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Journal of Experimental Psychology: Human Learning and Memory VOL. 6, No. 3

MAY 1980

The Free Recall of Category Examples Paul J. Gruenewald and Gregory R. Lockhead Duke University People recalled the names of as many animals, birds, foods, or cold foods as they could in IS-min or 30-min sessions. In each task, the rate of item production decreased with increasing time, and semantically related items were produced in spurts over time. The results are consistent with a proposed two-stage model in which people (a) search for semantic fields and (b) produce whatever items are encountered when a field is located. These related words are the clusters observed by Bousfield and Sedgewick. However, Bousfield's exponential model describes the data less well than does a simple hyperbolic model based on the two-stage process. It is proposed that time between clusters increases hyperbolically in these tasks, reflecting the search for semantic fields, and that the time between items within clusters, and the number of items in each cluster, are independent of time in the task, reflecting the production of items in discovered fields. On these bases an algorithm is introduced that partitions clusters by the temporal patterning between words in the protocols. The temporally based algorithm provides a description of the data that highly correlates with the semantic structure as depicted by judges' ratings. These correlated temporal and semantic measures may reflect aspects of the search process and the structure of memory. The unconstrained free-recall task, originated by Bousfield and Sedgewick (1944), requires subjects to produce as many exampies as they can of items from some known set or category. For example, the subject is ~ Based partly on "Rates of recalling category example*" presented at the 17th annual meeting of the Psychonotnic Society, St. Louis, Missouri, November 1976, by P. J. Gruenewald and G. R. Lockhead. We thank the assistants who helped in the analysis of these data; especially Christine Hutchinson, without whose assistance much of this analysis would not have been completed. Thanks, too, to M. C. King and J. E. R. Staddon for comments on an earlier draft of the manuscript.

asked to name all of the birds he or she can for the next 15 min. Constrained free-recall tasks, on the other hand (see Bousfield, 1953; Bousfield, Sedgewick, & Cohen, 1954), require the subject to recall items from a list generated by the experimenter and previously memorized by the subject. The constraint in these tasks arises from how the imenter selects the items to be recalled. r . , . . . Constrained and unconstrained tasks present the same problem to the subject: He or she must try to continue to produce items j of exampies that decreases in from a . . . /~i • • n size with each response. Characteristically, the rate of item production declines with increasing time in these tasks.

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Gruenewald, Department of Psychology, Duke UniBousfield and Sedgewick (1944) outlined versity, Durham, North Carolina, 27706. the two most notable features of such recall Copyright 1980 by the American Psychological Association, Inc. 0096-151S/80/0603-0225$00.75 225

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PAUL J. GRUENEWALD AND GREGORY R. LOCKHEAD

protocols. First, the cumulative function of different words produced over time is negatively accelerating. As time in the task progresses, it takes longer and longer for the subject to produce a new item. Second, the protocols are characterized by items produced in spurts or clusters. The subjects, for example, would produce clusters of cats or dogs in recalling animal names. We refer to the first aspect of the data as the general parametric problem of free recall and to the second aspect as the structural problem of free recall. In this article, these two aspects are related to data from a free-recall task and are both described in terms of a twoprocess model. The general parametric problem of the data is to model the decrease in item production rate with increasing time in the task. Typically, this decline has been defined as an exponential decay function (see Bousfield & Sedgewick, 1944; and Crowder's, 1976, summary). However, Bousfield et al. (1954) have demonstrated that a hyperbolic model is more successful than an exponential model in characterizing overall production rates in constrained free recall. A similar comparison has not been made for an unconstrained freerecall task. The first part of this article compares the hyperbolic and exponential forms to data from such a task. The structural problem presented by the data regards the clustering of items in the output protocols. Bousfield and Sedgewick (1944), and virtually all subsequent authors, have noted that items are frequently output in groups, rather than singly, in the protocols. This observation led to much of the subsequent constrained free-recall research. To better study associative clustering, researchers supply subjects with categorized lists to be learned and later recalled. This method facilitates the investigation of clustering by defining a priori the relations between items in the to-be-recalled list. Bousfield and Cohen (1955) have found that clusters of words appear to be composed of associatively or semantically related items. Verifications of this point can be found IO 0 2 CLUSTER SIZES

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Figure 6. The relative frequency of occurrence of different-size clusters as determined by the proposed algorithm (left panel) and by the judges' ratings (right panel) for each of the 15-min category tasks.

Figure 5), then the time between items was relatively brief compared to the slope of the hyperbolic function at that time, t, and the item was classified as being in the same cluster as the previous item. If the slope difference was less than .1, then the I IT was relatively long and the item was classified as a word beginning a new cluster. Some characteristics of the data in terms of these semantic and temporal criteria are described next. The Distribution of Cluster Sizes Figure 6 shows the relative frequency of different cluster sizes according to the slopedifference algorithm (left panel) and judges' ratings (right panel) for each 15-min category. The category distributions are all quite similar. Based on the criterion used with the judges' ratings, clusters containing only one word account for 46% of all clusters encountered, and for 22% of all the words produced. About 28% of all clusters are estimated to contain two words, and these clusters account for 27% of all words produced. There are considerably fewer clusters of Size 3 and more, but, except for birds, there are some clusters of all sizes from 1 through more than 10 for all the tasks. Note the similarity in the predictions of the two estimation methods as seen by comparing the two panels of Figure 6. Although

Clustering Over Time The model proposes that the negatively accelerated form of the cumulative functions of words over time (Figures 1 and 2) is due to a decrease in the frequency of occurrence of clusters. An alternative possibility that has been considered is that Figure 1 reflects a general decrease in the average number of items that occur in each cluster over time (McCleery, 1977). Indeed, Bousfield and Sedgewick (1944) thought that cluster size decreases with time in the task. To examine these alternatives, the ^-hr data from this experiment were averaged into 3-min intervals, and over subjects, for each recall condition and for each estimation procedure. As displayed in the top half of Figure 7, the average number of clusters produced decreases with time. Also, different categories produce different numbers of clusters over time. More clusters are produced when foods are recalled than for animals, perhaps even fewer for cold foods, and fewest of all for birds. This mirrors the total number of words that were produced. More words were recalled in the food category than any other category, and fewest words were recalled in the birds category (see Figure 1). The average number of items in each cluster for each time interval is displayed in the bottom half of Figure 7. Considering those estimates from the slope-difference algorithm (left panel), it appears that there is little relation between how many items are in a cluster and how long the average observer has been performing the task. This is consistent with the assumption that cluster size

FREE RECALL OF CATEGORY EXAMPLES is independent of time in the task. For the estimates from the judges' ratings, the first 9 or 12 min also show this apparent independence between time and cluster size. There are, however, confusing shifts in the size estimates at 15 min. Since there are rather few clusters this far into the task (see the top panel of Figure 7), this is probably noise. Even here, however, there is no strong suggestion that cluster sizes are decreasing with time in the task. In fact, a substantial decrease is seen only for the bird category, the category with fewest observations. The average cluster size of two of the remaining three categories (animals and cold foods), actually rises slightly. This analysis based on the 15-min data was also conducted on the protocols from observers producing animal names for 30 min. Again, there is a negatively decelerating decrease in the number of clusters produced

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Figure 8. The average time between clusters and the average time between items within clusters in S-min intervals for each of the tasks. (IIT = interitem times.)

over time according to both measures. Also, again, there is little evidence for any change in cluster size with time. The results are not shown because they add nothing new over those in Figure 7, except the observation that these conclusions also appear to hold over the 30-min recall period. Time Between Items and Time Between Clusters

12 ISO 3 6 TIME INTERVALS (minutes)

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Figure 7. The average number of clusters (top) and the average size of clusters (bottom) as a function of time in the task for each of the IS-min category tasks as determined by the slope-difference algorithm (left column) and by the judges' ratings (right column).

The average time from the end of one cluster to the beginning of the next cluster, as determined by the judges' ratings, was measured over 5-min intervals. These results comprise the upper functions in Figure 8. The lower functions in that figure show the measured average time between items within a cluster as time in the task increases. There are marked differences in these two time measures (recall that these data are from the judges' decisions that were made with no knowledge of any IITs), as follows: The times between clusters are regularly larger than are the times between items within clusters, and there is no overlap at any place. The average difference is about a factor of two at 5 min into the task and grows to about a factor of seven at 15 min. These


236 60 50 40 30 20 10

1-2 2-3 3-4 4-5 POSITION OF INTERVAL IN CLUSTER

Figure 9. The proportion of total time within a cluster taken up by successive interitem times for clusters of size three (circles), four (squares), and five (triangles). (Dashed lines represent chance performance for each associated function. Vertical bar lengths represent plus or minus 1 SB.)

measures from the semantic ratings suggest a monotonic increase in time between clusters as the task progresses, and that time between items within a cluster is independent of time in the task. These results are consistent with the two-process suggestions noted earlier. A comparable analysis using the slope difference algorithm is not presented because the algorithm assumes the differences observed in Figure 8. Temporal Relations Between Items Within Clusters The proportion of the total cluster duration that is accounted for by time between successive items within clusters, based on judges' checks, is shown in Figure 9 for Cluster Sizes 3, 4, and 5. The number of observations is small. There were 22 clusters Size 3, 17 of Size 4, and 10 of Size 5. The bars in the figure indicate plus or minus one standard error associated with each average. There is no regular pattern of times between items within clusters according to this analysis. The dashed lines indicate the chance proportions expected. Thus, in a cluster of Size 3, which has two IITs, if no difference in IITs for successive items occurred, then each interval would account for half of the total cluster time. Within each cluster size, each item appears to take as long to be pro-

duced as does any other item, as if a list is being read off. There is no information in this type of analysis for Cluster Sizes 1 and 2, and there were too few clusters larger than Size 5 to warrant presentation. The proportion of total cluster time accounted for by each IIT within a cluster was also calculated in terms of the slope-difference algorithm. The results are not shown because they are essentially identical with those from the judges' ratings. If anything, there is less dependence between the proportion of time accounted for and item position, by this temporal estimation procedure, than there is according to the ratings. There is no regular pattern of times between items within clusters. Each item appears to take as long as any other item to be produced in the cluster. Discussion Consistent with prior reports in the literature, the cumulative number of category exemplars produced over time takes the same general form for each of the four categories investigated and for each observer. Fewer and fewer items are produced over time in the task. This function is not exponential, however. The hyperbolic form (Equation 3) provides a better fit to the data. This study has also been repeated with an elderly population of subjects and a group of different college students (Horn, 1979). Horn's results are essentially identical to those reported here, both in qualitative form and in quantitative estimates of search rates and asymptotes. Overall, time between successive words in the unconstrained free-recall task grows in a manner consistent with the hyperbolic rather than the exponential function. When the hyperbolic output function is used as a baseline from which to predict clustering by shifts in IITs (the slope-difference algorithm), there is considerable agreement between these temporal measures and independent measures provided by the semantically based ratings of judges. Since the judges knew only the order of the emitted items in the protocols, they could make their ratings only on the basis of semantic relations between successive words. This provides

FREE RECALL OF CATEGORY EXAMPLES

237

strong support that the temporal and se- the sole source of the hyperbolic form of the mantic measures are related to the same cumulative function, (b) The time between search process (see Figure 5). Temporal items within clusters and the average numdifferences are related to semantic differences ber of items within each cluster are both conin the data and, hence, may reflect the de- stants ; that is, these factors contribute little pendency of the search process on semantic to the form of the function other than restructure. quiring the rescaling of Equation 3 to inEstimates of various features of clustering clude the number of items within clusters in the data from these two measuring tech- (Equations 4 and S). niques are comparable. The estimates of relaThe theoretical preference based on the extive frequency of cluster size (Figure 6) and ponential decay function has been to interof the number of clusters produced in each pret the search process in terms of a "reinterval (Figure 7, top panels) are in agree- placement" hypothesis (Bousfield & Sedgement. Whether average cluster size changes wick, 1944; Indow & Togano, 1970; Mazur with time in the task is unresolved, because & Hastie, 1978). The whole store of items is of noise in the data (Figure 7, bottom pan- searched, and as each new item is selected, it els) and the difficulty of demonstrating the is verbalized (and presumably tagged in null hypothesis. But the simplest estimate memory in some manner) and replaced in from both measures is that mean cluster size the pool to potentially be selected again. The does not deviate substantially from a con- success of any search through the store, then, stant over time in the task. Finally, it ap- is proportional to the number of new items pears that the time between successive items left to be produced. This type of search within clusters remains relatively constant. model, which produces an exponential enSome other studies, particularly studies us- velope, is clearly not supported by our data. ing constrained recall, report increasing times Rather, an interpretation in terms of the hybetween successive items within clusters (see perbolic form may be suggested. Prior sugearlier). This may be a measurement prob- gestions have been made to apply the hyperlem due to differences in the various tasks. bolic form to learning-curve and constrained For example, in constrained free recall, the free-recall data (Bousfield et al., 1954; Masubjects know about how many items there zur & Hastie, 1978; Thurstone, 1919), but are to be recalled in each cluster. This may we know of no comparable analyses that have induce them to search longer to produce all been made for its application to unconthe items within each predefined cluster. By strained free recall. the algorithm presented in this article, each The parameter m in the hyperbolic model such cluster may actually be a collection of (Equation 2) was defined by Bousfield et al. semantic fields. This search could then take (1954) as a search rate parameter related the form suggested by the hyperbolic model. to the number of items available to be reThe analyses presented, although mostly called, c. Indeed, considering our equivalent preliminary, suggest ways to further con- Equation 3, the value of b correlates with sider unconstrained free-recall data. The fol- the asymptote a over observers and categorlowing three topics concerning the process of ies in our data, r(22) = .879 (see Table 1). free recall are discussed next: The nature of However, although this correlation is high the hyperbolic model and some of its impli- for our sample, b is only indirectly related cations, the question of cluster size, and the to search rate; that is, what b actually pronotion of semantic fields. vides is a temporal benchmark reflecting the interaction between the subjects' search rate The Hyperbolic Model and the total available number of items, a, in The model of free recall presented by the underlying store. This is seen by observEquation 3 is based on two assumptions: (a) ing that b is the point in Equation 4 (and 5) The time to access new clusters or semantic at which, when t — b, half of the total availfields increases with time in the task and is able clusters, h (or items hk), have been

238


produced. When t = b, ne(b) = h/2 and «,(&) = hk/2.

(6)

Hence, when / < b, less than half of the available clusters (items) have been produced. The relation of b to search rate and to the total available store can be clarified by example. Consider two subjects whose data indicate equal cluster sizes and equivalent values of b, but different asymptotic values, A! > h). Although the search parameter, b, is the same for each person, Subject j's implied search rate is nonetheless the slower. According to Equation 6, Subject i must produce more words than Subject j in an equivalent amount of time. The search parameter, b, may be directly related to search rate by considering production rate when t — 0. The first derivative of Equation 4 defines the rate of production of clusters or semantic fields over time: (7)

When t = 0, that rate equals h/b. This may be interpreted as the rate at which the observer searches for relevant meanings in the initial stages of the production process. At this point, this search rate equals the maximum production rate. Were the subjects able to operate at this maximum production rate throughout the task, then the entire store of available items would be produced by time b. The production rate at t — 0 can be estimated for each subject's protocol given b and h. If variability in the data is sufficiently low for that measure to accurately estimate the initial production rate, then the following simple model of the recall process may be suggested: The observer searches the total pool of available clusters or semantic fields at a constant rate estimated by h/b, the maximum production rate at t = 0. In the initial stages of search and production, the maximum production rate equals the search rate, as any accessed semantic field will lead to unproduced items. The maximum production rate, however, cannot be maintained (even though search may continue at this same rate) because the availability of new clusters

decreases as more and more clusters are produced. This decrease produces the hyperbolic form and causes the departure of actual production rate from the maximum initial rate. Were the maximum production rate to be maintained throughout the task, then the cumulative function would be linear rather than hyperbolic, and the task would be completed for the observer when b = t, The cumulative function may be linear in some production data reported by Indow and Togano (1970). They had native Japanese subjects recall all the Japanese cities they could, but with the constraint that they list them in geographic order from north to south. Since instructions can thus affect recall, we are obviously still far from a complete recall model. Task constraints and the structure of memory may affect recall in ways that have not been included in the twoprocess model presented here, Cluster Size in Free Recall In practice, the search rate for items must be estimated from Equation 3, and an estimate of cluster size, k, must be provided. Only then can cluster search rate be determined. However, this important estimate of cluster size is difficult to make. Estimates from the slope-difference algorithm must be based on the cutoff selected for the classification of clusters by IITs. Maximizing the number of clusters of Size 2 or greater detected by the algorithm is not necessarily a nonarbitrary procedure for determining the slope-difference criterion. Judges' ratings do provide an independent check on the cluster size distribution, but these ratings also do not necessarily lead to a "true" estimate of average cluster size. Different judges may vary as to the clustering they indicate in the protocols. Hence, relative cluster sizes can be estimated, but the estimate of absolute cluster size remains problematic. A different theoretical definition of clusters and a different technique for estimating cluster sizes from what is proposed here has been suggested by Graesser and Mandler (1978) and by Mandler (1975). That model states that clusters in both constrained and unconstrained free-recall tasks reflect the span of

FREE RECALL OF CATEGORY EXAMPLES apprehension, and are generally of Size 5, plus or minus two items. Our measures, however, do not suggest this general value. In our estimates from judges' ratings (Figure 6, right panel), 3% of all clusters are Size 8 or greater and 74% are smaller than Size 3. Only 23% of the clusters are between three and seven words by this measure. The distribution is not symmetric about five items. These conclusions based on judges' checks apply equally well to the distribution of cluster sizes estimated from the slope-difference algorithm (Figure 6, left panel). Both distributions presented in Figure 6 appear to be in closer agreement with the motion of semantic fields than with the notion of a limited span of apprehension. The form of the distribution of cluster sizes suggests that most accessed meanings have single words associated with them and fewer meanings have large numbers of associated items. Graesser and Mandler (1978) used a different measurement technique for estimating cluster size than that presented here. They computed the mean number of items emitted in succession that had IITs less than some critical pause time. As the allowable pause time is made to increase, the average number of items that occur before a critically toolong pause is encountered must also increase. Graesser and Mandler found a tendency for this function of number of clustered items over increasing critical pause length to momentarily flatten at about Size 5, plus or minus two items. They took this apparent inflection as evidence that clusters tend to be of about this size on average. In performing these calculations, Graesser and Mandler (1978) omitted all single-item clusters from consideration. (They estimated that single-item clusters account for 13% of all items produced in their data.) The omission of these single items must inflate any estimate of average cluster size. A second inflation occurred in their taking of mean rather than median estimates of cluster size. The distribution of cluster sizes is positively skewed both in their data (p. 96) and in ours (Figure 6). Thus, although their solution is appealingly straightforward, their particular conclusions require modification.

239

Semantic Fields Earlier in this article, the notion of settiantic fields was presented in terms of a two-process model consisting of a search for meanings leading to the production of items associated with those meanings. Meanings or semantic fields are proposed to be what is searched for in the task. The words produced when a semantic field is accessed constitute a cluster in the protocol. By this distinction, a semantic field represents an organization of concepts or meanings (perhaps something like "pets"), whereas a cluster constitutes that set of associated words produced when the field is accessed (e.g., cat, dog, etc.). Thus, clusters produced when a field is accessed should contain conceptually or associatively related items (see Pollio et al., 1968; Schwartz & Humphreys, 1973). The suggestion is that words produced in a cluster are associated in terms of the semantic field accessed, a common meaning, rather than in terms of item-to-item associations. An indication that this may be fruitful to consider comes from examination of the few repetitions in the protocols. If we assume that subjects try to avoid repetitions in their production of items, then repetitions may only occur if the same item is accessed through a different semantic field and, thus, is not perceived as a repetition by the subject because a different idea is being expressed. Thus, the item cat may be produced by accessing a semantic field for pets and one for African mammals. Continuing in this anecdotal vein, we cite a subject who repeated the word beer. The first occurrence of beer, at 62 words into the protocol, was in the following cluster definable as alcoholic beverages: creme de cacao, whiskey sour, beer, scotch and soda, and so on. The second occurrence was at 246 words into the protocol and in a cluster definable as snacks: Chunky candy bcr, pretzel, beer, Michelob, and so on. Although item-to-item associations clearly occur, there are also many examples in the data similar to this one. These results are consistent with the suggestion that observers search for semantic fields.

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PAUL J. GRUENEWALD AND GREGORY R. LOCKHEAD Conclusion

People apparently produce items in unconstrained free recall by searching for semantic fields and by producing whatever items are discovered during that search. This process produces clusters of associatively related items that are separated in time. The hypothesis that this search for new semantic fields produces the cumulative hyperbolic function relating items produced to time in the task is supported by the present data. Clusters produced when semantic fields are located are of various sizes. They appear generally small (about 1 or 2 items much of the time), but occasional clusters of more than 10 items were also produced in the tasks. The production of items within clusters appears to be constant; item production does not depend on time in the task or on position of the item in a cluster in these data. Perhaps most importantly, the algorithm to measure these temporal relations between produced items provides cluster measures that correlate with those from independent semantic judgments. Hence, the temporal algorithm reflects the structure of semantic memory and the semantic search process. References Bousfield, W. A. The occurrence of clustering in the recall of randomly arranged associates. Journal of General Psychology, 1953, 49, 229240. Bousfield, W. A., & Cohen, B. H. The occurrence of clustering in the recall of randomly arranged words of different frequencies of usage. Journal of General Psychology, 1955, 52, 83-95. Bousfield, W. A., & Sedgewick, H. W. An analysis of sequences of restricted associative responses. Journal of General Psychology, 1944, 30, 149-165. Bousfield, W. A., Sedgewick, H. W., & Cohen, B. H. Certain temporal characteristics of the recall of verbal associates. American Journal of Psychology, 1954, 67, 111-118. Crowder, R. G. Principles of learning and memory. Hillsdale, N.J.: Erlbaum, 1976. Dean, P. Organisational structure and retrieval processes in long-term memory. Unpublished doctoral dissertation, University of California, San Diego, 1971. Friendly, M. L. In search of the M-gram: The structure of organization in free recall. Cognitive Psychology, 1977, 9, 188-249. Graesser, A., II, & Handler, G. Limited processing

capacity constrains the storage of unrelated sets of words and retrieval from natural categories. Journal of Experimental Psychology: Human Learning and Memory, 1978, 4, 86-100. Horn, R. W. Effects of age and cueing on retrieval from semantic memory (Doctoral dissertation, Duke University, 1979). Dissertation Abstracts International, 1979, 40, 1896B-1897B. (Order No. 7922752). Indow, T., & Togano, K. On retrieving sequence from long-term memory. Psychological Review,

1970, 77, 317-331. Kaplan, I. T., & Carvellas, T. Response probabilities in verbal recall. Journal of Verbal Learning and Verbal Behavior, 1969, 8, 344-349. Kellas, G., Ashcraft, M. H., Johnson, N. S., & Needham, S. Temporal aspects of storage and retrieval in free recall of categorized lists. Journal of Verbal learning and Verbal Behavior, 1973, 12, 499-511. Mandler, G. Memory storage and retrieval: Some limits on the reach of attention and consciousness. In P. M. A. Rabbitt & S. Dornic (Eds.), Attention and Performance V. New York: Academic Press, 1975. Mazur, J. E., & Hastie, R. Learning as accumulation: A reexamination of the learning curve. Psychological Bulletin, 1978, 85, 1256-1274. McCauley, C., & Kellas, G. Induced chunking: Temporal aspects of storage and retrieval. Journal of Experimental Psychology, 1974, 102, 260265. McCleery, R. H. On satiation curves. Animal Behavior, 1977, 25, 1005-1015. Miller, G. A., & Johnson-Laird, P. N. Language and perception, Cambridge, Mass.: Belknap Press, 1976. Miller, R. L. The linguistic relativity principle and Humboldtian ethnolinguistics. The Hague, The Netherlands: Mouton, 1968. Patterson, K. E., Meltzer, R. H., & Mandler, G. Inter-response times in categorized free recall. Journal of Verbal Learning and Verbal Behavior,

1971, 10, 417-426. Pollio, H. R., Kasschau, R. A., & DeNise, H. E. Associative structure and the temporal characteristics of free recall. Journal of Experimental Psychology, 1968, 76, 190-197. Pollio, H. R., Richards, S., & Lucas, R. Temporal properties of category recall. Journal of Verbal Learning and Verbal Behavior, 1969, 8, 529-536. Rubin, D. C., & Olson, M, J. Recall of semantic domains. Memory & Cognition, in press. Schwartz, R. M., & Humphreys, M, S. Similarity judgments and free recall of unrelated words. Journal of Experimental Psychology, 1973, 101, 10-15. Thurstone, L. L. The learning curve equation. Psychological Monographs, 1919, 26(3, Whole No. 114). Received September 14, 1979 Revision received December 6, 1979 •