Journal of Experimental Psychology 967, Vol. 7S, No. 4, 464-47 GENERALIZATION GRADIENTS AS INDICANTS OF LEARNING AND RETENTION OF A RECOGNITION TASK HARRY P. BAHRICK, SANDRA CLARK, AND PHYLLIS BAHRICK Ohio Wesleyan University Ss were required to select previously exposed pictures of common objects from among series of alternative pictures graded in similarity to the prototypes. Response frequencies were plotted in the form of generalization gradients, and such gradients were obtained following 4 stages of training and retention intervals. In Part II, Ss were trained by exposing the same prototype stimuli, but recognition tests consisted of alternatives at of homogeneous levels of similarity to the prototypes. Learning curves based upon the types of tests differ markedly in slope, reflecting the differential sensitivity of various dichotomous tests to the changes in the discriminability function. It was shown that the slope of each curve could be predicted accurately from the gradients obtained in Part I. Thus, generalization gradients were shown to be sensitive, parsimonious representations of the recognition learning process. The purpose of this study was to obtain a series of generalization gradients to reflect the acquisition and retention of a visual discrimination skill. A number of previous investigators (Hovland, 97; Jensen & Cotton, 96; Margolius, 9; Razran, 949) have obtained gradients of stimulus generalization at several stages of training. As Brown (96) and Prokasy and Hall (96) have pointed out, however, such gradients do not necessarily reflect discriminability functions. Stimulus generalization gradients may or may not reflect the ability of "s to discriminate among training and testing stimuli, depending upon a number of task and procedural variables. According to Gibson (99), primary stimulus generalization reflects the inability to discriminate among stimuli, but secondary or mediated generaliza- This research was supported entirely by Grant HD96-OS from the National Institutes of Health, United States Public Health Service. Now at Ohio State University. tion is based upon perceived similarity. In practice, an unequivocal distinction between these two kinds of situations is sometimes difficult. However, the interpretation of generalization gradients as indicants of discriminatory ability would appear to have considerable face validity when the gradient is obtained by requiring " to select a training stimulus from among a graded series of alternative stimuli. Stimulus generalization gradients based upon identification errors in such recognition tasks have been obtained by Ellis and Feuge (966), Postman (9), and others, but they have not been obtained for various time intervals of retention. There are several potential advantages to be gained from obtaining a series of such gradients, (a) They can provide a model from which the shape of learning and retention curves based upon a variety of dichotomous recognition indicants can be deduced parsimoniously, (b) They may be used to obtain a direct multicategory measure of stimulus and response learning at various stages of acquisi- 464
GENERALIZATION AS A MEASURE OF RECOGNITION LEARNING 46 tion and retention of paired-associate tasks, and (c) they may contribute to the resolution of questions regarding the nature of generalization, e.g., the shape of generalization gradients as a function of a variety of conditions. In Part II of the present study, data are presented relevant to the first of these applications. PART I Method Preparation of stimulus material. Pictures of 6 common objects were drawn so as to occupy an area of approximately. sq. in. each. One hundred variations of each picture were then drawn so that the drawings would resemble the prototypes by varying degrees. The variations were produced primarily by changing one or more details of the form of the object. Xerox copies were then obtained for all,66 drawings and these were used throughout the remainder of the investigation. Each set of drawings was rated independently by each of judges as to the degree of similarity of each variation to its prototype. The ratings were carried out along a 9-point scale. Following the method of equal-appearing intervals (Edwards, 97), medians and interquartile ranges of similarity ratings were obtained for each drawing. The range of each set of medians was then divided by five and the resulting interval was used to determine five equally spaced points along each of the similarity continua. Ten drawings were then chosen from each set of which best satisfied the following two requirements: (a) median similarity rating for two drawings each to fall as closely as possible, respectively, to each of the five points selected along the similarity continua; (6) interquartile range of similarity ratings assigned by the judges to be as small as possible. This selection procedure was followed for each of the 6 sets of drawings. The 6 variations which were chosen by the above method had a mean absolute distance of. from their respective calculated TABLE FREQUENCY DISTRIBUTIONS OF RECOGNITION RESPONSES AS A FUNCTION OF DEGREE OF TRAINING AND RETENTION INTERVAL Training Trials 9 9 99 8 8 8 8 Retention Interval hr. days wk. hr. days wk. hr. days wk. hr. days wk. 77 48 47 4 97 76 6 8 79 6 7 8 Error Magnitude 9 9 4 47 6 44 9 4 9 7 4 4 8 7 6 9 6 4 4 8 8 6 6 9 4 9 6 4 4 8 7 6 4 6 4 6 88 4 points (SD =.4). The mean interquartile range of the chosen variations was.7 (SD =.9) and the mean range of the medians was 7.44 for the 6 prototypes (SD =.6). Preparation of recognition tests. Figure shows one of the prototype drawings together with of the variants chosen by the above procedure to represent equal distances along the continuum of similarity to the prototype. Each prototype drawing was positioned randomly within one row of the recognition test among the deviant drawings chosen by the procedure described earlier. Two of the deviant drawings represented first-, second-, third-, fourth-, and fifthdegree similarity to the prototype, respectively. This procedure was followed for all 6 prototype drawings, and thus the recognition test consisted of 6 rows and columns of drawings. Three such tests were assembled, each with a different random sequence of rows and random position of 4 FIG.. One row from the recognition test.
466 H. P. BAHRICK, S. CLARK, AND P. BAHRICK drawings within each row. Figure shows one row from one of the tests. Numbers have been added to designate the degree of dissimilarity of each deviant drawing. Training procedure. One hundred and sixty male and female undergraduate volunteer s were assigned by systematic alternation to four groups of 4 s each. They were seated and instructed to observe the 6 prototype pictures to be exposed in the window of an oversized memory drum (4-in. circumference) located at eye level and at a distance of 6 in. from S. The s were instructed to observe each drawing in detail, but not to attempt to learn the sequence in which the drawings were shown. The 6 prototype drawings were exposed for sec. each in one of three random sequences. The sequences were alternated systematically for s receiving more than one exposure trial, and the assignment of the first sequence to s was randomized. The four groups were trained, respectively, for,, 9, and 8 trials, with an intertrial interval of 8 sec. The 4 s of each group were further subdivided into four subgroups of s each. These subgroups were administered recognition tests immediately after training, after hr., days, or wk., respectively. Recognition testing. The s were seated in front of the training drum and the recognition tests described earlier were presented iso IZ S 7 -^ EXPOSUfSf TKt/iLS -8-- 9 XP&SU&E TRIALS l< fxposv&f T&/&LS so i 4 FIG.. Generalization gradients at four stages of training.
GENERALIZATION AS A MEASURE OF RECOGNITION LEARNING 467 to them in the window of the drum, one row at a time. The s were told that one of the pictures shown in each row of the test had been presented during training, and they were instructed to mark the position of the previously presented picture in the appropriate space of an answer sheet within a time limit of 8 sec. At the expiration of that interval "s were forced to guess if they had made no response, and the next row of the test was exposed. The s in each group were assigned by systematic alternation to one of the three versions of the recognition tests in which the sequence of rows appeared in a different random order. iso Results and Discussion All recognition choices were scored as correct, or as first-, second-, third-, fourth-, or fifth-degree errors. The frequencies of these six response categories were then cumulated for "s of each subgroup and the results are shown in Table. Figure shows generalization gradients as a function of degree of training when recognition tests are administered immediately following training; Fig. shows the * a -4 ERROR MrtGN ITUD FIG.. Generalization gradients as a function of the retention interval.
468 H. P. BAHRICK, S. CLARK, AND P. BAHRICK change in the gradient as a function of the retention interval following 8 training trials. Evidence for the reliability of the technique was obtained by correlating the frequency of error choices for all pairs of matched stimuli. For this purpose the error choices of all SB were cumulated separately for each of the two first-, second-, third-, fourth-, and fifth-degree error alternatives provided on each of 6 rows of the recognition test, and the correlation based upon the resulting 8 paired scores was.89. It is apparent that the recognition technique using stimuli scaled for similarity provided a sensitive means of assessing the acquisition and retention of this visual recognition skill. The unidimensional method of similarity scaling used in this investigation, of course, does not reveal the various factors on which the judgments of similarity were based. This can be done only with multidimensional methods. The relative reliability of the ratings, however, as well as the comparatively smooth gradients, suggest that a single continuum can represent perceived similarity adequately, at least for the kinds of forms used here. PART II Part II of the experiment was designed to test the relations between the generalization gradients obtained in Part I and the slopes of learning curves based upon recognition tests of a particular difficulty level. It has frequently been pointed out (Bahrick & Bahrick, 964; Deese, 98, p. 4; Postman, Jenkins, & Postman, 948; Underwood, 949, p. ) that the probability of correct identification responses on a recognition test is a function of the degree of similarity of wrong alternatives to the correct alternative provided on the test. The gradients obtained in Part I, however, permit a quantitative prediction of performance on any recognition test for which the similarity level can be specified with respect to the similarity continuum established for the gradient. Performance on such tests can be predicted for any degree of training, or any retention interval for which gradients have been obtained. Thus, the gradients provide a parsimonious basis for predicting learning and retention curves based upon recognition tests of varying difficulty level. The following data were collected to test these predictions. Method Test construction. The scaled similarity values obtained in Part I for the,6 drawings were used to assemble recognition tests at three relatively homogeneous similarity levels for each of the prototype drawings. Tests of Similarity Level I were obtained by selecting four alternatives with minimum distance from the first of the five equally spaced points along the similarity continua. Analogous procedures were followed to obtain tests in which all four alternatives were of approximately second- and fifth-degree similarity level, respectively. The mean distance of the chosen alternatives to their respective reference points was.8 (SD =.). The first-, second-, and fifth-level similarity tests were assembled on separate charts each with 6 rows and columns. Each row represented a test for one of the 6 prototype pictures, with the prototype positioned randomly among the four alternatives. Three versions of each test were constructed in which the sequence of rows was varied randomly. Training. One hundred and twenty male and female s chosen from the same population as s in Part I were divided into 4 groups of s each, and were trained for I,, 9, and 8 exposure trials, respectively. Each group was further subdivided into three subgroups of s each, who were administered first-, second-, or fifth-degree similarity recognition tests, respectively, as described above. The recognition tests were administered immediately after training terminated. The procedure used was identical to that described in Part I.
GENERALIZATION AS A MEASURE OF RECOGNITION LEARNING 469 Results and Discussion Figure 4 shows predicted and empirical learning curves for the three groups. The predicted curves are based upon the generalization gradients obtained in Part I. To predict a particular score from the appropriate gradient, error frequencies corresponding to the degree of similarity of the particular test are cumulated with all error frequencies shown on the gradient for degrees of similarity less than the items used in that test, and the cumulative total is expressed as a percentage of the total number of responses on which the gradient is based. This predicted error percentage is then subtracted from to arrive at the predicted percentage of correct responses plotted in Fig. 4. For example, the prediction of the percentage of correct responses for a test of simitoo O 4 S 4 f f < 7 & 9 l O is 6 J7 & FIG. 4. Predicted and observed learning curves based upon recognition tests at three levels of similarity.
47 H. P. BAHRICK, S. CLARK, AND P. BAHRICK larity level two after three training trials is based on the following calculation: - 7 + + 7 6 = 8 These predictions rest upon the assumption that correct performance on each test requires a certain minimum level of discriminatory skill. By examining the gradient appropriate to the level of training, the similarity level corresponding to a particular test can be identified along the abscissa. The portion of the area under the gradient for error magnitudes greater than the critical level corresponds to the portion of total responses which can be expected to be in error on a test of this difficulty level. It can be seen that the predicted and observed acquisition functions correspond closely to each other. A chisquare test shows no significant differences (p >.) between the expected and observed frequencies. Differences in the probability of chance success on the tests used in Parts I and II have apparently produced only minor effects. The acquisition functions for first-, second-, and fifth-degree similarity differ markedly in slope. Thus, it would appear from the curve based upon fifthdegree similarity choices that no significant learning occurs after the first exposure trial, while the tests based upon alternatives of first-degree similarity reveal learning at much later stages of practice. Clearly, the tests differ in sensitivity, i.e., their capacity to reflect changes of the discriminability function during acquisition. Such systematic variation in the capacity of dichotomous indicants to reflect changes of underlying continuous distributions have been discussed extensively for both learning and retention curves (Bahrick, 96; Bahrick, Fitts, & Briggs, 97). It is apparent from the present analysis that a series of generalization gradients of the type presented here can provide a more inclusive and parsimonious representation of learning and retention of recognition tasks than any individual learning or retention curve based upon arbitrary and unspecified levels of similarity of the incorrect and correct alternatives. Yet, tests of arbitrary and unspecified degrees of similarity have served as the basis of nearly all prior generalizations regarding recognition memory, and thus a reexamination of these generalizations is necessary. Further development of the technique used here may prove to be of value in the analysis of the phenomena of perceptual learning and retention. REFERENCES BAHRICK, H. P. The ebb of retention. Psychol. Rev., 96, 7, 6-7. BAHRICK, H. P., & BAHRICK, P. O. A reexamination of the interrelations among measures of retention. Quart. J. exp. Psychol, 964, 6, 8-4. BAHRICK, H. P., FITTS, P. M., & BRIGGS, G. E. Learning curves: Facts or artifacts? Psychol. Bull., 97, 4, 6-68. BROWN, J. S. Generalization and discrimination. In D. I. Mostofsky (Ed.), Stimulus generalization. Stanford: Stanford Univer. Press, 96. Pp. 7-. DEESE, J. The psychology of learning. New York: McGraw-Hill, 98. EDWARDS, A. L. Techniques of attitude scale construction. New York: Appleton- Century-Crofts, 97. ELLIS, H. C, & FEUGE, R. L. Transfer of predifferentiation training to gradients of generalization in shape recognition. /. exp. Psychol., 966, 7, 9-4. GIBSON, E. J. A re-examination of generalization. Psychol. Rev., 99, 66, 4-4. HOVLAND, C. I. The generalization of conditioned responses. IV. The effects of varying amounts of reinforcement upon the degree of generalization of conditioned responses. /. exp. Psychol., 97,, 6-76. JENSEN, G. D., & COTTON, J. W. Running speed as a function of stimulus similarity
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