1707) required 25 blocks to master the conditional discriminations. In most blocks, the neither comparison was selected on all trials. In a few other blocks, the neither comparison was selected on most trials, with random selection of the fill-based comparisons on the remaining trials. Suddenly, correct comparison selections were occasioned by all of the trials on the training block. By the end of Phase 1, then, all subjects were responding differentially to adjacent stimuli along the fill dimension. Thus, both endpoint stimuli were fully disc riminable from their adjacent fill variants.

In Phases 2-5, comparison selection was 100% correct during the first training block for all subjects. These performances indicate that the endpoint variants were immediately and completely discriminated from the adjacent variants. Thus, the adjacent fill patterns must have been fully discriminable from each other prior to the initiation of training in each of these phases. This pattern of responding is all the more interesting when one recognizes that at the end of each prior phase, those same stimuli occasioned the selection of the same comparison: the neither comparison, and also occasioned differential feedback for these comparison selections. The occurrence of correct responding from the inception of training implies that two stimulus control topographies had been acquired during Phase 1. First, subjects learned to discriminate the specific adjacent stimuli used in Phase 1. Second, subjects learned that endpoint and adjacent stimuli occasioned differential comparison selection, regardless of stimulus val ue (Sidman, Wynne, Maguire, & Barnes, 1989).

The last four blocks run in Phases 1-5 of Experiment 2 were conducted under extinction conditions. Thus, the data collected under these conditions showed the maintenance of discriminability among stimuli when no feedback was provided for comparison selection. Table 3 shows the performances occasioned by each fill value used as a sample during the last four generalization test blocks presented at the end of each phase of Experiment 2.

Because all subjects responded in essentially the same manner, the data in Table 2 represented performances averaged across subjects. In each phase of Experiment 2, subjects almost always selected a given endpoint comparison in the presence of the same stimulus presented as a sample. They rarely, if ever, selected the neither comparison or the fill-based comparison that was the other endpoint stimulus. In addition, all of the intermediate fill values used as samples almost always occasioned the selection of the neither comparison. These data show the maintenance of discriminability between adjacent fill values in the absence of reinforcement.

Two criteria must be satisfied to conclude that stimuli are functioning as members of an open-ended class: common responding occasioned by many stimuli arrayed contiguously along some dimension, and discriminability among those stimuli. The results of Experiment 1 satisfied the first criterion by showing that the stimuli in a set occasioned the same response (conditional comparison selection). The results of Experiment 2 satisfied the second criterion by showing that many of the stimuli in a potential class were discriminable from each other.

The performances observed in the initial blocks of each phase of Experiment 2 support the view that many of the fill variants that had been used in Experiment 1 were discriminable from each other during Experiment 1. Thus, it seems plausible to conclude that discriminable variants were functioning as members of open-ended classes in Experiment 1 (Bourne, Dominowski, & Loftus, 1979; Cook et al., 1990; Lea, 1984).

General Discussion

Procedures that induce open-ended classes. Typically, open-ended classes are established by use of multiple exemplar training with differential reinforcement (Cook et al., 1990; Malott & Siddall, 1972; Markle, 1990; Wasserman et al., 1988; Wright et al., 1988). In a recent study, open-ended classes were established without the use of reinforcement (Reeve & Fields, 2001). Instead, Reeve induced classes by exposure to a forced choice generalization test conducted with no reinforcement. The same procedure was used to induce open-ended classes in the current experiment, thereby demonstrating the reliability of the effect reported by Reeve.

Because a unique procedure was used to establish open-ended classes and class width was influenced by test format, it is possible that the test format effect might be limited to classes that are formed by forced choice generalization testing. Further research will be needed to determine whether the differential effects of test format would also be seen with classes induced by multiple exemplar training with reinforcement.

Measurement of class width with different test formats. In the current experiment, the same nominal class had two different widths. Which class width would more accurately predict the variants that would occasion a response trained to one class member? One possibility is that the transfer would be predicted best by the broadest range of stimuli that function as a class. In this case, if class width had been measured with a test conducted in only one format and that format yielded the smaller class width, one would underestimate the range of stimuli to which the result would transfer. The other possibility is that transfer would be predicted by the narrowest range of stimuli that function as a class. In this case, if class width was measured with a test conducted in only one format and that format yielded the larger class width, one would overestimate the range of stimuli to which a response would transfer. In both cases, then, the predictive accuracy of function transfer would be compromised by the measuremen t of class width using tests conducted in only one format. According to this analysis, the predictive accuracy of function transfer should be optimized by the measurement of class width using tests conducted in both test formats.

This analysis also has implications for using mutual selection as a basis for defining class membership. According to the notion of mutual selection, the width of an open-ended class would include the range of variants that occasioned the selection of base stimuli during variant-to-base tests and were also selected during base-to-variant tests. The utility of defining class width in terms of mutual selection, however, will depend on the outcomes of function-transfer tests. If the range of variants to which a function transfers is predicted most accurately by the format that produces the narrower class width, mutual selection would be a desirable means of defining class width. If class width defined by mutual selection provides an accurate prediction of transfer for many different stimulus and response functions acquired by one class member, that width, then, might specify the "core" width of an open-ended class. Additional research, then, will clarify the utility of using mutual selection as a definitional pr operty of stimuli in open-ended classes.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]
Table 1

Symbolic Representation of Stimulus Triads in Phase 5

Type Sa Co+ Ca- #Trials

Variant-to-Base A1(23) A1(23) A2(77) 2
 A(26) Al (23) A2(77) 2
 A(29) Al (23) A2(77) 2
 A(32) Al (23) A2(77) 2
 A(35) Al (23) A2(77) 2
 A(38) Al (23) A2(77) 2
 A(41) Al (23) A2(77) 2
 A(44) Al (23) A2(77) 2
 A(47) Al (23) A2(77) 2
 A(50) Al (23) A2(77) 2
 A(53) Al (23) A2(77) 2
 A(56) Al (23) A2(77) 2
 A(59) Al (23) A2(77) 2
 A(62) Al (23) A2(77) 2
 A(65) Al (23) A2(77) 2
 A(68) Al (23) A2(77) 2
 A(71) Al (23) A2(77) 2
 A(74) Al (23) A2(77) 2
 A2(77) A1(23) A2(77) 2

Base-to-Variant A1(23) A1(23) A2(77) 2
Low Fill A1(23) A(26) A2(77) 2
 A1(23) A(29) A2(77) 2
 A1(23) A(32) A2(77) 2
 A1(23) A(35) A2(77) 2
 A1(23) A(38) A2(77) 2
 A1(23) A(41) A2(77) 2
 A1(23) A(44) A2(77) 2
 A1(23) A(47) A2(77) 2
 A1(23) A(50) A2(77) 2
 A1(23) A(53) A2(77) 2
 A1(23) A(56) A2(77) 2
 A1(23) A(59) A2(77) 2
 A1(23) A(62) A2(77) 2

Base-to-Variant A2(77) A2(77) A2(23) 2
High Fill A2(77) A(74) A2(23) 2
 A2(77) A(68) A2(23) 2
 A2(77) A(65) A2(23) 2
 A2(77) A(62) A2(23) 2
 A2(77) A(59) A2(23) 2
 A2(77) A(56) A2(23) 2
 A2(77) A(53) A2(23) 2
 A2(77) A(50) A2(23) 2
 A2(77) A(47) A2(23) 2
 A2(77) A(44) A2(23) 2
 A2(77) A(41) A2(23) 2
 A2(77) A(38) A2(23) 2

Note. In each trial block, Co+s appeared equally often on the left and
right. The numberals in parentheses indicate the value of the fill
pattern used for the indicated stimulus.

Table 2

Class Width Measured in Fill Units Presented as a Function of Class,
Test Format, and Subject

 Class width by Class width by
 test format test format
 Low Fill High Fill
Subject B-V * V-B # B-V V-B

1692 15.00 19.50 31.50 22.50
1707 18.00 24.00 21.00 15.75
1732 24.00 28.50 15.75 12.00

Average 19.00 24.00 22.75 16.75

 Difference in
 class width
 (B-V) - (V - B)
Subject Low Fill High Fill

1692 -4.5 +9.00
1707 -6.0 +5.25
1732 -4.5 +3.75

Average -5.0 +6.00

* During base-to-variant tests, class width was equal to the absolute
difference in the base value for a class and the variant most distant
from that base value that was selected on at least 88% of test trials.

# During variant-to-base tests, class width was equal to the absolute
difference in the base value for a class and the variant most distant
from that base value that occassioned the selection of the base stimulus
on at least 88% of test trials.

Table 3

Generalization Test Data From Last Four Blocks of Each Phase in
Experiment 2

Sample Variants

 Ends
Phase Low High Comp 23 26 29 32 35 38 41

1 23 77 Low 100 0 0 0 0
 NC 0 100 100 100 100
 High 0 0 0 0 0

2 26 74 Low 100 0 0 0 0
 NC 0 100 100 100 100
 High 2 0 0 0 0

3 32 68 Low 100 0 0 0
 NC 0 100 100 98
 High 0 0 0 2

4 38 62 Low 100 0
 NC 0 100
 High 0 0

5 44 56 Low
 NC
 High

Sample Variants

 Ends
Phase Low High Comp 44 47 50 53 56 59 62

1 23 77 Low
 NC
 High

2 26 74 Low 0
 NC 100
 High 0

3 32 68 Low 0 0
 NC 100 100
 High 0 0

4 38 62 Low 0 0 0 0
 NC 100 100 100 0
 High 0 0 0 100

5 44 56 Low 97 0 0 0 0
 NC 3 100 100 100 0
 High 0 0 0 0 100

Sample Variants

 Ends
Phase Low High Comp 65 68 71 74 77

1 23 77 Low 0 0 0 0 0
 NC 100 100 100 100 0
 High 0 0 0 0 100

2 26 74 Low 0 0 0 0
 NC 100 100 100 0
 High 0 0 0 100

3 32 68 Low 0 0
 NC 100 0
 High 0 100

4 38 62 Low
 NC
 High

5 44 56 Low
 NC
 High

Note. The last four blocks were conducted in the absence of differential
feedback. Relative frequency of selection of the low- and high-fill
comparison or the neither comparison (NC) in the presence of the sample
variants is indicated at the top of the table. Data were averaged across
subjects.


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This research was conducted with support from Contract DASW01-96-K-0009 from the U. S. Army Research Institute, and by PSC-CUNY Research Awards 68547, 69567, and 61617. We thank Xiqiang Zhu for his assistance in the development of the software used to produce the fill patterns, conduct the experiment, and analyze the data reported herein. Reprints can be obtained from Lanny Fields, Department of Psychology, Queens College/CUNY, 65-30 Kissena Boulevard, Flushing, NY 11367.
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