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One-trial versus incremental-paired associate learning
~O~RNAL OF VERBALLEARNINGAND VERBALBEHAVIOR 1, 14-21 (1962)
One-Trial Versus Incremental-Paired Associate Learning ~ KEITH A.
WOLLEN 2
State University o] Iowa, Iowa City, Iowa
In contrast with the traditional view that associations are formed gradually, Estes (1960) has recently espoused a theory that, on any given trial, associative strength either increases from 0% to 100% or does not increase at all. 3 Data allegedly in support of this all-or-none interpretation were reported by Estes, Hopkins, and Crothers (1960). These Es presented both members of pairedassociate items for one learning (L) trial followed by two successive test (T) trials on which only the stimulus member was shown. The sequence was thus L1 T1 T2. Both in that report and elsewhere (Estes, 1960), primary emphasis was placed upon the fact that the proportion of non-correct (N) items on T1 that became correct (C) on T2, henceforth abbreviated as C2:N1, was nearly zero. Estes argued that this proportion should have been greater than zero if N items had received associative strengthening on L~. On this basis, he concluded that these data support an allor-none theory but "appear incompatible with any theory which expresses learning in terms of increments" (Estes et al., 1960, p. 338). However, such conclusions seem unjustified on several accounts. In the first place, there is a strong possibility that the N items on T1 were more
difficult than the C pairs, in which case the increments in associative strength might not have been large enough to have been detected. Estes reasoned that this could not have been the case since the proportion of C2:N1 for items presented in an L1 T1 L2 T2 sequence was as large as the proportion correct on T1. However, such reasoning is most tenuous in view of the fact that the length of the list was reduced from eight items on L1 to four on L2 (of which an average of 40% had been C on T1), and the additional fact that short lists are learned more readily than long ones. Moreover, the two proportions might be expected to be approximately equal purely from the fact that the strengthening accrued on L1 may have offset the disadvantage of being more difficult. Secondly, although contrary to Estes' (1959) incremental theory, the extremely low proportion of C2:N1 for items presented in an L1 T1 T2 sequence is perfectly consonant with theories which incorporate the concept of a threshold (e.g., Hull, 1943; Spence, 1956). Such theories predict that response probability will remain zero until the excitatory strength has become superthreshold. Consequently, it is most reasonable that the N items on T1 had received an increment in associative strength even though few of these items became C on T2. Furthermore, the low proportion of C2:N1 might merely be the result of the fact that the N items, which were already below threshold, suffered some decrement due to "forgetting" and dropped even further below. Even if one were to grant that the C2:N1 data were evidence that N items on T1 had acquired no associative strength on L~, there would be no evidence that increments would be all-or-none in character when they
1 This paper is based upon a doctoral dissertation s u b m i t t e d to t h e State University of Iowa. T h e a u t h o r is indebted to R u d o l p h W. Schulz for his advice a n d assistance t h r o u g h o u t the course of this investigation. 2 N o w at W a s h i n g t o n State University, Pullman, Washington. A similar theory (Rock, 1957) h a s received extensive consideration elsewhere (e.g., P o s t m a n , in press; Underwood, Rehula, a n d Keppel, in press) and will n o t be considered here. 14
ONE-TRIAL LEARNING
do occur. I t would still be possible for response probability to remain zero for a few trials and then increase gradually. Finally, the use of a 4-sec. exposure time, a 4-sec. interitem interval, and a 60-sec. interlist interval probably encouraged rehearsal to the extent that essentially several "trials" were given with each presentation of the list. This fact alone would seem to preclude the interpretation of the above data as support for a one-trial theory. Estes has also indicated that according to his theory overlearning should not increase retention. In both paired-associate and free verbal recall experiments, he found that the proportion of C2:C1 was as large for items given in an L1 T1 T2 sequence as for those administered in an L1 L2 T1 T2 fashion. On the basis of these data, Estes concluded that "we must face the possibility that this empirical relation [that overlearning increases retention], like the classical acquisition curve, is an artifact of the confoundings inherent in the usual experimental paradigm" (Estes, 1960, p. 220). However, Estes' design itself was not entirely free of "confoundings." Had there been some way of assessing when each item became C, it would undoubtedly have been found that some items became superthreshold on L1 and others on L2. Thus it is not surprising that retention did not differ for the two conditions since a large proportion of the items in the L1 L2 T1 T2 condition were probably given no overlearning. Due to the equivocal nature of the evidence interpreted as support for the all-or-none conception, an attempt was made to design further tests of the theoretical alternatives which would be relatively free of the previously mentioned shortcomings. Basically, the following experiments demonstrate that the occurrence of an N response does not necessarily indicate that the associative strength of that response is zero. The primary test used in the following experiments is one suggested by Estes (1960, p. 217) as providing a "quite sharp" test of one-trial and incremental theories in the case of eyelid conditioning. The test, applied here to paired-associate learning, involves a trialby-trial analysis of the proportion (P~), where
15
P~ is defined as the ratio of the number of items which become C for the first time on Trial n to the number of items that have never been C prior to that trial. According to an all-or-none theory, each item in a list would have a certain fixed probability of being learned. This probability should remain constant over trials due to the assumption that N items have received no associative strengthening. However, the items that actually become C on each trial would tend to be those with the higher probabilities. Consequently, as training proceeded, the group of N items upon which P~ is based would become progressively more reduced to difficult pairs with low probabilities. Thus P~ should decrease as n increases. Moreover, the rate of decrease should be greater for easy lists than for equally-variable difficult ones since a larger proportion of the items would become C on each trial. In the unlikely event that all items were equally difficult, the theory would predict constant values of P~ over trials. This theory, incidentally, would have difficulty handling any situation in which the Ss learn all of the items inasmuch as the last P~ value in such cases must be 1.00. In sharp contrast, an incremental theory of the variety outlined in Fig. 1 predicts that Pn would increase with training. The upended distributions in Fig. 1 represent a list of items which differ in difficulty. In this theory, dif40, ,r\
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FIG. 1. Hypothetical growth of associative strength as a function of training trials for a distribution of items differing in difficulty. All units are completely arbitrary.
16
WOLLEN
ficulty may be based on initial differences in associative strength, on rates of growth, or on some combination of these two factors. The distributions are displaced upward as training progresses to represent the assumption that associative strength increases in a negatively accelerated fashion. Assuming that an item will become C when its associative strength becomes superthreshold, P , for a given trial would be the ratio of the shaded area for that trial to the area below threshold on the previous trial. As is apparent, these values would increase throughout training. Moreover, if difficulty is based on different rates of growth of associative strength, P~ would increase more rapidly for easy lists than for difficult ones since a larger proportion of the distribution would become superthreshold on each trial. Although the distributions in Fig. 1 are normal, the predictions would apply equally well to any unimodal or rectangular distribution. The present purpose is not to expound a particular incremental theory, but merely to demonstrate how such a formulation might account for the data. The major objective of Exp. I was to select two pools of items, one easy (E) and the other difficult (D), for use in Exp. II. A second objective was to test the apparent implication of an all-or-none theory that I) items should show no more shifts from C on one trial to N on the next than would E items. If, as Estes (1960) has maintained, an item becomes completely conditioned in one trial, it would seem to follow that the associative strength of both E and D items would be maximal and equal when both are C, and that E items would be "forgotten" as readily as D pairs. If D items were to accumulate associative strength more slowly than E items, an incremental theory would predict that the D pairs would remain in the region of the threshold for more trials and hence would be more likely to shift from C to N. The major objective of Exp. I I was to see whether the data support the all-or-none view that P~ would decrease more rapidly for E items than for D pairs, or the incremental interpretation that P , would increase in both instances. A second objective was to examine the effect of overlearning upon immediate and
delayed retention. According to Estes' all-ornone view, once an item becomes C, its associative strength is maximal and further learning trials should not increase subsequent retention. An incremental position, on the other hand, would be that strengthening is not necessarily complete when an item first becomes C. Therefore, overlearning should increase retention by strengthening associations further so that they would be less likely to drop below threshold. METHOD Subjects. The Ss were 136 students from the introductory psychology course at the State University of Iowa. All were naive with respect to verbal learning. A total of 8 Ss was assigned at random to each of eight lists in Exp. I. In Exp. II, 18 Ss were randomly assigned to each of four conditions. Apparatus. A 3 X 5.5 in. translucent screen was mounted in a 4 X 6 ft. opaque panel which also served to separate E from S. The learning materials were projected from behind the screen by means of a 2 X 2 in. LaBelle Professional "88" slide projector. The learning materials appeared as .25-in. high black letters on a white background. The slides used on L trials contained both stimulus and response units. The slides used on T trials were identical in every respect to those used on L trials except for the omission of the response member. Decade interval timers were employed to control the exposure, interitem, and intertrial intervals. Lists: Exp. I. The learning materials consisted of 96 consonant syllables paired randomly with 96 AA nouns taken from the Thorndike-Lorge list (1944). These 96 pairs were divided into eight lists of 12 items each such that no 2 syllables in any one list began with the same consonant. Procedure: Exp. I. Each S was given nine L and nine T trials, in alternate fashion, on the list to which he had been assigned. On L trials, a consonant syllable and a w o r d were presented together for 1 sec, and S was instructed to associate the word with the syllable. Each S was further urged to study each pair for the time that it was presented rather than concentrating upon only a few pairs each time through the list. On T trials, a syllable was shown alone for 2 sec., and S was asked to pronounce the appropriate response unit. The interitem interval was .3 sec. on both L and T trials. A response was designated C if it was given correctly within the 2-sec. exposure of the syllable on T trials. All other responses and omissions were termed N. It was heped that the relatively fast presentation rate would reduce excessive rehearsal within a trial.
17
ONE-TRIAL LEARNING The interval between each L trial and the subsequent T trial was approximately 10 sec., during which time S was told that a series of tests would be given. A 90-sec. interval was used between each T trial and the subsequent L trial to allow E sufficient time to arrange the slides in a new, predetermined, random order. To keep rehearsal at a minimum during the interval between L and T trials, S was given a rest-interval activity which involved drawing lines within the borders of circles, squares, rectangles, and triangles without touching the border lines. The Ss were told that the purpose of this test was to see how steady they were at various stages in learning. Immediately following the learning of the first list, each S was informed that he would be presented with an entirely new list and that his task would be the same as before. For purposes of deciding which list to give to each S, the eight lists were subdivided into the following four pairs: 1 & 2, 3 & 4, 5 & 6, and 7 & 8. Each S learned second whichever list of the pair he had not learned on the first occasion. Lists: Exp. H. The learning materials for Exp. II consisted of two pools of items, one E and the other D, which were obtained in the following m a n ner. Using the data of Exp. I, the trial number on which each item first became C was found for each S. Items which were never C on any of the nine training trials were arbitrarily given a score of 10. Then the median was computed separately for the eight scores obtained when the item appeared in a first-learned list, and for the eight scores obtained from lists learned second. The mean of these two medians defined the difficulty for each of the 96 items. From these, 36 with scores of less than four trials were designated as E, and 36 with scores of four or greater were called D. The mean difficulty was 2.84 for the E pool, and 5.22 for the D pool; the respective standard deviations were .60 and .81. Insofar as possible, items were picked which were low in intra-pool formal similarity of the stimulus members, and low in intra-pool similarity of meaning of the response units. The 36 items within each of the pools was further divided into three lists of 12 items each in such a manner that the mean difficulty of the lists was approximately equated. Procedure: Exp. II. On Day 1, each S commenced with the list to which he had been assigned. Training progressed as in Exp. I, except for the fact that, immediately following each T trial, all C items were replaced by new ones from the remaining items in the pool. Thus, on each trial S studied 12 pairs which, as yet, had never been C. The purpose of this procedure was to control for the possibility of an effective reduction in list length as some items became
C and hence required less attention. If such a reduction occurred, any increase in P,~ could be attributed either to the fact that short lists were learned more readily than longer ones or to an increase in guessing efficiency. Replacements were made so that, on any given trial, no two syllables would begin with the same letter. In order to provide suffÉcient time for E to make the required manipulations, it was necessary to increase the exposure time to 1.5 sec. and 2.5 sec. on L and T trials, respectively, and to increase to 110 sec. the interval between T and L trials. All other intervals were identical to those in Exp. I. Training continued until nine T trials had been given, until all of the original 12 pairs had become C, or until all of the replacement pairs had been used, whichever came first. Then the original 12 items present on the first trial were given another L trial followed by a T trial (T,~,). After 110 sec., half of the Ss in both E and D conditions were simply given another T (Tn+l) on the original 12 pairs and dismissed for the day. The remaining Ss were given 10 additional L trials between T n and "in+ 1. An intertrial interval of 60 sec. was used between the successive L trials, and an interval of 110 sec. was employed between the last L trial and
Tn+l. On Day 2, all Ss were given five successive T trials on the original 12 items of Day 1. The interval between the experimental sessions varied from 19.75 hr. to 28.25 hr., with a mean of 24.28 hr. for Ss given overlearning, and 23.96 hr. for the others. A 60-sec. interval was used between the successive T trials. As in Exp. I, S worked on the rehearsal-prevention task during all intertrial intervals except the 10 sec. between each L and the subsequent T trial. Before each T trial, S was warned that a test was coming and that he should get ready to respond. RESULTS AND DISCUSSION
Experiment I Shift Data. T h e p e r c e n t a g e o f s h i f t s f r o m C on one trial to N on the next were computed separately for E and D items. This was acc o m p l i s h e d b y d i v i d i n g , for e a c h S, t h e t o t a l number of shifts in E items by the total number of E items for which shifts were possible; the same procedure was followed for D items. The means of these values for the E items, expressed in percentages, were 57.1% for the lists learned first and 36.7% for the lists learned second. The analogous values for the D items were 72.5% and 60.8%. The difference between the E and the D pairs was significant, both for the lists
18
WOLLEN
learned first (t ~ 2.20, d/ ~- 63, P < .05) and for the lists learned second (t ~ 4.39, d] - - 63, P < .01). These data pose no problem for a strength theory since it is entirely reasonable that D items acquired increments in associative strength more gradually than E pairs. Consequently, D items would remain in the region of the threshold for more trials and would, therefore, be more likely to drop below. An all-or-none theory, on the other hand, assumes that once an item is C its associative strength is 100%. If the associative strengths of both E and D items were maximal and equal whenever they were C, it is not apparent why the D items were "forgotten" more frequently. Learning. Although the P~ curves were not a major objective of Exp. I, they were, nevertheless, examined. For each S, P~ values were computed by dividing the number of items that were C for the first time on a given trial by the number of items that had never been C prior to that trial. The means of these values for Trials 1 through 4 were .079, .161, .206, and .190 for the lists learned first, and .147, .285, .341, and .350 %r the lists learned second. The data are presented only for the first four trials since some Ss had learned all of the items by Trial 4 and therefore had no scores for the later trials. It is obvious that P~ increased as would be predicted by a strength theory. However, these data must be considered as merely suggestive since there m a y have been an effective reduction in list length as items became C. If so, the apparent increase may have been a result either of the fact that short lists are learned more readily than longer ones, or of increased guessing efficiency. Experiment II Learning. Following the procedure outlined
for Exp. I, P~ values were computed using only the data from the original 12 pairs with which each S commenced. The resulting curves, presented as solid lines in Fig. 2, show a distinct rise which was clearly significant (F = 38.78, d / ~- 1/70, P < .001). The curves continue only to Trial 4 since some Ss met the learning criterion at this point
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and hence had no P~ values for subsequent trials. These data provide strong support for a strength interpretation, but appear totally incompatible with an all-or-none conception. The incompatibility is especially pronounced in view of the fact that the presence of large differences between E and D items strongly suggests that differences would also obtain within each pool. If this were the case, an allor-none theory would predict that both curves would decrease, with the rate of decrease being greater for the E items. An inspection of Fig. 2 reveals that the E curve not only fails to decrease more rapidly, it actually tends to show a more rapid increase. However, the difference in rates did not attain statistical significance (F z 2.36, d] - - 1/70). Even if one were to assume no within-pool differences in difficulty, the data would still be incompatible with a one-trial interpretation since the curves should have been horizontal in such an event. In view of the extreme lack of correspondence of the data to a one-trial theory, other possible explanations were sought. One pos-
19
ONE-TRIAL LEARNING
sibility is that the procedure of replacing each item as soon as it was C was not entirely adequate as a control for an effective reduction in list length. The Ss might have disregarded the replacements and concentrated primarily upon the original 12 pairs. If this were the case, the effective list length would have become shorter as items became C, and either this factor in itself or an increase in guessing efficiency may have resulted in the rise in the curves. As a check on this possibility, the P~ values were recomputed including the data from the replacements as well as the original 12 pairs. The resulting values, represented by the broken-line curves in Fig. 2, were essentially the same as those based only on the original items. This makes the argument that the Ss neglected the replacement items seen unreasonable. The possibility of increased guessing efficiency seems highly unlikely since the chances of a correct guess should have been greatly reduced by the use of words as responses, and by the continual addition of new items to each S's list. Even if guessing efficiency had increased, it is extremely doubtful that it could have accounted for such a marked rise in the curves. Still other criticisms might be offered. As has been indicated, the incremental prediction that the P~ curve will rise is contingent upon a distribution of items which is either unimodal or rectangular. Thus there remains the possibility that the distributions were multimodal, in which case the data could not be construed as support for either theoretical point of view. However, this possibility seems remote in view of the fact that the lists used in Exp. I I were selected so that the distribution of difficulty scores would be approximately normal. Nevertheless, the difficulty scores may approximate a normal distribution for a group of Ss and still be quite differently shaped for individuals (e.g., J shaped, positively or negatively skewed, etc.). However, there is no apparent reason to believe that this departure from normality would result in multimodM distributions, and the predictions of an incremental theory would hold so long as the shapes were not multimodal. The question might also be raised as to
whether the P~ curve for some Ss might decrease although the curve for the entire group increased. More specifically, the P~ values might increase for fast learners but decrease for slow learners, or vice versa. To check on this possibility, values of P~ were computed for the fastest and the slowest learners within each level of item difficulty. Estimates of the speed of learning were obtained by dividing the total number of correct responses on all trials prior to Trial L~ by the number of trials taken to reach that point. Then the Ss were rank ordered on the basis of these values. Of the 36 Ss in the easy condition, P~ curves were found for the 9 fastest and the 9 slowest. Considering first only the data from the original 12 pairs, the P~ values for Trials 1 through 4 were .28, .40, .47, and .56 for the fast learners, and .06, .15, .18, and .13 for the slow learners. The analogous values for the Ss given difficult items were .13, .36, .33, and .41 for the fast learners, and .05, .06, .11, and .18 for the slow learners. As is immediately evident, these values increase for both fast and slow learners and for difficult as well as easy items. Essentially the same results were obtained when the replacement items were included in the analysis. Thus the rise in the curves shown in Fig. 2 could not be attributed to some artifact of the combination of data from fast and slow learners since the curves rise for both. Retention. For a measure of the effects of overlearning upon immediate retention, the percentages of C~+~:Cn (which is to be read, "percentage of C items on T~ that were C on T~+I") were computed separately for each S. The means of these individual percentages, disregarding the factor of list difficulty, are shown in the first row of Table 1. As would be expected from an incremental point of view, the Ss given overlearning recalled significantly more (F ~ 9.91, d] ~ 1/68, P < .01). This confirms a similar finding in TABLE 1 MEAN PERCENTAGE RETENTION ON DAY 2
Retention interval Immediate Delayed
No overlearning 78.6 66.8
Ten trials overlearning 92.2 83.0
20
WOLLEN
Exp. I of Estes et al. (1960). These Es found that the percentage of C2:C1 was 71% for items given in an L1 T1 T2 sequence, but was increased to 86% by the insertion of another L trial between T1 and T2. The effects of overlearning upon delayed retention were investigated by computing, for each S, the percentage of C items on T~ that were also C on T1 of D a y 2. The means of these values are presented in Row 2 of Table 1. The increase of 16.2% in recall for the Ss receiving overlearning was also significant (F = 9.28, d/--~ 1/68, P ~ .01). The overlearning data are clearly negative to an all-or-none theory since such a view maintains that once an item is C its associative strength is maximal. Consequently, overlearning should not have increased the amount of retention. The data are, however, in complete accord with a strength interpretation. At this point, an all-or-none theorist might argue that some responses were C on T~ due only to guessing, and that these responses had additional opportunities to become learned only for Ss given overlearning. If this were the case, the greater retention as a function of overlearning would not be surprising. As a check on this possibility, the data from both immediate and delayed retention were reanalyzed considering only the retention of C items on T~ which had also been C at some point in the previous training. I t was found that overlearning increased immediate retention from 82.7% to 93.0% and delayed retention from 70.1% to 83.6%. As an even more stringent check, the D a y 2 retention was computed for items which had been C on Tn+l as well as C on T~ and during previous training. In this case, overlearning still increased retention from 76.0% to 86.0%. Inasmuch as each item in these analyses had been C on two or more separate occasions, it is most doubtful that guessing had inflated the number of C responses on T~ to any appreciable degree. Consequently, it may be concluded that overlearning did, in fact, increase retention, and that a strength interpretation is indicated. In both the immediate and delayed retention analyses, the loss suffered by E items was significantly less than that for D pairs. This
strongly suggests that the associative strength of E pairs was greater than for D pairs. Such a consequence is incompatible with an all-ornone theory since the associative strength of both E and D items should have been maximal and equal. Thus there would be no reason to expect I) items to be forgotten more readily according to such a view. M e a n Correct on D a y 2. One of the main tenets of all-or-none theories has been that the occurrence of an N response indicates zero associative strength for that item. If this were the case, the mean number of C responses should have remained constant over the five T trials on D a y 2. However, the means for Trials 1 to 5 were 7.14, 7.47, 7.85, 7.78, and 8.03. The difference between Trials 1 and 5, which represents a gain of nearly one item, was significant (t z 6.08, d] ~ 71, P < .01). These data confirm a similar finding by Richardson (1958). Such findings are extremely difficult to reconcile with the all-ornone approach since they are strong evidence that at least some of the N items on T1 of Day 2 had a non-zero value of associative strength. Although Estes et al. attributed a similar rise to increased guessing efficiency, it is extremely doubtful that this factor could have accounted for the present results since the use of such a large number of items on Day 1 would greatly decrease the probability of a correct guess on D a y 2. A strength theorist might account for the gradual increase in number correct by invoking the concept of oscillatory inhibition (Spence, 1956). Since oscillatory inhibition is assumed to result from uncontrolled factors, it seems reasonable to argue that the number and extent of these factors would decrease as the S became readjusted to the situation. Therefore the increase in the mean number correct over the five T trials would be expected since progressively less inhibition would be present to subtract from the tendency to make the correct response. Another possibility is that the correct response tendencies become strengthened due to the fact that the Ss "know" when t h e y are correct. In summary, the data from the experiments reported herein provide compelling support for an incremental interpretation of learning
ONE-TRIAL LEARNING
but appear incompatible with an all-or-none conception. I t is undoubtedly the case that present all-or-none theories can be modified to account for these data. However, it would be extremely difficult to make such modifications in a manner that would enable the theories to account for all aspects of the data and at the same time avoid using an incremental factor of some variety. Perhaps the most likely candidate for a theory which would retain at least an element of the allor-none principle would be Estes' earlier (1959) version of a statistical learning theory. This approach assumes all-or-none learning with respect to individual stimulus elements, but predicts a gradual increase in the probability of a correct response rather than a jump from 0 to 1.00 in a single trial. Such a theory could handle the present data, but, of course, this formulation incorporates an incremental factor and therefore essentially reduces to an incremental theory. SUM:~/[ARY
Two experiments were conducted to test several implications of incremental and allor-none theories of learning. I n both experiments, Ss were given alternate learning and test trials on lists of word responses paired with consonant-syllable stimuli. The major findings were: (1) items learned late in training (difficult items) showed more shifts from correct on one trial to non-correct on the next than did those learned earlier (easy items); (2) the proportion of items never previously correct which became correct on each trial increased with training; (3) over-
21
learning increased both immediate and delayed retention; (4) the mean number of correct responses gradually increased over a series of five successive recall trials in spite of the fact that no learning trials were given. These findings were interpreted as compelling evidence for an incremental theory of learning, but incompatible with present all-or-none formulations. REFERENCES
ESTES, W. K. The statistical approach to learning theory. In S. Koch (Ed.), Psychology: A study ol a science. Vol. 2. New York: McGraw-Hill, 1959, Pp. 380-491. ESTES, W. K. Learning theory and the new :'mental chemistry." Psychol. Rev., 1960, 67, 207-223. ESTES, W. K., HOPKINS, B. L., AND CROTHERS, E. J. All-or-none and conservation effects in the learning and retention of paired associates. J. exp. Psychot., 1960, 60, 329-339. HULL, C. L. Principles o] behavior. New York: Appleton-Century, 1943. POSTMAN, L. Repetition and paired-associate learning. Amer. J. Psychol., in press. RICHARDSON, J. The relationship of stimulus similarity and number of responses. J. exp. Psychol., 1958, ~6, 478-484. RocK, I. The role of repetition in associative learning. Amer. J. Psychol., 1957, 70, 186-193. SPENCE, K. W. Behavior theory and conditioning. New Haven: Yale Univer. Press, 1956. TItORNDIKE,E. L., ANn LORGE,I. The teacher's wordbook o] 30,000 words. New York: Columbia Univer. Press, 1944. UNDERWOOD, B..[., REttULA, R., AND KEPPEL, G. Item selection in paired-associate learning. Amer. J. Psychol., in press.
(Received March 3, 1962)
One-Trial Versus Incremental-Paired Associate Learning ~ KEITH A.
WOLLEN 2
State University o] Iowa, Iowa City, Iowa
In contrast with the traditional view that associations are formed gradually, Estes (1960) has recently espoused a theory that, on any given trial, associative strength either increases from 0% to 100% or does not increase at all. 3 Data allegedly in support of this all-or-none interpretation were reported by Estes, Hopkins, and Crothers (1960). These Es presented both members of pairedassociate items for one learning (L) trial followed by two successive test (T) trials on which only the stimulus member was shown. The sequence was thus L1 T1 T2. Both in that report and elsewhere (Estes, 1960), primary emphasis was placed upon the fact that the proportion of non-correct (N) items on T1 that became correct (C) on T2, henceforth abbreviated as C2:N1, was nearly zero. Estes argued that this proportion should have been greater than zero if N items had received associative strengthening on L~. On this basis, he concluded that these data support an allor-none theory but "appear incompatible with any theory which expresses learning in terms of increments" (Estes et al., 1960, p. 338). However, such conclusions seem unjustified on several accounts. In the first place, there is a strong possibility that the N items on T1 were more
difficult than the C pairs, in which case the increments in associative strength might not have been large enough to have been detected. Estes reasoned that this could not have been the case since the proportion of C2:N1 for items presented in an L1 T1 L2 T2 sequence was as large as the proportion correct on T1. However, such reasoning is most tenuous in view of the fact that the length of the list was reduced from eight items on L1 to four on L2 (of which an average of 40% had been C on T1), and the additional fact that short lists are learned more readily than long ones. Moreover, the two proportions might be expected to be approximately equal purely from the fact that the strengthening accrued on L1 may have offset the disadvantage of being more difficult. Secondly, although contrary to Estes' (1959) incremental theory, the extremely low proportion of C2:N1 for items presented in an L1 T1 T2 sequence is perfectly consonant with theories which incorporate the concept of a threshold (e.g., Hull, 1943; Spence, 1956). Such theories predict that response probability will remain zero until the excitatory strength has become superthreshold. Consequently, it is most reasonable that the N items on T1 had received an increment in associative strength even though few of these items became C on T2. Furthermore, the low proportion of C2:N1 might merely be the result of the fact that the N items, which were already below threshold, suffered some decrement due to "forgetting" and dropped even further below. Even if one were to grant that the C2:N1 data were evidence that N items on T1 had acquired no associative strength on L~, there would be no evidence that increments would be all-or-none in character when they
1 This paper is based upon a doctoral dissertation s u b m i t t e d to t h e State University of Iowa. T h e a u t h o r is indebted to R u d o l p h W. Schulz for his advice a n d assistance t h r o u g h o u t the course of this investigation. 2 N o w at W a s h i n g t o n State University, Pullman, Washington. A similar theory (Rock, 1957) h a s received extensive consideration elsewhere (e.g., P o s t m a n , in press; Underwood, Rehula, a n d Keppel, in press) and will n o t be considered here. 14
ONE-TRIAL LEARNING
do occur. I t would still be possible for response probability to remain zero for a few trials and then increase gradually. Finally, the use of a 4-sec. exposure time, a 4-sec. interitem interval, and a 60-sec. interlist interval probably encouraged rehearsal to the extent that essentially several "trials" were given with each presentation of the list. This fact alone would seem to preclude the interpretation of the above data as support for a one-trial theory. Estes has also indicated that according to his theory overlearning should not increase retention. In both paired-associate and free verbal recall experiments, he found that the proportion of C2:C1 was as large for items given in an L1 T1 T2 sequence as for those administered in an L1 L2 T1 T2 fashion. On the basis of these data, Estes concluded that "we must face the possibility that this empirical relation [that overlearning increases retention], like the classical acquisition curve, is an artifact of the confoundings inherent in the usual experimental paradigm" (Estes, 1960, p. 220). However, Estes' design itself was not entirely free of "confoundings." Had there been some way of assessing when each item became C, it would undoubtedly have been found that some items became superthreshold on L1 and others on L2. Thus it is not surprising that retention did not differ for the two conditions since a large proportion of the items in the L1 L2 T1 T2 condition were probably given no overlearning. Due to the equivocal nature of the evidence interpreted as support for the all-or-none conception, an attempt was made to design further tests of the theoretical alternatives which would be relatively free of the previously mentioned shortcomings. Basically, the following experiments demonstrate that the occurrence of an N response does not necessarily indicate that the associative strength of that response is zero. The primary test used in the following experiments is one suggested by Estes (1960, p. 217) as providing a "quite sharp" test of one-trial and incremental theories in the case of eyelid conditioning. The test, applied here to paired-associate learning, involves a trialby-trial analysis of the proportion (P~), where
15
P~ is defined as the ratio of the number of items which become C for the first time on Trial n to the number of items that have never been C prior to that trial. According to an all-or-none theory, each item in a list would have a certain fixed probability of being learned. This probability should remain constant over trials due to the assumption that N items have received no associative strengthening. However, the items that actually become C on each trial would tend to be those with the higher probabilities. Consequently, as training proceeded, the group of N items upon which P~ is based would become progressively more reduced to difficult pairs with low probabilities. Thus P~ should decrease as n increases. Moreover, the rate of decrease should be greater for easy lists than for equally-variable difficult ones since a larger proportion of the items would become C on each trial. In the unlikely event that all items were equally difficult, the theory would predict constant values of P~ over trials. This theory, incidentally, would have difficulty handling any situation in which the Ss learn all of the items inasmuch as the last P~ value in such cases must be 1.00. In sharp contrast, an incremental theory of the variety outlined in Fig. 1 predicts that Pn would increase with training. The upended distributions in Fig. 1 represent a list of items which differ in difficulty. In this theory, dif40, ,r\
[ ',, I
"4 , ',
,:
I
Z
I ij
f
20
o l0
I
I
I
I
3
4
5
6
TRIAL
FIG. 1. Hypothetical growth of associative strength as a function of training trials for a distribution of items differing in difficulty. All units are completely arbitrary.
16
WOLLEN
ficulty may be based on initial differences in associative strength, on rates of growth, or on some combination of these two factors. The distributions are displaced upward as training progresses to represent the assumption that associative strength increases in a negatively accelerated fashion. Assuming that an item will become C when its associative strength becomes superthreshold, P , for a given trial would be the ratio of the shaded area for that trial to the area below threshold on the previous trial. As is apparent, these values would increase throughout training. Moreover, if difficulty is based on different rates of growth of associative strength, P~ would increase more rapidly for easy lists than for difficult ones since a larger proportion of the distribution would become superthreshold on each trial. Although the distributions in Fig. 1 are normal, the predictions would apply equally well to any unimodal or rectangular distribution. The present purpose is not to expound a particular incremental theory, but merely to demonstrate how such a formulation might account for the data. The major objective of Exp. I was to select two pools of items, one easy (E) and the other difficult (D), for use in Exp. II. A second objective was to test the apparent implication of an all-or-none theory that I) items should show no more shifts from C on one trial to N on the next than would E items. If, as Estes (1960) has maintained, an item becomes completely conditioned in one trial, it would seem to follow that the associative strength of both E and D items would be maximal and equal when both are C, and that E items would be "forgotten" as readily as D pairs. If D items were to accumulate associative strength more slowly than E items, an incremental theory would predict that the D pairs would remain in the region of the threshold for more trials and hence would be more likely to shift from C to N. The major objective of Exp. I I was to see whether the data support the all-or-none view that P~ would decrease more rapidly for E items than for D pairs, or the incremental interpretation that P , would increase in both instances. A second objective was to examine the effect of overlearning upon immediate and
delayed retention. According to Estes' all-ornone view, once an item becomes C, its associative strength is maximal and further learning trials should not increase subsequent retention. An incremental position, on the other hand, would be that strengthening is not necessarily complete when an item first becomes C. Therefore, overlearning should increase retention by strengthening associations further so that they would be less likely to drop below threshold. METHOD Subjects. The Ss were 136 students from the introductory psychology course at the State University of Iowa. All were naive with respect to verbal learning. A total of 8 Ss was assigned at random to each of eight lists in Exp. I. In Exp. II, 18 Ss were randomly assigned to each of four conditions. Apparatus. A 3 X 5.5 in. translucent screen was mounted in a 4 X 6 ft. opaque panel which also served to separate E from S. The learning materials were projected from behind the screen by means of a 2 X 2 in. LaBelle Professional "88" slide projector. The learning materials appeared as .25-in. high black letters on a white background. The slides used on L trials contained both stimulus and response units. The slides used on T trials were identical in every respect to those used on L trials except for the omission of the response member. Decade interval timers were employed to control the exposure, interitem, and intertrial intervals. Lists: Exp. I. The learning materials consisted of 96 consonant syllables paired randomly with 96 AA nouns taken from the Thorndike-Lorge list (1944). These 96 pairs were divided into eight lists of 12 items each such that no 2 syllables in any one list began with the same consonant. Procedure: Exp. I. Each S was given nine L and nine T trials, in alternate fashion, on the list to which he had been assigned. On L trials, a consonant syllable and a w o r d were presented together for 1 sec, and S was instructed to associate the word with the syllable. Each S was further urged to study each pair for the time that it was presented rather than concentrating upon only a few pairs each time through the list. On T trials, a syllable was shown alone for 2 sec., and S was asked to pronounce the appropriate response unit. The interitem interval was .3 sec. on both L and T trials. A response was designated C if it was given correctly within the 2-sec. exposure of the syllable on T trials. All other responses and omissions were termed N. It was heped that the relatively fast presentation rate would reduce excessive rehearsal within a trial.
17
ONE-TRIAL LEARNING The interval between each L trial and the subsequent T trial was approximately 10 sec., during which time S was told that a series of tests would be given. A 90-sec. interval was used between each T trial and the subsequent L trial to allow E sufficient time to arrange the slides in a new, predetermined, random order. To keep rehearsal at a minimum during the interval between L and T trials, S was given a rest-interval activity which involved drawing lines within the borders of circles, squares, rectangles, and triangles without touching the border lines. The Ss were told that the purpose of this test was to see how steady they were at various stages in learning. Immediately following the learning of the first list, each S was informed that he would be presented with an entirely new list and that his task would be the same as before. For purposes of deciding which list to give to each S, the eight lists were subdivided into the following four pairs: 1 & 2, 3 & 4, 5 & 6, and 7 & 8. Each S learned second whichever list of the pair he had not learned on the first occasion. Lists: Exp. H. The learning materials for Exp. II consisted of two pools of items, one E and the other D, which were obtained in the following m a n ner. Using the data of Exp. I, the trial number on which each item first became C was found for each S. Items which were never C on any of the nine training trials were arbitrarily given a score of 10. Then the median was computed separately for the eight scores obtained when the item appeared in a first-learned list, and for the eight scores obtained from lists learned second. The mean of these two medians defined the difficulty for each of the 96 items. From these, 36 with scores of less than four trials were designated as E, and 36 with scores of four or greater were called D. The mean difficulty was 2.84 for the E pool, and 5.22 for the D pool; the respective standard deviations were .60 and .81. Insofar as possible, items were picked which were low in intra-pool formal similarity of the stimulus members, and low in intra-pool similarity of meaning of the response units. The 36 items within each of the pools was further divided into three lists of 12 items each in such a manner that the mean difficulty of the lists was approximately equated. Procedure: Exp. II. On Day 1, each S commenced with the list to which he had been assigned. Training progressed as in Exp. I, except for the fact that, immediately following each T trial, all C items were replaced by new ones from the remaining items in the pool. Thus, on each trial S studied 12 pairs which, as yet, had never been C. The purpose of this procedure was to control for the possibility of an effective reduction in list length as some items became
C and hence required less attention. If such a reduction occurred, any increase in P,~ could be attributed either to the fact that short lists were learned more readily than longer ones or to an increase in guessing efficiency. Replacements were made so that, on any given trial, no two syllables would begin with the same letter. In order to provide suffÉcient time for E to make the required manipulations, it was necessary to increase the exposure time to 1.5 sec. and 2.5 sec. on L and T trials, respectively, and to increase to 110 sec. the interval between T and L trials. All other intervals were identical to those in Exp. I. Training continued until nine T trials had been given, until all of the original 12 pairs had become C, or until all of the replacement pairs had been used, whichever came first. Then the original 12 items present on the first trial were given another L trial followed by a T trial (T,~,). After 110 sec., half of the Ss in both E and D conditions were simply given another T (Tn+l) on the original 12 pairs and dismissed for the day. The remaining Ss were given 10 additional L trials between T n and "in+ 1. An intertrial interval of 60 sec. was used between the successive L trials, and an interval of 110 sec. was employed between the last L trial and
Tn+l. On Day 2, all Ss were given five successive T trials on the original 12 items of Day 1. The interval between the experimental sessions varied from 19.75 hr. to 28.25 hr., with a mean of 24.28 hr. for Ss given overlearning, and 23.96 hr. for the others. A 60-sec. interval was used between the successive T trials. As in Exp. I, S worked on the rehearsal-prevention task during all intertrial intervals except the 10 sec. between each L and the subsequent T trial. Before each T trial, S was warned that a test was coming and that he should get ready to respond. RESULTS AND DISCUSSION
Experiment I Shift Data. T h e p e r c e n t a g e o f s h i f t s f r o m C on one trial to N on the next were computed separately for E and D items. This was acc o m p l i s h e d b y d i v i d i n g , for e a c h S, t h e t o t a l number of shifts in E items by the total number of E items for which shifts were possible; the same procedure was followed for D items. The means of these values for the E items, expressed in percentages, were 57.1% for the lists learned first and 36.7% for the lists learned second. The analogous values for the D items were 72.5% and 60.8%. The difference between the E and the D pairs was significant, both for the lists
18
WOLLEN
learned first (t ~ 2.20, d/ ~- 63, P < .05) and for the lists learned second (t ~ 4.39, d] - - 63, P < .01). These data pose no problem for a strength theory since it is entirely reasonable that D items acquired increments in associative strength more gradually than E pairs. Consequently, D items would remain in the region of the threshold for more trials and would, therefore, be more likely to drop below. An all-or-none theory, on the other hand, assumes that once an item is C its associative strength is 100%. If the associative strengths of both E and D items were maximal and equal whenever they were C, it is not apparent why the D items were "forgotten" more frequently. Learning. Although the P~ curves were not a major objective of Exp. I, they were, nevertheless, examined. For each S, P~ values were computed by dividing the number of items that were C for the first time on a given trial by the number of items that had never been C prior to that trial. The means of these values for Trials 1 through 4 were .079, .161, .206, and .190 for the lists learned first, and .147, .285, .341, and .350 %r the lists learned second. The data are presented only for the first four trials since some Ss had learned all of the items by Trial 4 and therefore had no scores for the later trials. It is obvious that P~ increased as would be predicted by a strength theory. However, these data must be considered as merely suggestive since there m a y have been an effective reduction in list length as items became C. If so, the apparent increase may have been a result either of the fact that short lists are learned more readily than longer ones, or of increased guessing efficiency. Experiment II Learning. Following the procedure outlined
for Exp. I, P~ values were computed using only the data from the original 12 pairs with which each S commenced. The resulting curves, presented as solid lines in Fig. 2, show a distinct rise which was clearly significant (F = 38.78, d / ~- 1/70, P < .001). The curves continue only to Trial 4 since some Ss met the learning criterion at this point
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TRIAL FIO. 2. M e a n proportion (Yn) of items never previously correct which became correct on each trial. T h e solid curves are based on the original 12 items only, whereas the broken curves are based on the original 12 items plus all replacement pairs used.
and hence had no P~ values for subsequent trials. These data provide strong support for a strength interpretation, but appear totally incompatible with an all-or-none conception. The incompatibility is especially pronounced in view of the fact that the presence of large differences between E and D items strongly suggests that differences would also obtain within each pool. If this were the case, an allor-none theory would predict that both curves would decrease, with the rate of decrease being greater for the E items. An inspection of Fig. 2 reveals that the E curve not only fails to decrease more rapidly, it actually tends to show a more rapid increase. However, the difference in rates did not attain statistical significance (F z 2.36, d] - - 1/70). Even if one were to assume no within-pool differences in difficulty, the data would still be incompatible with a one-trial interpretation since the curves should have been horizontal in such an event. In view of the extreme lack of correspondence of the data to a one-trial theory, other possible explanations were sought. One pos-
19
ONE-TRIAL LEARNING
sibility is that the procedure of replacing each item as soon as it was C was not entirely adequate as a control for an effective reduction in list length. The Ss might have disregarded the replacements and concentrated primarily upon the original 12 pairs. If this were the case, the effective list length would have become shorter as items became C, and either this factor in itself or an increase in guessing efficiency may have resulted in the rise in the curves. As a check on this possibility, the P~ values were recomputed including the data from the replacements as well as the original 12 pairs. The resulting values, represented by the broken-line curves in Fig. 2, were essentially the same as those based only on the original items. This makes the argument that the Ss neglected the replacement items seen unreasonable. The possibility of increased guessing efficiency seems highly unlikely since the chances of a correct guess should have been greatly reduced by the use of words as responses, and by the continual addition of new items to each S's list. Even if guessing efficiency had increased, it is extremely doubtful that it could have accounted for such a marked rise in the curves. Still other criticisms might be offered. As has been indicated, the incremental prediction that the P~ curve will rise is contingent upon a distribution of items which is either unimodal or rectangular. Thus there remains the possibility that the distributions were multimodal, in which case the data could not be construed as support for either theoretical point of view. However, this possibility seems remote in view of the fact that the lists used in Exp. I I were selected so that the distribution of difficulty scores would be approximately normal. Nevertheless, the difficulty scores may approximate a normal distribution for a group of Ss and still be quite differently shaped for individuals (e.g., J shaped, positively or negatively skewed, etc.). However, there is no apparent reason to believe that this departure from normality would result in multimodM distributions, and the predictions of an incremental theory would hold so long as the shapes were not multimodal. The question might also be raised as to
whether the P~ curve for some Ss might decrease although the curve for the entire group increased. More specifically, the P~ values might increase for fast learners but decrease for slow learners, or vice versa. To check on this possibility, values of P~ were computed for the fastest and the slowest learners within each level of item difficulty. Estimates of the speed of learning were obtained by dividing the total number of correct responses on all trials prior to Trial L~ by the number of trials taken to reach that point. Then the Ss were rank ordered on the basis of these values. Of the 36 Ss in the easy condition, P~ curves were found for the 9 fastest and the 9 slowest. Considering first only the data from the original 12 pairs, the P~ values for Trials 1 through 4 were .28, .40, .47, and .56 for the fast learners, and .06, .15, .18, and .13 for the slow learners. The analogous values for the Ss given difficult items were .13, .36, .33, and .41 for the fast learners, and .05, .06, .11, and .18 for the slow learners. As is immediately evident, these values increase for both fast and slow learners and for difficult as well as easy items. Essentially the same results were obtained when the replacement items were included in the analysis. Thus the rise in the curves shown in Fig. 2 could not be attributed to some artifact of the combination of data from fast and slow learners since the curves rise for both. Retention. For a measure of the effects of overlearning upon immediate retention, the percentages of C~+~:Cn (which is to be read, "percentage of C items on T~ that were C on T~+I") were computed separately for each S. The means of these individual percentages, disregarding the factor of list difficulty, are shown in the first row of Table 1. As would be expected from an incremental point of view, the Ss given overlearning recalled significantly more (F ~ 9.91, d] ~ 1/68, P < .01). This confirms a similar finding in TABLE 1 MEAN PERCENTAGE RETENTION ON DAY 2
Retention interval Immediate Delayed
No overlearning 78.6 66.8
Ten trials overlearning 92.2 83.0
20
WOLLEN
Exp. I of Estes et al. (1960). These Es found that the percentage of C2:C1 was 71% for items given in an L1 T1 T2 sequence, but was increased to 86% by the insertion of another L trial between T1 and T2. The effects of overlearning upon delayed retention were investigated by computing, for each S, the percentage of C items on T~ that were also C on T1 of D a y 2. The means of these values are presented in Row 2 of Table 1. The increase of 16.2% in recall for the Ss receiving overlearning was also significant (F = 9.28, d/--~ 1/68, P ~ .01). The overlearning data are clearly negative to an all-or-none theory since such a view maintains that once an item is C its associative strength is maximal. Consequently, overlearning should not have increased the amount of retention. The data are, however, in complete accord with a strength interpretation. At this point, an all-or-none theorist might argue that some responses were C on T~ due only to guessing, and that these responses had additional opportunities to become learned only for Ss given overlearning. If this were the case, the greater retention as a function of overlearning would not be surprising. As a check on this possibility, the data from both immediate and delayed retention were reanalyzed considering only the retention of C items on T~ which had also been C at some point in the previous training. I t was found that overlearning increased immediate retention from 82.7% to 93.0% and delayed retention from 70.1% to 83.6%. As an even more stringent check, the D a y 2 retention was computed for items which had been C on Tn+l as well as C on T~ and during previous training. In this case, overlearning still increased retention from 76.0% to 86.0%. Inasmuch as each item in these analyses had been C on two or more separate occasions, it is most doubtful that guessing had inflated the number of C responses on T~ to any appreciable degree. Consequently, it may be concluded that overlearning did, in fact, increase retention, and that a strength interpretation is indicated. In both the immediate and delayed retention analyses, the loss suffered by E items was significantly less than that for D pairs. This
strongly suggests that the associative strength of E pairs was greater than for D pairs. Such a consequence is incompatible with an all-ornone theory since the associative strength of both E and D items should have been maximal and equal. Thus there would be no reason to expect I) items to be forgotten more readily according to such a view. M e a n Correct on D a y 2. One of the main tenets of all-or-none theories has been that the occurrence of an N response indicates zero associative strength for that item. If this were the case, the mean number of C responses should have remained constant over the five T trials on D a y 2. However, the means for Trials 1 to 5 were 7.14, 7.47, 7.85, 7.78, and 8.03. The difference between Trials 1 and 5, which represents a gain of nearly one item, was significant (t z 6.08, d] ~ 71, P < .01). These data confirm a similar finding by Richardson (1958). Such findings are extremely difficult to reconcile with the all-ornone approach since they are strong evidence that at least some of the N items on T1 of Day 2 had a non-zero value of associative strength. Although Estes et al. attributed a similar rise to increased guessing efficiency, it is extremely doubtful that this factor could have accounted for the present results since the use of such a large number of items on Day 1 would greatly decrease the probability of a correct guess on D a y 2. A strength theorist might account for the gradual increase in number correct by invoking the concept of oscillatory inhibition (Spence, 1956). Since oscillatory inhibition is assumed to result from uncontrolled factors, it seems reasonable to argue that the number and extent of these factors would decrease as the S became readjusted to the situation. Therefore the increase in the mean number correct over the five T trials would be expected since progressively less inhibition would be present to subtract from the tendency to make the correct response. Another possibility is that the correct response tendencies become strengthened due to the fact that the Ss "know" when t h e y are correct. In summary, the data from the experiments reported herein provide compelling support for an incremental interpretation of learning
ONE-TRIAL LEARNING
but appear incompatible with an all-or-none conception. I t is undoubtedly the case that present all-or-none theories can be modified to account for these data. However, it would be extremely difficult to make such modifications in a manner that would enable the theories to account for all aspects of the data and at the same time avoid using an incremental factor of some variety. Perhaps the most likely candidate for a theory which would retain at least an element of the allor-none principle would be Estes' earlier (1959) version of a statistical learning theory. This approach assumes all-or-none learning with respect to individual stimulus elements, but predicts a gradual increase in the probability of a correct response rather than a jump from 0 to 1.00 in a single trial. Such a theory could handle the present data, but, of course, this formulation incorporates an incremental factor and therefore essentially reduces to an incremental theory. SUM:~/[ARY
Two experiments were conducted to test several implications of incremental and allor-none theories of learning. I n both experiments, Ss were given alternate learning and test trials on lists of word responses paired with consonant-syllable stimuli. The major findings were: (1) items learned late in training (difficult items) showed more shifts from correct on one trial to non-correct on the next than did those learned earlier (easy items); (2) the proportion of items never previously correct which became correct on each trial increased with training; (3) over-
21
learning increased both immediate and delayed retention; (4) the mean number of correct responses gradually increased over a series of five successive recall trials in spite of the fact that no learning trials were given. These findings were interpreted as compelling evidence for an incremental theory of learning, but incompatible with present all-or-none formulations. REFERENCES
ESTES, W. K. The statistical approach to learning theory. In S. Koch (Ed.), Psychology: A study ol a science. Vol. 2. New York: McGraw-Hill, 1959, Pp. 380-491. ESTES, W. K. Learning theory and the new :'mental chemistry." Psychol. Rev., 1960, 67, 207-223. ESTES, W. K., HOPKINS, B. L., AND CROTHERS, E. J. All-or-none and conservation effects in the learning and retention of paired associates. J. exp. Psychot., 1960, 60, 329-339. HULL, C. L. Principles o] behavior. New York: Appleton-Century, 1943. POSTMAN, L. Repetition and paired-associate learning. Amer. J. Psychol., in press. RICHARDSON, J. The relationship of stimulus similarity and number of responses. J. exp. Psychol., 1958, ~6, 478-484. RocK, I. The role of repetition in associative learning. Amer. J. Psychol., 1957, 70, 186-193. SPENCE, K. W. Behavior theory and conditioning. New Haven: Yale Univer. Press, 1956. TItORNDIKE,E. L., ANn LORGE,I. The teacher's wordbook o] 30,000 words. New York: Columbia Univer. Press, 1944. UNDERWOOD, B..[., REttULA, R., AND KEPPEL, G. Item selection in paired-associate learning. Amer. J. Psychol., in press.
(Received March 3, 1962)