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Effect of context on verbal recall
JOURNAL OF VERBAL LEARNING AND VERBAL BEHAVIOR
10, 207-212 (1971)
Effect of C o n t e x t on V e r b a l Recall I IRA T. KAPLAN AND THOMAS CARVELLAS New York University Medical Center, New York, New York 10016
AND WILLIAM METLAY Hofstra University, Hempstead, New York 11550
Sixty-seven Ss were presented with samples of English text in which one word had been replaced by a blank and were allowed 15 min to list all the words that might have been the one deleted. The context surrounding the blank varied from 0 to 40 words. Increasing the amount of context decreased the number of words that S could produce to fit the context, but increased the proportional recall rate, that is, the proportion of the total number of words recallable that was produced per unit time. The results were interpreted in terms of a search model for verbal recall, in which the context determines the number of target words, the number of items in memory through which S searches for target words, and the rate at which he scans these items.
Word fluency is the ability to produce words rapidly. It is measured by the number of words in a specified category that S can write in a fixed amount of time. Thurstone's (1938) factor analysis of the answers to m a n y intelligence-test items led him to conclude that word fluency is one of seven primary mental abilities. Guilford (1967) considers word fluency a component of a more general ability to produce both verbal and nonverbal material rapidly. Experimental studies of verbal fluency have shown that the rate at which S produces words in a specified category decreases as he exhausts his supply of recallable words, so that the cumulative number of responses recalled as a function of time is a negatively accelerated curve that approaches a horizontal asymptote. Bousfield and Sedgewick (1944) observed this characteristic curve with a variety of categories, e.g., birds, U.S. cities, and showed that the cumulative distri-
butions could be described by an exponential curve of the form F = T(1 - e-m),
(1)
where F i s the frequency of responses given by time t, T is the limiting number of words recallable, a n d p is a parameter that determines the proportional rate at which this limit is approached: the larger the value of p, the more rapidly the curve approaches its asymptote. Johnson, Johnson, and M a r k (1951) pointed out that an individual's word-fluency score can be analyzed into the two factors identified by Eq. 1 : (a) the S's total supply of words in the specified category, and (b) his rate of depleting this supply. Comparing the p and T values obtained for different Ss, these authors discovered a negative correlation between proportional rate and total words recallable. In their experiment the Ss were z This investigation was supported by PHS Research given 15 rain to list all the U.S. cities they Grant EY-00384 from the National Eye Institute, and could think of and, in another task, all the animal names of two or more syllables. When by Hofstra University Grant 0580. 207
208
KAPLAN, CARVELLAS, AND METLAY
Eq. 1 was fitted to the data for individual Ss, it was found that Ss with high T values generally had low p values. In other words, Ss who produced more responses took longer to produce any given proportion of them. The inverse relation between proportional response rate and total words recallable applies not only to the performance of different Ss on the same task, but also to performance by the same Ss under different task conditions. Kaplan, Carvellas, and Metlay (1969) had their Ss make up four-letter words from sets of 5-10 different letters. Of course, S produced more words when he had more letters to work with. But fitting Eq. 1 to the data showed that while T increased with the size of the letter set, p decreased. In fact, p was inversely proportional to T. The authors also analyzed the original data of Bousfield and Sedgewick (1944) and found a negative correlation between the p and T values calculated for the 14 different categories of that experiment. Indow and Togano (1970) observed that a decrease in proportional respons6 rate accompanied an increase in total words recallable when Ss were retested on the same category at 2-3-month intervals. On four separate occasions the Ss listed all the female names they could recall, and Eq. 1 was fitted to the results of each session. From one session to the next, Tincreased andp decreased in such a way that, as in the word-formation task, the two parameters were inversely proportional. Both the exponential form of the cumulative response curves and the inverse relation between p and T can be accounted for by a simple search model of verbal recall. Assume that the stimuli and instructions of a wordproduction task activate a file of information stored in S's memory. The model describes verbal recall as a sequence of trials, on each of which S selects one item at random from the file and tests it to determine whether it is a word that he has already produced. If it is, he does not give it again. There are T items in the file, all of which are members of the specified
category, and every item remains in the file after it is examined, so that the total is always T. Then if F is the number of words already produced, the probability of finding a new target on any single trial is ( T - F)/T. By defining a sampling rate, k, in trials per unit time, an equation can be written for the rate at which S finds new targets as a function of time:
dF
k
~- = ~, (T-- F).
(2)
The exponential function of Eq. 1 is obtained by integrating Eq. 2 and substituting k
p = ~.
(3)
Thus the inverse relation between p and T follows from the hypothesis that each item examined is randomly selected from S's total supply of words in the specified category. The random-search model makes the simplifying assumption that every word in the memory file has the same probability of being selected on any trial. Although there is evidence that the words in a category have different probabilities of being emitted (Aborn & Rubenstein, 1958; Kaplan & Carvellas, 1969; Shepard, 1963), this fact does not invalidate the basic argument that the proportional response rate should decrease as the number of words that S searches through increases. The inverse relation between p and T observed in all the preceding studies may not hold for two conditions of an experiment by Christensen, Guilford, and Wilson (1957). Their Ss were presented with a brief story and allowed 12 min to write as many appropriate titles as they could. In one condition they were requested only to list relevant titles; in the other the titles had to be both relevant and clever. The added constraint of cleverness had the effect of reducing both the proportional response rate and the total number of titles produced in the allotted time. Although the estimated Tvalues were not given, the decrease in the number of titles produced suggests that
209
EFFECT OF CONTEXT ON VERBAL RECALL
T decreased as well. A simultaneous decrease in p and T is, however, inconsistent with the simple search m o d e l described above. The p u r p o s e of the present study was to investigate the effect of contextual c o n s t r a i n t u p o n the relationship between p r o p o r t i o n a l response rate a n d total words recallable, a n d to i n c o r p o r a t e this effect into a m o r e complete search m o d e l of verbal recall.
words were not allowed. In order to mark time on the response sheets, the Ss were instructed to draw a line under their last response whenever E said, "Now." This signal was given at every 30-sec interval for 15 min, at which time the Ss were told to stop. The Ss were encouraged to write down any response they were unsure of and to keep trying if they were momentarily unable to think of a response. To insure that the Ss understood the time-marking procedure, a practice session in which they listed threedigit numbers that summed to 14 preceded the experiment proper.
METHOD Subjects. Sixty-seven students from introductory psychology courses at Hofstra University served as Ss. Stimulus materials. Each S received a 5 x 8-in. card on which a sample of context was typed. The six samples of context contained 0,1,2, 4,10, and 40 words. Zero context was represented by a card bearing the statement, "No context." The five other contexts were selections of text from books. Passages containing proper nouns, foreign words, or stereotyped phrases were avoided. For 2-40 words of context, the middle word of each sample was replaced by an underlined blank space. With the 1-word context, the word preceded the blank. Procedure. Each context condition was administered to a different group of 9-12 Ss. The Ss first received a stimulus card face down and a response sheet. They were then told that the cards contained some phrases or part of a phrase, one word of which had been left blank, and that their task was to list as many words as they could that might be the missing word. The Ss in the 0-context condition were told simply to list as many words as they could think of. Proper nouns and foreign
RESULTS Increasing the a m o u n t of context decreased the n u m b e r of words p r o d u c e d in 15 min. I n the 0-context condition, S listed a n average of 235.2 words. W i t h 1 a n d 2 words of context, the n u m b e r o f responses fell to 140.6 a n d 56.5, respectively. The effect of further increases in context was less p r o n o u n c e d : 4, 10, a n d 40 words reduced the n u m b e r of responses to 64.5, 45.4, a n d 15.8. Figure 1 shows how these responses were p r o d u c e d as a f u n c t i o n of time. T h e points in each d i s t r i b u t i o n represent the m e a n cumulative frequency of words per S in each context condition. All the distrib u t i o n s show a gradual decline in response rate with time. The curves d r a w n t h r o u g h each set of points i n Figure 1 are graphs of the exponential
200
1
loc z 4 2 10
• •
,
.
5
10
.
_
_40~
15
T,me (m,nutes)
FIG. 1. Cumulative frequency of words produced as a function of time with 0--40 words of context.
210
KAPLAN, CARVELLAS, AND METLAY
- .5 ~ W o r d
Formation
n "a_lO
-15 11o
'
115
'
21o
Log T
'
2'5
'
FIG. 2. Log p versus log T for phrase-completion and word-formation tasks. function given in Eq. 1. The curves were fitted by an optimization procedure that minimized the sum of deviations squared. 2 The parameters T a n d p of the fitted curves estimate the limiting number of responses and the proportional recall rate. There was considerable change in both factors as a function of context. With 0 context the cumulative response curve rose toward an estimated limit, T, of 742 words. As the amount of context increased, T decreased to 263, 87, 149, 87, and 19 words. The proportional rate, on the other hand, increased with the amount of context: from .025 per min with no context, to .050, .064, .037, .048, and •105 per rain for 1- to 40-word contexts. Thus, a 4-fold increase in p was assooated with a 39-fold decrease in T. The relationship between p and T can be seen more clearly in Figure 2, where log p is plotted against log T. The coordinates of each circle represent the p and T values obtained with a given amount of context, from 40 words of context at the highest circle to 0 words at the lowest. The straight line through these points has the equation log p = - .473 .391 log T, or in unlogged f o r m p = .337/T "39z. In contrast, the results of the word-formation experiment (Kaplan et al., 1969), indicated by 2 The authors are grateful to M. Goldberg, W. Kern, and J. Ne~ditch for writing the computer program that calculated the fitted curves.
the squares in Figure 2, are described by the equation p = 4.01/T L°°. In that experiment, S's task was to make up all the four-letter words he could from sets of 5-10 letters. Each successive square, from left to right, represents thep and Tvalues obtained with one additional letter in the set. In general, the effect of increasing the number of letters that S worked with was similar to decreasing the amount of context in the present experiment, i.e., p decreased while T increased. In the wordformation task, however, p decreased more rapidly as a function of T than it did in the phrase-completion task. The context in which recall took place was apparently not limited to the stimuli and instructions provided by E, but included the whole of S's environment. The constraining effect of the nonverbal environment was evident in the 0-context condition of the present experiment. One sign of this constraint is that the fitted cumulative response curve approaches a limit of 742 words, which is far less than the thousands of words in common use. This is not to say that the environment ruled out certain potential responses, but rather that words which lacked an external stimulus were unlikely to be suggested in the first place. The influence of objects in the environment becomes more apparent when the words produced by different Ss are compared.
211
EFFECT OF CONTEXT ON VERBAL RECALL
Certain words were listed by a majority of the Ss, e.g., the words boy, girl, hair, head, foot, hand, arm, watch, paper, read, and write were given by 7 or more of the 11 Ss in this condition. As more verbal context was introduced in the other conditions, the influence of background stimuli became less significant.
words that satisfy the contextual constraints. The memory file contains N items, of which T are targets. As before, each randomly selected item remains in the file after it is examined, so that the total is always N. The probability of finding a new target on any single trial now becomes (T-F)/N. Consequently, Eq. 2 becomes dF
DISCUSSION
The effect of contextual constraint was to increase S's proportional response rate while decreasing his total words recallable, but the change in p was proportionately smaller than the change in T. According to Eq. 3 of the model, this result indicates that the scanning rate, k, decreased as the amount of context increased. However, if S tests each randomly selected item merely to determine whether it has already been produced, the context should not affect the scanning rate. The change in scanning rate suggests that S tests each item not only to avoid gwing the same response twice, but also to decide whether it satisfies the constraints imposed by the context. The memory file, therefore, must include inappropriate items as well as words that fit the context. In the phrase-completion task, for example, the two-word context " m a y to" might suggest words like have, has, had, of which only have is grammatically correct. Or if S's task as to make up four-letter words from the letters r a tp e, he might think of such potential responses as rat, trap, trip, of which only the second contains the required number of specified letters. This hypothesis, that me target words are part of a larger search set, agrees with the models of verbal recall developed by Kaplan et al. (1969), Shiffrin and Atkinson (1969), and Indow and Togano (1970). The model described in the introduction can be modified to incorporate the results of the present experiment by assuming that the context activates a file of information stored in memory, which S then searches for target
aT -
(T-F),
(4)
and Eq. 3 is replaced by k
P = 9
(5)
In the word-formation task, Tls the number of four-letter words that S can make from the stimulus letters, and N represents the unknown number of items, both word and nonword, suggested by the letters. As the number of stimulus letters increases, T increases and presumably N does also. The S's task, however, is always the same, regardless of the number of letters presented, namely, to form four-letter words. Thus, if S always works with four letters at a time, it is reasonable to assume that the time required to form and test a trial solution does not vary with the number of stimulus letters, and that the ratm of solutions to total items also remains constant. In other words, both the scanning rate k and the ratio TIN = C are invariant. Substituting TIC for N in Eq. 5 yields the relation P-
kC T'
(6)
that is, p is inversely proportional to T. Th~s equation agrees with the experimental result: p = 4.01/T. In the phrase completion task, on the other hand, p ~s less than inversely proportlonal to T because the task becomes more exacting as the amount of context increases. Every word in the context presumably exerts some constraint on the choice of words to fill the blank, so that increasing context must increase the number of criteria that a potential response word has to satisfy. Therefore, the
212
KAPLAN, CARVELLAS, AND METLAY
greater the amount of context, the more extensive the testing of a trial word, and so the slower the scanning rate k. But with more tests, the less likely is the word to survive at all, so that increased context probably reduces the ratio T I N = C as well. Returning to Eq. 6, it can be seen that such a decrease in k or C modifies the inverse relation between p and T. More context reduces both T and kC, with the result that p changes less than T, as indicated by the fractional exponent in the expression given earlier: p = .337/T "391. In most of the studies cited in the introduction, an increase in p was associated with a decrease in T, which follows from Eq. 6 when k and C are relatively constant. An exception to this trend was the experiment of Christensen et al. (1957) in which S produced fewer responses at a slower proportional rate when he was asked to make up titles that were both clever and relevant, rather than merely relevant. This atypical result has a reasonable explanation in terms of the revised model: The added requirement of cleverness, although it reduces the number of acceptable responses T probably has little effect on the number of titles N that S searches through. It should, however, reduce S's scanning rate k since he must test each potential response for cleverness as well as for relevance. Thus the proportional response rate becomes slower, because the numerator of Eq. 5 grows smaller while the denominator remains unchanged. In summary, the hypothesis that verbal recall involves random search through a file of items stored in memory leads to an exponential function that describes the cumulative distribution of response times. As S produces responses, their cumulative frequency asymptotically approaches the number of target words in the file. The rate at which this hmlt is approached is directly proportional to the
rate at which S scans the file, and inversely proportional to the total number of items in the file. Contextual constraint reduces both the number of targets and the total number of items, so that a decrease in the limiting number of words produced is associated with an increase in the proportional rate of recall. When the constraint also reduces the scanning rate, however, this moderates the increase in the proportional recall rate. REFERENCES ABORN, M., & RUBENSTEIN,H. Perception of contextually dependent word-probabilities. American Journal of Psychology, 1958, 71,420-422. BOUSFIELD,W. A., & SEDGEWlCK,C. H. W. An analysis of restricted associative responses. Journal of GeneralPsychology, 1944, 30, 149-165. CHRISTENSEN,P. R., GUILFORD,J. P., & WILSON,R. C. Relations of creative responses to working time and instructions. Journal of Experimental Psychology, 1957, 53, 82-88. GUILFORD,J. P. The nature of human intelligence. New York: McGraw-Hill, 1967. INDOW,T., & TOGANO,K. On retrieving sequence from long-term memory. Psychological Review, 1970, 77, 317-331. JOHNSON, D. M., JOHNSON, R. C., & MARK, A. L. A mathematical analysis of verbal fluency. Journal of General Psychology, 1951, 44, 121-128. KAPLAN, ]. T., & CARVELLAS,T. Response probabilities in verbal recall. Journal of Verbal Learning and Verbal Behavior, 1969, 8, 344-349. KAPLAN,I. T., CARVELLAS,T., & METLAY,W. Searching for words in letter sets of varying size. Journal of ExperimentalPsychology, 1969, 82, 377-380. SrlEPARD, R. N. Production of constrained associates and the informational uncertainty of the constraint. American Journal of Psychology, 1963, 76, 218-228. SmrrRiN, R. M., & ArKINSON, R. C. Storage and retrieval processes in long-term memory. Psychological Review, 1969, 76, 179-193. THURSTONE,L. L. Primary mental abihttes. Chicago: Univer. of Chicago Press, 1938. (Received November 9, 1970)
10, 207-212 (1971)
Effect of C o n t e x t on V e r b a l Recall I IRA T. KAPLAN AND THOMAS CARVELLAS New York University Medical Center, New York, New York 10016
AND WILLIAM METLAY Hofstra University, Hempstead, New York 11550
Sixty-seven Ss were presented with samples of English text in which one word had been replaced by a blank and were allowed 15 min to list all the words that might have been the one deleted. The context surrounding the blank varied from 0 to 40 words. Increasing the amount of context decreased the number of words that S could produce to fit the context, but increased the proportional recall rate, that is, the proportion of the total number of words recallable that was produced per unit time. The results were interpreted in terms of a search model for verbal recall, in which the context determines the number of target words, the number of items in memory through which S searches for target words, and the rate at which he scans these items.
Word fluency is the ability to produce words rapidly. It is measured by the number of words in a specified category that S can write in a fixed amount of time. Thurstone's (1938) factor analysis of the answers to m a n y intelligence-test items led him to conclude that word fluency is one of seven primary mental abilities. Guilford (1967) considers word fluency a component of a more general ability to produce both verbal and nonverbal material rapidly. Experimental studies of verbal fluency have shown that the rate at which S produces words in a specified category decreases as he exhausts his supply of recallable words, so that the cumulative number of responses recalled as a function of time is a negatively accelerated curve that approaches a horizontal asymptote. Bousfield and Sedgewick (1944) observed this characteristic curve with a variety of categories, e.g., birds, U.S. cities, and showed that the cumulative distri-
butions could be described by an exponential curve of the form F = T(1 - e-m),
(1)
where F i s the frequency of responses given by time t, T is the limiting number of words recallable, a n d p is a parameter that determines the proportional rate at which this limit is approached: the larger the value of p, the more rapidly the curve approaches its asymptote. Johnson, Johnson, and M a r k (1951) pointed out that an individual's word-fluency score can be analyzed into the two factors identified by Eq. 1 : (a) the S's total supply of words in the specified category, and (b) his rate of depleting this supply. Comparing the p and T values obtained for different Ss, these authors discovered a negative correlation between proportional rate and total words recallable. In their experiment the Ss were z This investigation was supported by PHS Research given 15 rain to list all the U.S. cities they Grant EY-00384 from the National Eye Institute, and could think of and, in another task, all the animal names of two or more syllables. When by Hofstra University Grant 0580. 207
208
KAPLAN, CARVELLAS, AND METLAY
Eq. 1 was fitted to the data for individual Ss, it was found that Ss with high T values generally had low p values. In other words, Ss who produced more responses took longer to produce any given proportion of them. The inverse relation between proportional response rate and total words recallable applies not only to the performance of different Ss on the same task, but also to performance by the same Ss under different task conditions. Kaplan, Carvellas, and Metlay (1969) had their Ss make up four-letter words from sets of 5-10 different letters. Of course, S produced more words when he had more letters to work with. But fitting Eq. 1 to the data showed that while T increased with the size of the letter set, p decreased. In fact, p was inversely proportional to T. The authors also analyzed the original data of Bousfield and Sedgewick (1944) and found a negative correlation between the p and T values calculated for the 14 different categories of that experiment. Indow and Togano (1970) observed that a decrease in proportional respons6 rate accompanied an increase in total words recallable when Ss were retested on the same category at 2-3-month intervals. On four separate occasions the Ss listed all the female names they could recall, and Eq. 1 was fitted to the results of each session. From one session to the next, Tincreased andp decreased in such a way that, as in the word-formation task, the two parameters were inversely proportional. Both the exponential form of the cumulative response curves and the inverse relation between p and T can be accounted for by a simple search model of verbal recall. Assume that the stimuli and instructions of a wordproduction task activate a file of information stored in S's memory. The model describes verbal recall as a sequence of trials, on each of which S selects one item at random from the file and tests it to determine whether it is a word that he has already produced. If it is, he does not give it again. There are T items in the file, all of which are members of the specified
category, and every item remains in the file after it is examined, so that the total is always T. Then if F is the number of words already produced, the probability of finding a new target on any single trial is ( T - F)/T. By defining a sampling rate, k, in trials per unit time, an equation can be written for the rate at which S finds new targets as a function of time:
dF
k
~- = ~, (T-- F).
(2)
The exponential function of Eq. 1 is obtained by integrating Eq. 2 and substituting k
p = ~.
(3)
Thus the inverse relation between p and T follows from the hypothesis that each item examined is randomly selected from S's total supply of words in the specified category. The random-search model makes the simplifying assumption that every word in the memory file has the same probability of being selected on any trial. Although there is evidence that the words in a category have different probabilities of being emitted (Aborn & Rubenstein, 1958; Kaplan & Carvellas, 1969; Shepard, 1963), this fact does not invalidate the basic argument that the proportional response rate should decrease as the number of words that S searches through increases. The inverse relation between p and T observed in all the preceding studies may not hold for two conditions of an experiment by Christensen, Guilford, and Wilson (1957). Their Ss were presented with a brief story and allowed 12 min to write as many appropriate titles as they could. In one condition they were requested only to list relevant titles; in the other the titles had to be both relevant and clever. The added constraint of cleverness had the effect of reducing both the proportional response rate and the total number of titles produced in the allotted time. Although the estimated Tvalues were not given, the decrease in the number of titles produced suggests that
209
EFFECT OF CONTEXT ON VERBAL RECALL
T decreased as well. A simultaneous decrease in p and T is, however, inconsistent with the simple search m o d e l described above. The p u r p o s e of the present study was to investigate the effect of contextual c o n s t r a i n t u p o n the relationship between p r o p o r t i o n a l response rate a n d total words recallable, a n d to i n c o r p o r a t e this effect into a m o r e complete search m o d e l of verbal recall.
words were not allowed. In order to mark time on the response sheets, the Ss were instructed to draw a line under their last response whenever E said, "Now." This signal was given at every 30-sec interval for 15 min, at which time the Ss were told to stop. The Ss were encouraged to write down any response they were unsure of and to keep trying if they were momentarily unable to think of a response. To insure that the Ss understood the time-marking procedure, a practice session in which they listed threedigit numbers that summed to 14 preceded the experiment proper.
METHOD Subjects. Sixty-seven students from introductory psychology courses at Hofstra University served as Ss. Stimulus materials. Each S received a 5 x 8-in. card on which a sample of context was typed. The six samples of context contained 0,1,2, 4,10, and 40 words. Zero context was represented by a card bearing the statement, "No context." The five other contexts were selections of text from books. Passages containing proper nouns, foreign words, or stereotyped phrases were avoided. For 2-40 words of context, the middle word of each sample was replaced by an underlined blank space. With the 1-word context, the word preceded the blank. Procedure. Each context condition was administered to a different group of 9-12 Ss. The Ss first received a stimulus card face down and a response sheet. They were then told that the cards contained some phrases or part of a phrase, one word of which had been left blank, and that their task was to list as many words as they could that might be the missing word. The Ss in the 0-context condition were told simply to list as many words as they could think of. Proper nouns and foreign
RESULTS Increasing the a m o u n t of context decreased the n u m b e r of words p r o d u c e d in 15 min. I n the 0-context condition, S listed a n average of 235.2 words. W i t h 1 a n d 2 words of context, the n u m b e r o f responses fell to 140.6 a n d 56.5, respectively. The effect of further increases in context was less p r o n o u n c e d : 4, 10, a n d 40 words reduced the n u m b e r of responses to 64.5, 45.4, a n d 15.8. Figure 1 shows how these responses were p r o d u c e d as a f u n c t i o n of time. T h e points in each d i s t r i b u t i o n represent the m e a n cumulative frequency of words per S in each context condition. All the distrib u t i o n s show a gradual decline in response rate with time. The curves d r a w n t h r o u g h each set of points i n Figure 1 are graphs of the exponential
200
1
loc z 4 2 10
• •
,
.
5
10
.
_
_40~
15
T,me (m,nutes)
FIG. 1. Cumulative frequency of words produced as a function of time with 0--40 words of context.
210
KAPLAN, CARVELLAS, AND METLAY
- .5 ~ W o r d
Formation
n "a_lO
-15 11o
'
115
'
21o
Log T
'
2'5
'
FIG. 2. Log p versus log T for phrase-completion and word-formation tasks. function given in Eq. 1. The curves were fitted by an optimization procedure that minimized the sum of deviations squared. 2 The parameters T a n d p of the fitted curves estimate the limiting number of responses and the proportional recall rate. There was considerable change in both factors as a function of context. With 0 context the cumulative response curve rose toward an estimated limit, T, of 742 words. As the amount of context increased, T decreased to 263, 87, 149, 87, and 19 words. The proportional rate, on the other hand, increased with the amount of context: from .025 per min with no context, to .050, .064, .037, .048, and •105 per rain for 1- to 40-word contexts. Thus, a 4-fold increase in p was assooated with a 39-fold decrease in T. The relationship between p and T can be seen more clearly in Figure 2, where log p is plotted against log T. The coordinates of each circle represent the p and T values obtained with a given amount of context, from 40 words of context at the highest circle to 0 words at the lowest. The straight line through these points has the equation log p = - .473 .391 log T, or in unlogged f o r m p = .337/T "39z. In contrast, the results of the word-formation experiment (Kaplan et al., 1969), indicated by 2 The authors are grateful to M. Goldberg, W. Kern, and J. Ne~ditch for writing the computer program that calculated the fitted curves.
the squares in Figure 2, are described by the equation p = 4.01/T L°°. In that experiment, S's task was to make up all the four-letter words he could from sets of 5-10 letters. Each successive square, from left to right, represents thep and Tvalues obtained with one additional letter in the set. In general, the effect of increasing the number of letters that S worked with was similar to decreasing the amount of context in the present experiment, i.e., p decreased while T increased. In the wordformation task, however, p decreased more rapidly as a function of T than it did in the phrase-completion task. The context in which recall took place was apparently not limited to the stimuli and instructions provided by E, but included the whole of S's environment. The constraining effect of the nonverbal environment was evident in the 0-context condition of the present experiment. One sign of this constraint is that the fitted cumulative response curve approaches a limit of 742 words, which is far less than the thousands of words in common use. This is not to say that the environment ruled out certain potential responses, but rather that words which lacked an external stimulus were unlikely to be suggested in the first place. The influence of objects in the environment becomes more apparent when the words produced by different Ss are compared.
211
EFFECT OF CONTEXT ON VERBAL RECALL
Certain words were listed by a majority of the Ss, e.g., the words boy, girl, hair, head, foot, hand, arm, watch, paper, read, and write were given by 7 or more of the 11 Ss in this condition. As more verbal context was introduced in the other conditions, the influence of background stimuli became less significant.
words that satisfy the contextual constraints. The memory file contains N items, of which T are targets. As before, each randomly selected item remains in the file after it is examined, so that the total is always N. The probability of finding a new target on any single trial now becomes (T-F)/N. Consequently, Eq. 2 becomes dF
DISCUSSION
The effect of contextual constraint was to increase S's proportional response rate while decreasing his total words recallable, but the change in p was proportionately smaller than the change in T. According to Eq. 3 of the model, this result indicates that the scanning rate, k, decreased as the amount of context increased. However, if S tests each randomly selected item merely to determine whether it has already been produced, the context should not affect the scanning rate. The change in scanning rate suggests that S tests each item not only to avoid gwing the same response twice, but also to decide whether it satisfies the constraints imposed by the context. The memory file, therefore, must include inappropriate items as well as words that fit the context. In the phrase-completion task, for example, the two-word context " m a y to" might suggest words like have, has, had, of which only have is grammatically correct. Or if S's task as to make up four-letter words from the letters r a tp e, he might think of such potential responses as rat, trap, trip, of which only the second contains the required number of specified letters. This hypothesis, that me target words are part of a larger search set, agrees with the models of verbal recall developed by Kaplan et al. (1969), Shiffrin and Atkinson (1969), and Indow and Togano (1970). The model described in the introduction can be modified to incorporate the results of the present experiment by assuming that the context activates a file of information stored in memory, which S then searches for target
aT -
(T-F),
(4)
and Eq. 3 is replaced by k
P = 9
(5)
In the word-formation task, Tls the number of four-letter words that S can make from the stimulus letters, and N represents the unknown number of items, both word and nonword, suggested by the letters. As the number of stimulus letters increases, T increases and presumably N does also. The S's task, however, is always the same, regardless of the number of letters presented, namely, to form four-letter words. Thus, if S always works with four letters at a time, it is reasonable to assume that the time required to form and test a trial solution does not vary with the number of stimulus letters, and that the ratm of solutions to total items also remains constant. In other words, both the scanning rate k and the ratio TIN = C are invariant. Substituting TIC for N in Eq. 5 yields the relation P-
kC T'
(6)
that is, p is inversely proportional to T. Th~s equation agrees with the experimental result: p = 4.01/T. In the phrase completion task, on the other hand, p ~s less than inversely proportlonal to T because the task becomes more exacting as the amount of context increases. Every word in the context presumably exerts some constraint on the choice of words to fill the blank, so that increasing context must increase the number of criteria that a potential response word has to satisfy. Therefore, the
212
KAPLAN, CARVELLAS, AND METLAY
greater the amount of context, the more extensive the testing of a trial word, and so the slower the scanning rate k. But with more tests, the less likely is the word to survive at all, so that increased context probably reduces the ratio T I N = C as well. Returning to Eq. 6, it can be seen that such a decrease in k or C modifies the inverse relation between p and T. More context reduces both T and kC, with the result that p changes less than T, as indicated by the fractional exponent in the expression given earlier: p = .337/T "391. In most of the studies cited in the introduction, an increase in p was associated with a decrease in T, which follows from Eq. 6 when k and C are relatively constant. An exception to this trend was the experiment of Christensen et al. (1957) in which S produced fewer responses at a slower proportional rate when he was asked to make up titles that were both clever and relevant, rather than merely relevant. This atypical result has a reasonable explanation in terms of the revised model: The added requirement of cleverness, although it reduces the number of acceptable responses T probably has little effect on the number of titles N that S searches through. It should, however, reduce S's scanning rate k since he must test each potential response for cleverness as well as for relevance. Thus the proportional response rate becomes slower, because the numerator of Eq. 5 grows smaller while the denominator remains unchanged. In summary, the hypothesis that verbal recall involves random search through a file of items stored in memory leads to an exponential function that describes the cumulative distribution of response times. As S produces responses, their cumulative frequency asymptotically approaches the number of target words in the file. The rate at which this hmlt is approached is directly proportional to the
rate at which S scans the file, and inversely proportional to the total number of items in the file. Contextual constraint reduces both the number of targets and the total number of items, so that a decrease in the limiting number of words produced is associated with an increase in the proportional rate of recall. When the constraint also reduces the scanning rate, however, this moderates the increase in the proportional recall rate. REFERENCES ABORN, M., & RUBENSTEIN,H. Perception of contextually dependent word-probabilities. American Journal of Psychology, 1958, 71,420-422. BOUSFIELD,W. A., & SEDGEWlCK,C. H. W. An analysis of restricted associative responses. Journal of GeneralPsychology, 1944, 30, 149-165. CHRISTENSEN,P. R., GUILFORD,J. P., & WILSON,R. C. Relations of creative responses to working time and instructions. Journal of Experimental Psychology, 1957, 53, 82-88. GUILFORD,J. P. The nature of human intelligence. New York: McGraw-Hill, 1967. INDOW,T., & TOGANO,K. On retrieving sequence from long-term memory. Psychological Review, 1970, 77, 317-331. JOHNSON, D. M., JOHNSON, R. C., & MARK, A. L. A mathematical analysis of verbal fluency. Journal of General Psychology, 1951, 44, 121-128. KAPLAN, ]. T., & CARVELLAS,T. Response probabilities in verbal recall. Journal of Verbal Learning and Verbal Behavior, 1969, 8, 344-349. KAPLAN,I. T., CARVELLAS,T., & METLAY,W. Searching for words in letter sets of varying size. Journal of ExperimentalPsychology, 1969, 82, 377-380. SrlEPARD, R. N. Production of constrained associates and the informational uncertainty of the constraint. American Journal of Psychology, 1963, 76, 218-228. SmrrRiN, R. M., & ArKINSON, R. C. Storage and retrieval processes in long-term memory. Psychological Review, 1969, 76, 179-193. THURSTONE,L. L. Primary mental abihttes. Chicago: Univer. of Chicago Press, 1938. (Received November 9, 1970)