the generality of the retention interval model

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The Generality of the RetentionInterval ModelChizuko Izawa aa Tulane University , USAPublished online: 06 Jul 2010.

To cite this article: Chizuko Izawa (1983) The Generality of the RetentionInterval Model, The Journal of General Psychology, 108:1, 113-134, DOI:10.1080/00221309.1983.9711485

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The Journal of General Psychology, 1983, 108, 113-134.

T H E GENERALITY OF THE RETENTION INTERVAL MODEL*'

Tulune University

CHIZUKO IZAWA

SUMMARY Elaborations and refinements were made for core constructs of the reten-

tion interval (RI) model that specified a major difference between anticipation and study-test methods to be short-term memory (STM) processes in differential retention intervals. Subsequent developments reinforce the model and suggest that basic processes per each type of event are, respectively, the same for both methods (except for quantitatively differential retention intervals t the identity hypothesis. The RI model unveiled another major factor, learning difficulty, that controls performance differences between the two methods. By encompassing new developments, the generality of the RI model was tested in a variety of situations. The model seems to hold firmly for a wide range of paired-associate and verbal discrimination learning paradigms including such cross-variations as the following: mixed vs. unmixed list design, constant vs. random item presentation orders, forward vs. backward associations, part vs. whole list designs, and visual vs. auditory modalities. Other theories, in contrast, seem to lack mechanisms to cope with inconsistent data, prevalent throughout the vast scope of learning situations.

A. INTERVAL MODEL

The retention interval (RI) model (46) was formulated to account for varied performance differences between anticipation and study-test (rein-

* Received in the Editorial Office, Provincetown, Massachusetts, on August 31, 1982. Copyright, 1983, by the Journal Press.

' The present research was supported in part by BRSG Grant SO7 RR07040, awarded by the Biomedical Research Support Grant Program, Division of Research Resources, National Insti- tutes of Health. The author is grateful to Professor Moriji Sagara for his comments, and to Kim Vaz for her general clerical assistance.

Requests for reprints should be directed to the author at the address shown at the end of this article.

ANTICIPATION AND STUDY-TEST METHODS AND THE RETENTION

113

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114 JOURNAL O F GENERAL PSYCHOLOGY

forcement-test, RT) methods prevalent in the literature, for which no ade- quate account was available for decades. The feedback position based on Skinner’s operant conditioning principle, the anticipation method, illus- trated by Equation 1 in Figure 1 (the same principle that holds for the “teaching machine”), should be superior to the study-test method expressed by Equation 2 . In these equations, a and b, respectively, stand for the stimulus and response terms of a pair for an n-item list in paired-associate learning (PAL) with a randomized presentation order from cycle to cycle, and subscripts identify individual items (1 n) . The theoretical expecta- tion follows from the fact that the former enjoys immediate feedback, while the latter does not. The feedback position, however, has not yet seen empirical support to any substantial degree.

In contrast, the task alteration position (e.g., 8) assumes that the anticipation method, where studying and testing tasks are always intermixed and thereby confusing to the S, would be inferior to the study-test method where no such confusion exists. Similarly, the differential acquisition position (e.g., 55) also assumes better learning for the study-test than the anticipation method. The latter positions are often supported by data, but only to a limited degree. Quite mysteriously, other data also frequently show that performance levels for the two methods are nearly the same: for references, see, for example, Izawa, Hayden, and Isham (51) and Kanak, Cole, and Eckert (5 6).

None of the above positions can accommodate the negligible differences between the two methods. To fully account for all data resulting in either large or small superiority of the study-test method vis-8-vis the anticipation method, a viable theory must encompass both types of results. To this end, the retention interval (RI) model was formulated on the basis of the retention (S-T) interval-the period between an item presented as a study (S) event, boxed in solid lines, and its test (T) event, boxed in broken lines for I t e m j in Equations 1 and 2 , respectively-for an individual item, frequently being longer under the anticipation method than under the study-test method in terms of intervening events (cf. 36, 37, 38).

The retention (S-T) interval with the anticipation method contains from 0 to 4n - 4 intervening events, with a mean of 2n - 2, while that with the study-test method has from 0 to 2n - 2 intervening events with a mean of n - 1; these intervening events are known to distribute triangularly (probability density functions) as entered in Figure 2 [adopted from Izawa (36)l. Given the identical lower limits and different upper limits, the two triangular distributions necessarily overlap. The overlap area shows that the reten-

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CHIZUKO IZAWA 115

- a3- , a3-b3, a6- , at-b6. ... ,, 0.- 1, aj-bj, ... , a4- , a4-br.

a,-b,, a2-b2, ... ,I.J-"J) ... , a,,-b,,; IInttencyCcL IntCnvatl;

a3- , ai- , ... .:%- 1, ... , a4- ; frntencycte ~ n t m v a t ~ ; a6-b6, aj-bj, .. . , an-b,,, . . . , aZ-b2; h t c n c h d e Inte~~vat l j

L l A

L L d

a7- , al- , ... , as- ' "i' .

} I 3 1

al bl. at . b2 '~2, 5 , ... , aj bj,m, ... , b,, a,,* a,, i

(IntehcycCe I n # u w a c ) ; ... , 6 a b3 a3, 9 , a6 bt, at , ... * ~ j , 'b-al 1 "i * 4 4, a4 -

b, a7, aI bl* ... , as bs* ... , b a 1 i i'

a,- , al-b,* a2- , a2-b2, ... * aj- ,m ,.. , an- , a,,-bn;

Ifntwqcte I n t e n d l ;

b7- , b l - I ... , b5- ... , bj - . 1 FIGURE 1

ITEM PRESENTATION PARADIGMS FOR ANTICIPATION AND STUDY-TEST METHODS,

DISCRIMINATION LEARNING (EQUATIONS 3 AND 4), AND BACKWARD-PAIRED-ASSOCIATE RESPECTIVELY, IN PAIRED-ASSOCIATE LEARNING (EQUATIONS 1 AND 2), VERBAL

LEARNING (EQUATIONS 5 AND 6)

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116 JOURNAL OF GENERAL PSYCHOLOGY

Study -Test +

Number of intervening events between an S and its srb~ent T FIGURE 2

RETENTION INTERVAL DISTRIBUTION OF PAIR LIST Theoretical distributions of the intervening events in the retention interval-the period

between a presentation of both stimulus and response terms of a pair (study, S. event) and the subsequent presentation of the stimulus term alone (test. T, event) for the same pair-of the n- pair list under both study-test and anticipation methods, presented in random order from cycle to cycle (36).

tion intervals for both methods are most often of the same length, while the nonoverlap areas correspond to the probability that the retention interval is longer with the anticipation method than with the study-test method.

At the end of the study event, items within the list become (a) critical items which reside in the unstable short-term memory (STM) store, or ( b ) noncritical items which do not reside in STM. The latter consist of two types: those which are not learned as yet, and thereby had no opportunity to enter STM, and the others which may have been in STM earlier, but went already into the stable long-term memory (LTM) store.

Items never learned earlier are unlikely to be recalled correctly over short

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CHIZUKO IZAWA 117

as well as long retention intervals. The well learned items residing in LTM, on the other hand, are likely to be recalled correctly independent of the length of the retention interval, the mean difference being on the order of t z - 1 intervening events. Neither of the two types of noncritical items, however, differentiates between the study-test and anticipation methods.

In contrast, critical items residing temporarily in unstable STM are likely to survive only in short retention intervals (lags), but are not likely to do so in long ones. Therefore, if a sufficient number of critical items are generated and fall into the nonoverlap areas, differential survival rates of critical items between study-test and anticipation methods are likely to lead to superior performance for the former. If, however, only an insufficient number of critical items are generated, regardless of where they may fall in the distribution curves, overall impact on performance differences between the two methods may not be substantial.

Thus, inconsistent results which puzzled investigators for decades can be accounted for at long last by short-term memory processes (d. 5 , 13, 19, 52, 67, 72, 73, 76,87,100,102) that occur in the retention interval under the list design, via the RI model.

B. DIFFERENTIAL LEARNING SITUATIONS This core issue can be pursued further. According to the model, the

magnitude of the superiority of the study-test method over the anticipation method depends closely on the presence or absence of a sufficient number of critical items that fall into the nonoverlap areas in Figure 2 which generate differential retention intervals between the two methods. Any given learning situation may belong to one of the following three possibilities: Situations A, B, and C, which will henceforth be referred to as such.

Situation A results when a sufficiently large number of critical items are generated and the great majority of them fall into the nonoverlapping areas in the distributions of intervening events in the retention interval (Figure 2 ) , thus producing differential retention intervals between the two methods. Here, critical items are likely to survive in the short retention intervals (lags) as with the study-test method, but not in the long ones as with the anticipation method. The remaining critical items (small in number) that fall into the overlap area do not differentiate between the two methods in terms of the retention interval length. Thus, Situation A is likely to produce a large advantage for the study-test method over the anticipation method, as illus- trated in the left panel of Figure 3.

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n-1 ? 211-2 study- Antici - Test pation

Situation 6

Tesi pation

Situation C

b: 2

Small (Nonsig.) Diff.

study- mix Antici- Test pation

NUMBER OF INTERVENING EVENTS IN RETENTION INTERVAL

Perf. Diff. in favor I of ST Method

FIGURE 3 STUDY-TEST AND ANTICIPATION METHODS COMPARISON

Three theoretically possible situations, for which differential retention intervals between study-test and anticipation methods determine the degree of superiority of the former as compared to the latter, using the known forgetting processes (in terms of correct responses).

Extensive quantitative analyses of comparisons of the two methods via the RI model (e.g., 43, 44, 45, 46, 47, 48) amply indicate that acquisition processes of both methods may differ little, as evidenced by the close agreements of parameter values (for the same intercycle intervals for both methods), which leads to the identity hypothesis, to be developed in detail subsequently. For the current purpose, it suffices to state as follows: the identity hypothesis assumes that acquisition effects on study (S) events as well as those on test (T) and intervening events differ little between the two methods, and that the only differences between them are the differential retention intervals as spelled out by the RI model (Figure 2): i.e., the time when performance is measured, as entered in Figure 3. Thus, one memory curve is entered per panel in Figure 3, which drops over time following the usual course, Jost's law (54).

Situation B , nonetheless, occurs when a great majority of critical items, even if generated in great quantity, fall into the overlap area; critical items

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CHIZUKO IZAWA 119

here have retention intervals of the same length and therefore their differential losses between the methods are highly unlikely. The remaining critical items falling into the nonoverlap areas are likely to be lost differentially between the methods, but since they are so few in number, their impact on overall performance is expected to be negligible; see the center panel of Figure 3.

Situation C ensues when an insufficient number of critical items is generated in STM. In this situation, the absolute number of critical items falling into the nonoverlap areas is even smaller, independent of whether they are in the majority or in the minority. Hence, differential loss of critical items in the nonoverlap areas in the differential retention intervals between the methods are unlikely to lead to a large advantage for the study-test method, as seen in the right panel of Figure 3. In an extreme case where no critical items fall into the nonoverlap areas (possible in Situations B and C), the two methods are likely to produce identical performance levels, the curve in Figure 3 thus becoming horizontal.

The above delineation of the three possible situations, derived from the RI model, provides a new insight into crucial factors other than the retention interval, as well as examining the generality of the RI model. Note that the retention interval represents only one primary factor that controls performance levels for both study-test and anticipation methods.

While significant performance differences in favor of the study-test method are likely only in Situation A, nonsignificant ones are likely in both Situations B and C . To view this differently, Situation C occurs when learning conditions generate mainly noncritical items, while Situations A and B result when conditions produce predominantly critical items. This state of affairs leads us directly to the learning difficulty factor.

C. LEARNING DIFFICULTY (a) If a given list is extremely difficult to learn, few items can be acquired

that will become critical in STM. In the absence of sufficient critical items, Situation C is likely to result, leading to a small advantage only for the study-test method. If learning is impossible and no items can be learned at all, the probability of an incorrect response must be 1; be its retention interval short or long, the same performance levels occur for both item presentation methods!

(b) Similarly, when learning is unduly easy, items are bound to be learned well and possibly overlearned, thus entering LTM quickly, with few items left behind in STM as critical items, leading to Situation C. No tangible

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differential losses of critical items are likely in the retention intervals, resulting in no pronounced superiority for the study-test method as compared to the anticipation method.

(c) However, when learning is only intermediately difficult, more than a sufficient number of items may be acquired and enter STM, becoming critical. Two types of outcomes are possible here: on one hand, if a great majority of the critical items falls into the nonoverlap areas in Figure 2 (shorter retention interval for the study-test method), Situation A is the likely result where differential retention intervals lead to a substantial advantage for the study-test method. On the other hand, if a great majority falls into the overlap area instead, with equal retention intervals for both methods, Situation B is likely to result where the superiority of the study-test method is inconsequential.

The foregoing, derived from the RI model, suggests that the possibility of impressive superiority of the study-test method over the anticipation method (Situation A) is most likely when learning is moderately difficult, with an unimpressive advantage as another possibility (Situation B) notwithstanding. In contrast, when learning is either very easy or very difficult (two extremes), only negligible performance differences between the two methods are very likely, as in Situation C . The above may be summarized as in Figure 4. The vertical distance between the two curves (shaded by lines) indicates net performance differences between the methods. Extreme left and right positions, respectively, result when learning is very difficult or very easy, whereas mid-range areas result when learning is intermediately difficult to various degrees. At times, however, the absolute performance differences in favor of the study-test method may be quite small (Situation B) even in the middle positions on the horizontal axis in Figure 4 (the difficulty dimension).

Thus, by means of the RI model, we procured an additional factor that controls performance levels for both anticipation and study-test methods. Learning difficulty may be determined by a host of variables including list length, a family of variables relevant to learning materials, and operational variables such as presentation rates and acquisition stages, as well as subject variables involving learning ability, developmental stages, and others.

D. GENERALITY OF THE RETENTION INTERVAL MODEL With the learning difficulty dimension specified as another primary factor

in addition to the retention interval, the next step in our theoretical endeavor is to determine the generality of the retention interval (RI) model.

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1.1

P c

I s b a

a

08 DIFFERENCES ARE MAXIMUM 4: THE ~ l l c puToF#AIycE LEVEL

t

0 DIFFICULT INTERMEDIATE EASY

Learning Difficulty Dimemrion

FIGURE 4

CHIZUKO IZAWA 121

5

STUDY-TEST AND ANTICIPATION METHODS P E R F O W C E S The curvilinear relationships in performance differences between study-test and anticipation

methods in favor of the former when Situation A is possible as a function of the learning difficulty dimension.

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The RI model was formulated and tested primarily via data in PAL with the unmixed list design in a random item presentation order, commonest in the field. To assess the model’s generality to other situations, representative learning situations relevant to our concern are examined below.

1. Verbal Discrimination Learning (VDL) The distinction, once clear and simple, between recall (as retrieval) and

recognition (as decision) learning (e.g., 60, 66) has been challenged both theoretically and empirically over the past decades, and similarities as well as differences between them have been keen targets of investigation and debate (e.g., 6, 14, 20, 42, 58, 69, 79, 85, 90, 94, 95). It seems necessary, then, to examine to what extent a theory based on recall data can hold for recognition data.

Consider two-choice recognition learning in VDL, and let aj and b, be the correct (old) and the distractor (new) items. Two VDL anticipation cycles for an unmixed n-item list may be administered as in Equation 3 in Figure 1, where the left-right positions on Ts and the item presentation order within the cycle are randomized, respectively, whereas VDL under the study-test method proceeds as in Equation 4 in Figure 1.

The superficial reversal in form notwithstanding, the basic features of S and T arrangements in Equations 3 and 4 remain identical with those in Equations 1 and 2 , respectively. All temporal intervals for the two methods in VDL, therefore, are the same as those in PAL. Thus, if recognition and recall learning share common characteristics, the RI model should also hold here, expecting either significant or nonsignificant superiority for the study- test method over the anticipation method. The predictions are indeed supported in VDL data: a large advantage was reported for the study-test method by, for example, Battig and Switalski (9, unmixed), Ingison and Ekstrand (31) and Izawa and Morrison (49, Exper. 3), but only a small one by Rowe and Paivio (84) and Izawa and Morrison (49, Exper. 1 & 2). Apparently, retention loss processes during acquisition in VDL are similar to those in PAL, in line with the model.

2. Constant Presentation Order in Paired-Associate and Verbal Discrimination Learning

The commonly used random item-presentation order from cycle to cycle was directly incorporated into the RI model; the triangular distributions of the retention interval thereof were specified (Figure 2). Such randomization, however, is not a necessary condition for the model. Consider a situation

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CHIZUKO IZAWA 123

where the items are always presented in a constant order. All n items on the list have the identical retention interval without variations, with n - 1 and 2n - 2 intervening events, respectively, for study-test and anticipation methods. The means with a constant order are identical to those with a random one.

If sufficient critical items are generated, the model would expect a substantial advantage for the study-test method over the anticipation method to be highly likely (Situation A). If, however, an insufficient number of critical items are generated, the methods are likely to differ little (Situation C). A differentiation between random and constant item presentations via the RI model may boil down to the presence or absence, respectively, of Situation B.

The predicted large and small advantages of the study-test method over the anticipation method are both well borne out. Significantly better performance was obtained by Battig, Brown, and Nelson (1 1, Exper. 1) and Izawa (40), but a nonsignificant one by Battig et al. (11, Exper. 4) and Izawa (39), both in PAL. VDL with constant presentation orders also resulted in a similar state of affairs (e.g., 31). Thus, extant data seem to support the model.

3 . Backward Associations

Both formulation and tests of the RI model were achieved primarily with forward (u-6) associations in PAL. Given that relationships between forward and backward (b-u) associations have been widely debated (e.g., 4, 23, 30, 32, 33, 63, 71, 91, 97, 104), it seems essential to determine the ability of the RI model for 6-a associations, in order to see the issue from the current perspective.

Backward associations in PAL are commonly measured in one of two ways: (a) at varied acquisition stages with pairs presented in both directions throughout (bidirectional training), or (b) after reaching a criterion in a-b direction (unidirectional training). In either case, backward recall may be made as in Equations 5 and 6 in Figure 1 for anticipation and study-test methods, respectively.

Except for the direction of the T event (b-a), the temporal relationships between the methods in Equations 5 and 6 are identical to those in a-b directions in Equations 1 and 2, including the most important retention intervals (between boxes in solid and broken lines). Then, measured by 6-a associations, the FU model would expect either a large or a small advantage for the study-test method over the anticipation method.

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In fact, the two types of backward association data resulted in a significant superiority of the study-test method in, for example, Izawa (44, Exper. 1 & 2) and Schild and Battig (86), but a nonsignificant one in Goss and Nodine (28, Exper. 7, 8, & 11) and Izawa (44, Exper. 3). The same outcomes are apparent in Wright (105) when his Table 3 included all incorrect responses, as well as for both recognition measures and the mixed- list design.

4. Auditory Item Presentations

In spite of extensive comparisons over a long period of time, relative efficacy of visual and auditory modes beyond the modality effects of immediate memory (e.g., 68, 991, continue to be highly variable (e.g., 12, 18, 21, 24, 59, 65, 75, 88, 92, 93). Thus, some theories were specifically formulated for auditory stimuli (e.g., 61, 70, 77).

The RJ model, however, is not modality specific. Can a model based on visual data explain auditory data? Auditory presentations with anticipation and study-test methods are the same as visual ones in Equations 1 and 2, respectively. Then, for the same reason as with visual data, auditory data should be explicated via the RI model, which expects both large and small superiority for the study-test method to the anticipation method (Situation A and B-C, respectively).

Auditory data are, unfortunately, very scarce, but vary grossly: Barch and Levine (7) obtained significant superiority for the anticipation method with Morse-code-signal-two-digit pairs, but the complete opposite in favor of the study-test method with word-two-digit pairs. The latter findings were supported by Battig and Wu (10) and Kanak et al. (56, Exper. 3).

The former, the superiority of the anticipation method, however, is highly unusual and challenges the Rl model, requiring close scrutiny. The two experiments involved were conducted in groups, large in one (5-30 Ss) and small in the other (1-2), with proctors. The S recorded hidher own responses at designated locations on the answer sheet, and had to start (not complete) responding (writing) before the auditory pair presentation with the anticipation method in order to get a credit (judgment made by the proctor). The procedures seem to differ significantly from other studies in which responding must be completed prior to the onset of the pair presentation, effectively controlled by the E who records the response for the S, who is usually run individually.

Deviations of procedures may in part account for Barch and Levine’s unusual results. Take an example: a false “correct” might have occurred if

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CHIZUKO IZAWA 125

the S had started writing on time (thereby judged as valid by the proctor) but had changed the response after listening to the pair (correct response). No such possibility existed for the study-test method, thereby resulting in inferior scores.

To clear up any possibilities of such artifacts, Barch and Levine’s experiment was rerun twice with modifications, so that the Ss were run individually with oral responses recorded by the E (41, 50). The superiority of the anticipation method could not be replicated in either of the two studies; instead, little differences resulted between the two methods. An additional study with difficult CVC-CVC pairs (5 1) produced nonsignificance again. Repeated failures of replications seem to suggest that the superiority of the anticipation method, if any, is too tangential at best to merit further discus- sion.

The frequently demonstrated small differences between the methods can- not adequately be accounted for by Barch and Levine’s position that differential encoding processes were involved in the methods when stimuli were difficult; the RI model can explain nonsignificance when learning is difficult via Situation C (Figures 3 & 4), as well as the superior performance for the study-test method via Situation A.

5 . Learning

While the RI model was formulated via unmixed-list data, its derivative, the identity hypothesis, suggests that outcomes of mixed-list data (the two methods mixed) should be predictable. Data by Battig and Wu (10) and Battig and Switalski (9) provide the testing ground, where two mixed-lists were run, respectively, in PAL and VDL: the test (Tkseparate group-a block of six Ts (study-test items), followed by a mixture of their S among six anticipation items (T immediately followed by its S); and the correct-items (Weparate group-a mixture of six Ts (study-test items) among six anticipation items, followed by six Ss (study-test items).

The FtI model seems to explicate highly complex and seemingly inconsistent results of the two studies more ably than any other theories, such as feedback, different-encoding or different-acquisition, or task-alternation positions. When each method in each mixed list was considered separately, the crucial mean S-T intervals that differentiate the two methods here had 2n - 2 (n/2 to 7n/2 - 4) intervening events for the anticipation method, and n - 1 (0 to 2n - 2) for the study-test items, respectively, in each mixed list- the same means as with the unmixed list. The model would expect, then, either

Mixed-List Designs itt Paired-Associate and Verbal Discrimination

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small (Situation B or C) or large (Situation A) advantages for the study-test method over the anticipation method. The predictions were indeed borne out, the former as in the T-separate condition by Battig and Wu, and the latter as in all other conditions of that study plus Battig and Switalski.

When the mean retention intervals for the two mixed lists are considered as a whole (anticipation plus study-test), each had 3(n - 1)/2 intervening events. Via the identity hypothesis, the two mixed lists should produce about the same performances. This turned out to be precisely the case in both of the above studies.

The mean S-T intervals of the two mixed lists, (3n - 3)/2, are at the midpoint in length between those of the unmixed study-test (n - 1) and the unmixed anticipation (2n - 2) methods (see Figure 3). Considering STM properties of greater loss early in the retention interval than late Uost’s law), a substantial advantage for the unmixed study-test condition over the two mixed ones may be expected, provided Situation A is generated. This indeed turned out to be the case in the above studies. However, performance differentials between the mixed lists and unmixed anticipation conditions were expected to be smaller (Figure 3); thus the superiority of the mixed lists with the shorter S-T interval over the unmixed anticipation condition would be less robust; while significance is possible, it would not always be so, even if a Situation A case were to be generated, but much less so in case of a Situation C . This state of affairs, predictable from the identity hypothesis and the RI model, is clearly borne out in the above two studies.

Experiment 6 by Cofer et al. (16) was ingeniously designed. In Condition RAN, tasks alternate as T S T S without immediate feedback but with random TS combinations as, for example, a, - , a4 - b4, uj - , a6 - b6, . . . . Condition DUB was similarly constructed with T and S events appearing in twos as T T S S T T S S . . . . In both conditions, random item presentation orders were restricted in such a way that both T-S and S-T intervals contained approximately 16 intervening events; the same held for the stan- dard study-test condition.

From the feedback position, the anticipation condition should excel over the other three conditions. Via differential acquisition and task alternation positions, the study-test condition should be superior to all others, with the latter further expecting the next best, being Condition DUB, followed by Conditions RAN and anticipation with little difference between the last two. None of these predictions, however, materialized overall. The four conditions did not differ significantly.

In contrast, the identity hypothesis expects the same performances for

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Conditions RAN, DUB, and study-test on the ground that their S-T intervals were about the same. As for differences between anticipation and study-test methods, due to an easy learning situation created by Cofer et al., only few critical items remained in STM, generating Situation C (Figure 31, thus leading to nonsignificance. Hence, little differences in all conditions can be well accommodated by the model, and the identity hypothesis seems to have received further support.

6 . Part-Whole Presentations While all the above discussions were based on the whole presentation

mode where all n items were given on every cycle, the RI model may be examined via the part-whole presentation mode where a list is divided into m equal parts. The S begins learning with the first part and upon completing it, proceeds to the second, and to the third, . . . , until the last part has been learned. The relative relationships, of the S-S, T-T, and T-S and S-T intervals for each of the m sublists, between the two methods remain the same as for the whole list, with each becoming nearly l lm th. The crucial mean S-T intervals, for example, contained 2(n/m - 1) vs. dm - 1 intervening events for the anticipation us. study-test method.

Consequently, if sufficient critical items are generated and fall into the nonoverlap areas (Situations A), the study-test method is likely to be superior to the anticipation method. But, each part being only nlm in length, that advantage may be quite small within each sublist; short-list effects (37). Nonetheless, possibilities of Situations B and C notwithstanding, when all sublists are accumulated, the sum total may possibly become large enough to achieve significance. This predicted state of affairs, via the RI model, did occur in Goss and Nodine (28, Expers. 9 & 10) with n = 12 and m = 3.

The several representative situations reviewed above amply demonstrate that the theoretical orientation of the RI model and the identity hypothesis seem to have considerable generality in PAL and VDL. Furthermore, the applicability of the RI model to instructional contexts with prose sentences seems plausible in the light of findings with sentences which paralleled the results of PAL (e.g., 83).

E. OTHER THEORETICAL APPROACHES The most striking result by far in the quantitative examinations of the RI

model (43,45,46,47,48) was the fact that the same sets of parameter values satisfactorily predicted data for all relevant conditions with both study-test and anticipation procedures in every experiment. All events, both S and T

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events as well as the intercycle (tr), intervening study (is), and test ( tT) intervals generate, respectively, the same effects under the two item- processing procedures, leading to the identity hypothesis. The difference is simply a matter of different arrangements for these events, resulting in inherently differential retention interval lengths between the methods, as specified by the RI model.

Via the identity hypothesis, constant performance is expected across the item presentation methods, given a constant retention interval, in a manner somewhat analogous to Weber’s law. Differential performances may be expected from differential retention intervals (the RI model), although other factors controlling learning difficulty also participate in determining the size of the differences in favor of the study-test-method. The soundness of the hypothesis was clearly supported by our pilot studies.

Memory is theoretically postulated in many ways (e.g., 2 , 3, 26, 53, 74, 78, 82, 103). Of these, the time-dependent retention processes of the activation theory (e.g., 1, 17, 62, 64, 78) may appear to resemble those of the present concern. In models of Anderson or of Collins and Loftus, for example, memory is postulated to be an interlinked network of propositional or conceptual nodes. During retrieval, concepts are assumed to be activated, and activation spreads through the network. Of particular interest here is the time taken for activation to spread. This time-dependent aspect, however, was questioned recently by Ratcliff and McKoon (81).

Nonetheless, it should be noticed that the similarity in some key ter- minologies, such as lag effects and those of intervening events of the activation (e.g., 17, p. 419) and IU models is only superficial, not substantive. First, the activation theory concerns itself with the time-dependent processes occurring from the time of onset of the retrieval signal to the emission of the response-i.e., the processes on the test (T) event-since such processes might reveal certain memory structures or representations. In sharp diver- gence, a primary focus of the RI model is upon the time-dependent processes occurring from the study (S) event up to the T event instead, but not on T event processes per se. While the retention intervals differ between study- test and anticipation methods, T event processes may differ little between the methods (a test operates identically for both; cf. the identity hypothesis). Thus, the activation theory may offer less than meets the eye in specifying differences, if any, between the methods.

Second, while the notion of activation is highly provocative, it seems both difficult and unnecessary to assume a complex network of conceptual, propositional, or hierarchical nodes between an S event and the subsequent

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T event of the same item. Even when the “priming technique” (e.g., 80, 98) is considered, to regard the S event as the “prime” for the T event of the same item requires significantly expanded theoretical modifications. The S and T events in PAL are distinctly different from the word being presented twice-first as a prime, and the second time as a test to be simply named, the response measure being the latency (cf. 98). Even if some mechanisms could be devised to justify a study event as the trigger of activation, and the test event as the point at which to measure the effects of such activation, such an approach would still have to utilize differential retention interval (time- dependent) phenomena specified by the RI model. Consequently, the fate of the activation theory in the present context seems to differ little from others that have some accommodation of, or relevancy to, the retention interval.

The effects of the retention interval in one context or another have been extensively investigated both empirically and theoretically since Ebbinghaus (22). His famous forgetting curve with the list design and Jost’s law have repeatedly been replicated not only with lists, but also with items (e.g., 13, 27, 57, 67, 76, 89, 106). A number of theories address themselves to retention phenomena in various ways [e.g. (IS, 25,34,35, 101, 103), as well as those cited above].

Yet, the mere existence of empirical findings or that of theoretical postu- lates done did not automatically resolve the problems of our present concern, in spite of sometimes apparent relevance. History showed us that mere demon- strations of spacing or lag effects with items did not resolve spaced practice effects with lists either empirically or theoretically: e.g., Hintzman (29) with items vs. Underwood (96) with lists. By the same token, the above extant theories or others alone did not automatically provide solutions to our problem. As J. R. Anderson implied, applications of any theoretical positions to other domains or interests “will be forthcoming only by dint of much effort” (1, p. 536). The present research presented a sample of such effort, and clarified the issue to a previously impossible extent, via the retention interval model.

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the generality of the retention interval model

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