- Email: [email protected]
Effect of word frequency on thinking of a word
JOURNAL OF VERBAL LEARNINC AND VERBAL BEHAVIOR 5, 4 3 4 - 4 4 0
(1966)
Effect of Word Frequency on Thinking of a Word 1 CARL"P. DUNCAN Northwestern University, Evanston, Illinois Three experiments were performed to determine the effect of word frequency on thinking of a word. In all experiments Ss were given certain characteristics of words, such as the first letter, the last letter, the number of letters, or the class of the object named by the word, and were asked to think of a word fitting the given characteristics. In all experiments, more words of higher frequency were emitted than were words of lower frequency. In general, the tendency to emit words of higher relative frequencies held throughout the whole range of absolute frequencies. Not all high-frequency words that could have been emitted were emitted. The findings were interpreted in terms of a combination of the spew hypothesis, and of incomplete sampling from a population of words.
In certain kinds of problem solving, S must search among a population of possible responses until he hits upon, if he does, the particular response defined as the solution. As S emits responses, often implicitly, in his search, what variables determine which responses occur and which do not occur? I t seems reasonable to assume that one such variable will be the frequency, in S's past experience, with which he has encountered the responses. In general, responses known or assumed to have occurred more frequently in S's experience should be more likely to occur to him during searching or thinking. This hypothesis concerning the effects of response frequency on thinking derives chiefly from two sources. One is the spew hypothesis of Underwood and Schulz (1960), according to which verbal units are emitted in the order of frequency of experience with the units. These authors summarize a number of studies in which the spew hypothesis was supported in relatively free responding 1 This study was supported by Grant HD 00901, National Institute of Child Health and Human Development, National Institutes of Health, U.S. Public Health Service. Thanks are due I. David Isaacs, Gordon Wood, Judith Hanson, and Linda Shaffer. 434
situations such as free association. The other source is the study of Mayzner and Tresselt (1958) in which anagram solution times vary inversely with Thorndike-Lorge (1944) frequency of the solution words. It is Mayzner and Tresselt's theory that in attempting to solve an anagram, S generates implicit responses as some function of frequency. With an anagram, S has all the letters of the solution word presented to him. Letter hypotheses (Rhine, 1959), letter orders Mayzner and Tresselt, 1958; Teraoka, 1959), and frequencies of letter combinations (Dominowski and Duncan, 1964; Mayzner and Tresselt, 1959) become variables influencing solution. In the present study, an attempt was made to minimize the effects of letter variables and to maximize the frequency of the word as a whole. The S was asked to think of a word that meets certain specifications. The specifications served both to narrow the response population to be searched to the point where there was some probability that S would discover the word, and also to restrict, sometimes to a single word, the number of words that met the specifications, problems of this type should be solved more readily if the solution is a high-frequency rather than a low-frequency word.
435
WORD FREQUENCY AND T H I N K I N G
EXPERIMENT I
Method Words. The source of words was the five-letter words from Thorndike and Lorge (1944). The set of words to be used was obtained by selecting 20 subsets of words. The words in each subset had the same first letter and the same last letter. The 20 pairs of initial and final letters were: bd (thus including such words as brand, beard, blind, etc.), bh, bn, ck, cl, cp, fk, Jr, In, rnh, pk, pr, rl, rt, sk, sin, td, tr, wh, wt. These subsets ranged in number of five-letter words available (i.e., listed in Thorndike and Lorge) from six words (both In and pk) to 36 words (sk). The total number of words, all 20 subsets combined, was 266. Within each subset there was one or more words of T-L frequency of less than one per million words (Thorndike and Lorge General Count). Also within each subset there was one or more words of frequency of A (here taken as 50) or AA (here taken as 100), except for ]k, where the highest-frequency word was 44, and pk, highest frequency 28. The mean frequencies of the 20 subsets ranged from 11.4 to 39.1. The 20 median frequencies ranged from 1.5 to 26.0. For all 266 words in the population the mean frequency was 22.97, the median frequency 8.8. Subjects. The Ss were 60 students from introductory psychology classes in which students are required to serve in experiments. Procedure. After E and S had sat down facing each other across a table, E said to S, "I want you to guess some five-letter English words. I will give you the first letter and the last letter of one o[ these words. Then you try and tell me what the five-letter word is. None of the words which you are to guess is in plural form, and none is capitalized such as proper names or brand names. O.K., here is the first one." The E then gave the first letter of a problem item, paused a moment, then gave the last letter. The S was given 60 sec in which to respond. If S gave an unacceptable response, e.g., not a five-letter word, E pointed out the error and S was allowed the remainder of the 60-sec period to make another response. After S had responded with an acceptable response, or after 60 see had elapsed, E said, "Let's try another one." The E continued until all 20 letter pairs had been presented to each S. The 20 letter pairs were presented in a different haphazard order for each S.
Results O f the total possible 1200 responses (60 Ss X 20 guesses), 806 usable responses were o b t a i n e d , for a m e a n of 13.43 (aM z .44)
words per S. I n addition, there were 58 responses consisting of words, e.g., boxed, for which a T - L f r e q u e n c y is not available. T h e s e responses are not included in the data. F o r each S separately, b o t h the m e a n T - L f r e q u e n c y and the m e d i a n f r e q u e n c y of the words S g a v e w e r e determined. O v e r all Ss, the m e a n of the m e a n s was 41.91, 0.~i z 1.13. T h e m e a n of the m e d i a n s was 35.07, o.~i 2.02; the m e d i a n of the m e d i a n s was 32.0. T h e m e a n f r e q u e n c y of the p o p u l a t i o n of words was 22.97; thus, it can be seen t h a t either of the o b t a i n e d m e a n s is higher by a t-value of at least 5. F o r 58 of the 60 Ss, the m e a n f r e q u e n c y of S's responses was h i g h e r than the p o p u l a t i o n m e a n ; for 59 Ss the median f r e q u e n c y of their responses was higher t h a n the p o p u l a t i o n m e d i a n f r e q u e n c y (8.8). A n o t h e r c o m p a r i s o n is o b t a i n e d b y examining not total responses, b u t o n l y the n u m ber of different w o r d s emitted. O v e r all Ss, 186 words out of the p o p u l a t i o n of 266 words were g i v e n at least once, 80 were not given. O f the 133 words a b o v e the m e d i a n freq u e n c y (8.8) of the p o p u l a t i o n , 113 were given. Of the words below the median, only 73 were given. F o r the 186 e m i t t e d words, the m e a n T - L f r e q u e n c y was 28.60, 0~ 2.38 ( m e d i a n f r e q u e n c y was 15.3): thus, t h o u g h this is a fairly large sample of the p o p u l a t i o n , the m e a n f r e q u e n c y is signific a n t l y higher (t ~= 2.39) t h a n the population m e a n f r e q u e n c y (22.97). F o r the 80 words not e m i t t e d , the m e a n f r e q u e n c y was 8.79, o~i z 2.04 ( m e d i a n f r e q u e n c y was 2.1). I n T a b l e 1, f r e q u e n c y classes (first c o l u m n ) TABLE
I
POPULATION ~VORDS, EMITTED WORDS, AND TOTAL RESPONSES IN VARIOUS FREQUENCY CATEGORIES IN EXP. I
Frequency class
Population words
Emitted words
Total responses
A and AA 18-49 8-17 3-7 1-2 Less than 1
.~2 44 43 41 41 45
46 40 30 29 24 17
311 202 108 96 41 48
436
DUNCAN
h a v e been set up t h a t contain r o u g h l y equal n u m b e r s of p o p u l a t i o n words (second colu m n ) . C o l u m n 3 shows the n u m b e r of differe n t words e m i t t e d , a n d C o l u m n 4 shows total responses, for e a c h of the f r e q u e n c y classes. I t is clear t h a t b o t h n u m b e r of different words e m i t t e d and total responses decrease as freq u e n c y decreases. F o r all 266 p o p u l a t i o n words, the correlation b e t w e e n f r e q u e n c y of the w o r d and n u m b e r of times it was e m i t t e d was .44; for the 186 w o r d s t h a t were given at least once, the correlation was .40. EXPERIMENT I I I n Exp. I, each of the subsets of words associated w i t h a letter pair c o n t a i n e d several words. T h e S was free to give a n y one of the words in a subset t h a t he could t h i n k of. Since e v e n the smallest subset c o n t a i n e d six words, while the largest c o n t a i n e d 36 words, the task was s o m e t h i n g of a " f r e e r e s p o n s e " s i t u a t i o n like those in which U n d e r w o o d and Schulz (1960) found e v i d e n c e for the spew hypothesis. T h e purpose of Exp. I I was to test the effect of T - L f r e q u e n c y in a task w h e r e the n u m b e r of a c c e p t a b l e responses was severely restricted.
Method Words. The words were 34 pairs of words from Thorndike and Lorge (1944). Each of the 68 words had five letters. The two words within each pair had the same initial letter and the same final letter (initial and final letters were themselves identical in only two of the 34 pairs). The two words of a pair had different T-L frequencies. Hereafter, the word of higher frequency in a pair will be called the HF (high frequency) word and the other word will be called the LF (low frequency) word, regardless of the absolute frequency. The presence of a difference in frequency between the words of a pair is the independent variable;-the expectation is that the HF word will be more readily emitted when S is required to think of a word. Among the 68 words there were words of high absolute frequency (A or AA), and words of low absolute frequency (less than one per million). The diffelence in frequency between the words of a pair also varied, e.g., earth (AA) vs. epoch (5), until (AA) vs. usual (A), borax (2) vs. beaux (1).
Pilot work had revealed that there were pairs of words (from Thorndike and Lorge) for which Ss could think of too many alternative responses; the 34 pairs finally used do not include such pairs. It was also discovered that Ss found the task difficult. Because of this, the 34 pairs were divided into two sets, A and B, of 17 pairs each, and any one S worked on only one set. (To obtain an equal number of pairs in each set, one pair of words was used in which the two words had the same frequency, viz. outdo and outgo, both having frequency of one.) The two sets were roughly equivalent in absolute frequencies of words and in differences of frequency between words of a pair. Subjects. The Ss were 80 students from introductory psychology courses. Half were assigned Set A, half Set B. Procedure. After g and S sat down facing each other across a table, E said, "I want you to guess some five-letter English words. I will give you the first and the last letter of one of the words. Then you try to tell me what the five-letter word is. None of the words that you are to guess is plural form, and none is capitalized, such as proper names or brand names. O.K., here is the first one." The E then gave the first letter, paused momentarily, and gave the last letter. If S said either of the words in a pair, E gave him the next item. If S had not responded after 60 sec had elapsed, E said, "Let's try another," and gave S the letters for the next item. A different haphazard order of presentation of the 17 items in a set was used for each S. For each item, there were only two words available, one being of higher frequency than the other.
Results Since there was little difference in response to Sets A and B, the d a t a were c o m b i n e d . F o r all 80 Ss, the m e a n t o t a l n u m b e r of responses was 4.13. Since the m a x i m u m possible was 17, the task was r a t h e r difficult. ( T h e Ss g a v e a total of 28 responses t h a t were n o t counted, either because t h e y were not clearly words, or do not a p p e a r in T h o r n d i k e and Lorge.) F o r each S, the total n u m b e r of responses was b r o k e n down into those t h a t were H F responses, i.e., where S g a v e the higher-freq u e n c y w o r d f r o m a, pair, and those t h a t were L F responses. T h e m e a n n u m b e r of H F responses was 2.69 (aM ~--.21). T h e m e a n n u m b e r of L F responses was 1.44 (o.~t --~ .13).
WORD FREQUENCY AND T H I N K I N G
The difference between these means yields t (related measures) - - 4.77, p < .001. For the 34 H F words, the median frequency was 10.5. Over all 80 Ss, a total of 215 responses was given which were H F words; 144 were responses of words above the median frequency, 71 were responses of words below the median frequency. For the 34 H F words, the correlation between T - L frequency and n u m b e r of responses was .47. For the 34 L F words, the median frequency was 1.0. A total of 115 responses was given which were L F words; 84 of these were of words above the median frequency, 31 of words below the median. The correlation between T-L frequency and number of responses to L F words was .56. For all 68 words, the median T-L frequency was 3.0. Of the total 330 responses made, 233 were of words above the median frequency, 97 of words below the median. For all 68 words, the correlation between T-L frequency and n u m b e r of responses was
437
the higher-frequency word and must guess the lower-frequency word, or vice versa. Experiment I I I was also designed to determine the effect of frequency on guessing when S is encouraged to try to think of more than one word per item. I n Exps. I and II, S was not required to produce more than one word per item. I n Exp. III, the question is raised whether more higher-frequency words would be guessed than lower-frequency words if S were given an opportunity to produce both the higher- a n d the lower-frequency word for each item.
Method
Words. The words were 17 pairs of words from Thorndike and Lorge (1944). Both words in a pair were names of objects that belonged to the same class, e.g., trees (willow and walnut). Both words in a pair began with the same first letter and had the same number of letters (3, 4, 5, or 6 letters). Within each pair, one of the words had a higher T-L frequency than the other, and again will be identified as the HF word and the LF word. Over the 17 pairs, 13 different classes of objects were .55. represented; trees, musical instruments, vegetables, and birds were represented twice each (the two EXPERIMENT I I I pairs for each of these latter four categories began I n Exp. I I the task was rather difficult; with different letters and differed in length of words). the mean number of words given was small in The 17 HF words ranged in frequency from 3 per million to AA; the median frequency was 22. comparison to the total possible. So in Exp. The LF words ranged in frequency from 1 to 19; I I I another set of pairs of words was used, a the median was 5. set that pilot work indicated would elicit Conditions. There were four groups, differentiated more responses. on the basis of the word or words that Ss were to Experiment I I I was also designed to ob- emit. tain certain other kinds of information. The In Group E (either), S could give either the HF following question was asked: When S is re- or the LF word for each item. After a word was quired to guess a w o r d from a pair of words, emitted, or after 60 sec had elapsed with no response, E gave S the next item; thus, Group E is a replicaone of them of higher T-L frequency than tion, with the new items, of Exp. II. the other, will the probability of guessing one In Group L (low frequency), E gave S the HF of the pair change if S is told the other word? word /or each pair (see Procedure), leaving S If S is told one of the two possible words just with only the LF word remaining to be guessed as he starts trying to think of a word that (though S would not know that this was the case). will meet the specifications given him, then Group H (high frequency) is the opposite of Group he no longer has a choice, since only one word L. Group H Ss were given the LF word of each pair, and thus had only the HF word left to be remains to be guessed. Also, knowing one of guessed. In Group B (both), Ss were asked to give the words might either facilitate or inhibit two words (i.e., both the LF and HF words) for guessing the other. If such a transfer occurs, each item. Subjects. There were 30 Ss, students from introit may vary depending on whether S is given
438
DUNCAN
ductory psychology classes, in each of the four groups. Students were assigned to groups in turn. Procedure. After E and S h a d sat down facing each other across a table, E gave the general instructions for all groups. These were to the effect that S was to guess words that were n a m e s of objects, a n d that E would give S the class of object (such as Animals, or P a r t of the Body), the n u m b e r of letters in the word, a n d the first letter. Groups L a n d H were also told they would be given an example of a word t h a t fit the specifications. Group B was given the general instructions a n d told that they were to think of two words that fit the specifications. In Groups E, L, a n d H, Ss were allowed 60 see per item. T h e Ss in Group B were allowed 2 rain per item. It is recognized t h a t these Ss were free to take either more than or less than 1 min to think of one word, thereby leaving less than or more t h a n 1 rain to think of another word. T h e data will suggest that this was probably not a serious problem. A different h a p h a z a r d order of presentation of the 17 items was used for each S.
Results Table 2 shows the mean number of words (HF, LF, or both) given by the four groups. Among the groups, three comparisons of H F and LF means can be made: within Group E, between Groups L and H, and within Group B. In all three cases the H F mean was significantly higher than the LF mean. Within Group E, the t (related measures) between the means was 7.68. Between Groups L and H, t (independent measures) was 5.83. Within Group B, t (related measures) was 11.12. As expected, the items used in Exp. III were easier than those used in Exp. II, as suggested by higher means in Group E for both HF and LF words in Exp. III, while the advantage of H F over LF words is, if anything, greater in Exp. III. Comparisons across groups may be made TABLE 2 MEAN NUMBER OF HIGH-FREQUENCY AND OF Low-FREQUENCY WORDS GIVEN BY EACtI GROUP m ExP. III Group E L H B
HF
OM
8.80
A1
9.60 11.63
.43 .28
LF
~
3.83 6.33
.31 .36
7.27
.34
to determine if the different methods of eliciting HF and/or LF words did in fact produce differences in mean number of words emitted. The H F means will be considered first. Comparison of H F means of Group E, H, and B yielded F(2,87) ~ 14.71, p ~ .01. The difference between the H F means of Groups E and H is not significant (t ---- 1.48) ; thus, giving S the LF word in Group H, leaving only the H F word to be guessed, did not increase the number of H F words. However, the procedure used with Group B did increase the number of H F words. The H F mean for Group B is significantly higher than the HF means for Group E (t = 5.25) and for Group H (t z 3 . 7 7 ) . The mean (11.63) for Group B is, of course, based both on those items where the first response was an H F word, plus those items where S, after giving an LF word as his first response, managed to give the H F word as a second response. An H F mean for Group B that should not be greatly different from the means of Groups E and H would be the mean of first responses only. This H F mean for Group B was 9.73, and it does not differ significantly from Group E (t z 1.83) or from Group H (t z .25). Thus, an increased total number of H F words was obtained only by allowing another guess (Group B) on those items where the first response was an LF word. It may also be noted that although the experimental procedure permitted Ss in Group B up to 2 rain. (vs. 1 rain in all other groups) to think, this did not increase the number of HF words that were first responses. The F(2,87) for the three LF means was 27.72, p ( .01. Comparison of Groups E and L yields t z 5.25; thus, giving the Group L Ss the H F words, leaving only the LF words to be guessed, significantly increased the number of LF words emited. Group B also produced significantly more LF words than Group E (t z 7.23), and Group L (t ~ 1.97). If the Group B mean is reduced by including only those LF words that were the first responses (Mean z 4 . 1 7 ) , then Groups B and E do
WORD FREQUENCY AND THINKING
not differ ( t - - . 7 4 ) , but now Group L is significantly higher than Group B (t - - 4.36). Comparison of Groups E and B revealed that the interaction of groups with frequency was not significant (F less than 1.0). The preceding analyses of the H F and LF means yield the following conclusions: (a) no procedure significantly increased the number of H F words given as first responses; (b) giving Ss the H F words (Group L) significantly increased the number of LF words thought of as first responses; (c) when Ss were allowed to attempt a second response (Group B), both the numbers of H F and of LF words guessed were significantly increased. So far, the words emitted have simply been classed as HF or LF, and the results have been analyzed in terms of numbers of such words in each class. Since the mean number emitted, shown in Table 2, was less in every case than the number possible (17 H F and 17 LF), it is of interest to examine the actual T-L frequencies of the words that were emitted. The mean T-L frequency of the 17 H F words was 28.71. The H F words emitted by Groups E, H, and B had mean T-L frequencies of 34.05, 34.72, and 32.07 respectively. The standard errors of these three means were 1.68, 1.54, and 1.36, respectively; thus, in all cases the sample (HF words emitted) mean frequencies were higher than the population mean frequency by t's of at least 2.4 (even though in Group B, the mean number of H F words emitted, 11.63, is 68% of the available words). The mean T-L frequency of the 17 LF words was 6.47. The mean frequencies of the LF words emitted by Groups,'E, L, and B, were 7.76, 8.27, and. 7.73, with standard errors of .51, .37, and .34, respectively. Thus the LF words emitted also tended, by t's of at least 2.5, to be those of higher frequencies. DISCUSSION
Mayzner and Tresselt (1958) found that solution time of anagrams varied as a func-
439
tion of the Thorndike-Lorge frequency of the solution words, a result which has been confirmed by O'Connell and Duncan (1961). Mayzner and Tresselt suggested that the anagram stimulus generates implicit responses by S, and that words of higher frequency in S's past experience should occur earlier among the implicit responses. This notion that order of occurrence of words should vary directly with word frequency is what Und~rwood and Schulz (1960) called the spew hypothesis. The spew hypothesis, as applied to problem solving, may be considered to be a part of response-hierarchy theory, a more general approach to problem solving that has been discussed elsewhere (Duncan, 1959; Maltzman, 1955). Briefly, a problem is assumed to elicit several responses varying in habit strength, a response hierarchy. The order of responses in the hierarchy will be determined by a number of variables, e.g., recency, set, frequency, etc. The spew hypothesis refers only to the frequency variable. Applied to the present study, the spew hypothesis seems adequate to account, in part, for the main findings. In all three experiments, the instructions restricted, to varying degrees, the response space or word population that S had to search. However, S was still free to make a number of implicit responses while searching. If it can be assumed that implicit words of higher T-L frequencies occur either earlier, or in greater numbers, or both, as compared to lower-frequency words, then one may say that if the solution to a problem is a high-frequency word, the probability of occurrence of the solution is increased. At the same time, it is worth noting that the spew hypothesis, if true, only a~sures that some high-frequency words will occur prior to low-frequency words. In a problemsolving situation, where the number of responses acceptable as solutions may be limited to a few or only one, S's implicit responses may be in accord with spew, but still
440
DUNCAN
not include the solution response. In the present Exp. I every S failed to give a word to at least one, and usually to several, of the items, even though all the items included one or more high frequency words. In Group H of Exp. I I I , only one of two words was allowed as the solution for each item. Since the lower-frequency word of each pair was given to these Ss, only the higher-frequency word remained to be guessed. Some of these words were also of high absolute frequency; even so, not all of them were guessed. These were failed problems. Thus, the spew hypothesis alone cannot account for the fact that some one-solution problems will not be solved even if the solutions are high-frequency words. It also cannot account for the fact that with multiple-solution problems, some of the solutions will be low-frequency words, even when high-frequency words are available and acceptable. The spew hypothesis may be limited by inadequate sampling. When S samples words in attempting to think of a solution word., the sample apparently includes more high-frequency words than low-frequency words, but probably does not include all possible high- or low-frequency words in the population specified by the problem stimuli. Thus, it is suggested that when S is trying to think of a word, a combination of sampling and spew determine that (a) only part of the words, of high or of low frequency, that might occur do occur, and, (b) of those words that do occur, high-frequency words occur earlier and in greater number than low-frequency words. Finally, it is worth noting that the tendency to emit words of higher frequency (relative to some other words) held in general throughout the entire range of absolute frequency. This is suggested in part by the data in Table 1. Another indication comes from Exp.
I I and I I I . In these experiments, all of the following numerical differences were found (regardless of whether one or two words were available to be guessed): (a) the higherfrequency word of a pair of words was emitted more often than the lower-frequency word, (b) among the higher-frequency words that were emitted, more of them were words with absolute frequencies above the median frequency of their own distribution than below the median, (c) in those cases where the lower-frequency word of a pair was emitted, more of such words had absolute frequencies above the median frequency of their own distribution than below the median. REFERENCES
DOMINOWSKI, R. L., ANn DUI~CAZ%C. P. Anagram solving as a function of bigram frequency. J. verb. Learn. verb. Behav., 1964, 3, 321-325. DU~CCAN,C. P. Recent research on human problem solving. Psyehol. Bull., 1959, 56, 397-429. MALTZMAN,I. Thinking: From a behavioristic point of view. Psyehol. Rev., 1955, 62, 275-286. MAYZNER, M. S., AND TRESSELT, M. E. Anagram
solution times: a function of letter order and word frequency. J. exp. Psychol., 1958, 56, 376379. MAYZNER, M. S., AND TRESSELT, M. E. Anagram solution times: a function of transition probabilities. J. Psychol., 1959, 47, 117-126. O'CONNELL, E. J., JR., ANn DUNCAN, C. P. Anagram solving as a function of letter spacing. Psychol. Rep., 1961, 8, 117-118. RHINE, R. J. The relation of achievement in problem solving to rate and kind of hypotheses produced. J. exp. Psychol., 1959, 57, 253-256.
TERAOKA, T. Effects of letter-orders and material words on the anagram solution. ]ap. J. Psychol., 1959, 30, 253-263. TI-IORNDIKE,E. L., ANDLORGE,I. The teacher's word book o/ 30,000 words. New York: Teachers Coll., Columbia Univer. Press, 1944. UNDERWOOD, B. J., AND SCHULZ, R. W. Meaninglulness and verbal learning. Chicago: Lippincott, 1960. (Received January 25, 1965)
(1966)
Effect of Word Frequency on Thinking of a Word 1 CARL"P. DUNCAN Northwestern University, Evanston, Illinois Three experiments were performed to determine the effect of word frequency on thinking of a word. In all experiments Ss were given certain characteristics of words, such as the first letter, the last letter, the number of letters, or the class of the object named by the word, and were asked to think of a word fitting the given characteristics. In all experiments, more words of higher frequency were emitted than were words of lower frequency. In general, the tendency to emit words of higher relative frequencies held throughout the whole range of absolute frequencies. Not all high-frequency words that could have been emitted were emitted. The findings were interpreted in terms of a combination of the spew hypothesis, and of incomplete sampling from a population of words.
In certain kinds of problem solving, S must search among a population of possible responses until he hits upon, if he does, the particular response defined as the solution. As S emits responses, often implicitly, in his search, what variables determine which responses occur and which do not occur? I t seems reasonable to assume that one such variable will be the frequency, in S's past experience, with which he has encountered the responses. In general, responses known or assumed to have occurred more frequently in S's experience should be more likely to occur to him during searching or thinking. This hypothesis concerning the effects of response frequency on thinking derives chiefly from two sources. One is the spew hypothesis of Underwood and Schulz (1960), according to which verbal units are emitted in the order of frequency of experience with the units. These authors summarize a number of studies in which the spew hypothesis was supported in relatively free responding 1 This study was supported by Grant HD 00901, National Institute of Child Health and Human Development, National Institutes of Health, U.S. Public Health Service. Thanks are due I. David Isaacs, Gordon Wood, Judith Hanson, and Linda Shaffer. 434
situations such as free association. The other source is the study of Mayzner and Tresselt (1958) in which anagram solution times vary inversely with Thorndike-Lorge (1944) frequency of the solution words. It is Mayzner and Tresselt's theory that in attempting to solve an anagram, S generates implicit responses as some function of frequency. With an anagram, S has all the letters of the solution word presented to him. Letter hypotheses (Rhine, 1959), letter orders Mayzner and Tresselt, 1958; Teraoka, 1959), and frequencies of letter combinations (Dominowski and Duncan, 1964; Mayzner and Tresselt, 1959) become variables influencing solution. In the present study, an attempt was made to minimize the effects of letter variables and to maximize the frequency of the word as a whole. The S was asked to think of a word that meets certain specifications. The specifications served both to narrow the response population to be searched to the point where there was some probability that S would discover the word, and also to restrict, sometimes to a single word, the number of words that met the specifications, problems of this type should be solved more readily if the solution is a high-frequency rather than a low-frequency word.
435
WORD FREQUENCY AND T H I N K I N G
EXPERIMENT I
Method Words. The source of words was the five-letter words from Thorndike and Lorge (1944). The set of words to be used was obtained by selecting 20 subsets of words. The words in each subset had the same first letter and the same last letter. The 20 pairs of initial and final letters were: bd (thus including such words as brand, beard, blind, etc.), bh, bn, ck, cl, cp, fk, Jr, In, rnh, pk, pr, rl, rt, sk, sin, td, tr, wh, wt. These subsets ranged in number of five-letter words available (i.e., listed in Thorndike and Lorge) from six words (both In and pk) to 36 words (sk). The total number of words, all 20 subsets combined, was 266. Within each subset there was one or more words of T-L frequency of less than one per million words (Thorndike and Lorge General Count). Also within each subset there was one or more words of frequency of A (here taken as 50) or AA (here taken as 100), except for ]k, where the highest-frequency word was 44, and pk, highest frequency 28. The mean frequencies of the 20 subsets ranged from 11.4 to 39.1. The 20 median frequencies ranged from 1.5 to 26.0. For all 266 words in the population the mean frequency was 22.97, the median frequency 8.8. Subjects. The Ss were 60 students from introductory psychology classes in which students are required to serve in experiments. Procedure. After E and S had sat down facing each other across a table, E said to S, "I want you to guess some five-letter English words. I will give you the first letter and the last letter of one o[ these words. Then you try and tell me what the five-letter word is. None of the words which you are to guess is in plural form, and none is capitalized such as proper names or brand names. O.K., here is the first one." The E then gave the first letter of a problem item, paused a moment, then gave the last letter. The S was given 60 sec in which to respond. If S gave an unacceptable response, e.g., not a five-letter word, E pointed out the error and S was allowed the remainder of the 60-sec period to make another response. After S had responded with an acceptable response, or after 60 see had elapsed, E said, "Let's try another one." The E continued until all 20 letter pairs had been presented to each S. The 20 letter pairs were presented in a different haphazard order for each S.
Results O f the total possible 1200 responses (60 Ss X 20 guesses), 806 usable responses were o b t a i n e d , for a m e a n of 13.43 (aM z .44)
words per S. I n addition, there were 58 responses consisting of words, e.g., boxed, for which a T - L f r e q u e n c y is not available. T h e s e responses are not included in the data. F o r each S separately, b o t h the m e a n T - L f r e q u e n c y and the m e d i a n f r e q u e n c y of the words S g a v e w e r e determined. O v e r all Ss, the m e a n of the m e a n s was 41.91, 0.~i z 1.13. T h e m e a n of the m e d i a n s was 35.07, o.~i 2.02; the m e d i a n of the m e d i a n s was 32.0. T h e m e a n f r e q u e n c y of the p o p u l a t i o n of words was 22.97; thus, it can be seen t h a t either of the o b t a i n e d m e a n s is higher by a t-value of at least 5. F o r 58 of the 60 Ss, the m e a n f r e q u e n c y of S's responses was h i g h e r than the p o p u l a t i o n m e a n ; for 59 Ss the median f r e q u e n c y of their responses was higher t h a n the p o p u l a t i o n m e d i a n f r e q u e n c y (8.8). A n o t h e r c o m p a r i s o n is o b t a i n e d b y examining not total responses, b u t o n l y the n u m ber of different w o r d s emitted. O v e r all Ss, 186 words out of the p o p u l a t i o n of 266 words were g i v e n at least once, 80 were not given. O f the 133 words a b o v e the m e d i a n freq u e n c y (8.8) of the p o p u l a t i o n , 113 were given. Of the words below the median, only 73 were given. F o r the 186 e m i t t e d words, the m e a n T - L f r e q u e n c y was 28.60, 0~ 2.38 ( m e d i a n f r e q u e n c y was 15.3): thus, t h o u g h this is a fairly large sample of the p o p u l a t i o n , the m e a n f r e q u e n c y is signific a n t l y higher (t ~= 2.39) t h a n the population m e a n f r e q u e n c y (22.97). F o r the 80 words not e m i t t e d , the m e a n f r e q u e n c y was 8.79, o~i z 2.04 ( m e d i a n f r e q u e n c y was 2.1). I n T a b l e 1, f r e q u e n c y classes (first c o l u m n ) TABLE
I
POPULATION ~VORDS, EMITTED WORDS, AND TOTAL RESPONSES IN VARIOUS FREQUENCY CATEGORIES IN EXP. I
Frequency class
Population words
Emitted words
Total responses
A and AA 18-49 8-17 3-7 1-2 Less than 1
.~2 44 43 41 41 45
46 40 30 29 24 17
311 202 108 96 41 48
436
DUNCAN
h a v e been set up t h a t contain r o u g h l y equal n u m b e r s of p o p u l a t i o n words (second colu m n ) . C o l u m n 3 shows the n u m b e r of differe n t words e m i t t e d , a n d C o l u m n 4 shows total responses, for e a c h of the f r e q u e n c y classes. I t is clear t h a t b o t h n u m b e r of different words e m i t t e d and total responses decrease as freq u e n c y decreases. F o r all 266 p o p u l a t i o n words, the correlation b e t w e e n f r e q u e n c y of the w o r d and n u m b e r of times it was e m i t t e d was .44; for the 186 w o r d s t h a t were given at least once, the correlation was .40. EXPERIMENT I I I n Exp. I, each of the subsets of words associated w i t h a letter pair c o n t a i n e d several words. T h e S was free to give a n y one of the words in a subset t h a t he could t h i n k of. Since e v e n the smallest subset c o n t a i n e d six words, while the largest c o n t a i n e d 36 words, the task was s o m e t h i n g of a " f r e e r e s p o n s e " s i t u a t i o n like those in which U n d e r w o o d and Schulz (1960) found e v i d e n c e for the spew hypothesis. T h e purpose of Exp. I I was to test the effect of T - L f r e q u e n c y in a task w h e r e the n u m b e r of a c c e p t a b l e responses was severely restricted.
Method Words. The words were 34 pairs of words from Thorndike and Lorge (1944). Each of the 68 words had five letters. The two words within each pair had the same initial letter and the same final letter (initial and final letters were themselves identical in only two of the 34 pairs). The two words of a pair had different T-L frequencies. Hereafter, the word of higher frequency in a pair will be called the HF (high frequency) word and the other word will be called the LF (low frequency) word, regardless of the absolute frequency. The presence of a difference in frequency between the words of a pair is the independent variable;-the expectation is that the HF word will be more readily emitted when S is required to think of a word. Among the 68 words there were words of high absolute frequency (A or AA), and words of low absolute frequency (less than one per million). The diffelence in frequency between the words of a pair also varied, e.g., earth (AA) vs. epoch (5), until (AA) vs. usual (A), borax (2) vs. beaux (1).
Pilot work had revealed that there were pairs of words (from Thorndike and Lorge) for which Ss could think of too many alternative responses; the 34 pairs finally used do not include such pairs. It was also discovered that Ss found the task difficult. Because of this, the 34 pairs were divided into two sets, A and B, of 17 pairs each, and any one S worked on only one set. (To obtain an equal number of pairs in each set, one pair of words was used in which the two words had the same frequency, viz. outdo and outgo, both having frequency of one.) The two sets were roughly equivalent in absolute frequencies of words and in differences of frequency between words of a pair. Subjects. The Ss were 80 students from introductory psychology courses. Half were assigned Set A, half Set B. Procedure. After g and S sat down facing each other across a table, E said, "I want you to guess some five-letter English words. I will give you the first and the last letter of one of the words. Then you try to tell me what the five-letter word is. None of the words that you are to guess is plural form, and none is capitalized, such as proper names or brand names. O.K., here is the first one." The E then gave the first letter, paused momentarily, and gave the last letter. If S said either of the words in a pair, E gave him the next item. If S had not responded after 60 sec had elapsed, E said, "Let's try another," and gave S the letters for the next item. A different haphazard order of presentation of the 17 items in a set was used for each S. For each item, there were only two words available, one being of higher frequency than the other.
Results Since there was little difference in response to Sets A and B, the d a t a were c o m b i n e d . F o r all 80 Ss, the m e a n t o t a l n u m b e r of responses was 4.13. Since the m a x i m u m possible was 17, the task was r a t h e r difficult. ( T h e Ss g a v e a total of 28 responses t h a t were n o t counted, either because t h e y were not clearly words, or do not a p p e a r in T h o r n d i k e and Lorge.) F o r each S, the total n u m b e r of responses was b r o k e n down into those t h a t were H F responses, i.e., where S g a v e the higher-freq u e n c y w o r d f r o m a, pair, and those t h a t were L F responses. T h e m e a n n u m b e r of H F responses was 2.69 (aM ~--.21). T h e m e a n n u m b e r of L F responses was 1.44 (o.~t --~ .13).
WORD FREQUENCY AND T H I N K I N G
The difference between these means yields t (related measures) - - 4.77, p < .001. For the 34 H F words, the median frequency was 10.5. Over all 80 Ss, a total of 215 responses was given which were H F words; 144 were responses of words above the median frequency, 71 were responses of words below the median frequency. For the 34 H F words, the correlation between T - L frequency and n u m b e r of responses was .47. For the 34 L F words, the median frequency was 1.0. A total of 115 responses was given which were L F words; 84 of these were of words above the median frequency, 31 of words below the median. The correlation between T-L frequency and number of responses to L F words was .56. For all 68 words, the median T-L frequency was 3.0. Of the total 330 responses made, 233 were of words above the median frequency, 97 of words below the median. For all 68 words, the correlation between T-L frequency and n u m b e r of responses was
437
the higher-frequency word and must guess the lower-frequency word, or vice versa. Experiment I I I was also designed to determine the effect of frequency on guessing when S is encouraged to try to think of more than one word per item. I n Exps. I and II, S was not required to produce more than one word per item. I n Exp. III, the question is raised whether more higher-frequency words would be guessed than lower-frequency words if S were given an opportunity to produce both the higher- a n d the lower-frequency word for each item.
Method
Words. The words were 17 pairs of words from Thorndike and Lorge (1944). Both words in a pair were names of objects that belonged to the same class, e.g., trees (willow and walnut). Both words in a pair began with the same first letter and had the same number of letters (3, 4, 5, or 6 letters). Within each pair, one of the words had a higher T-L frequency than the other, and again will be identified as the HF word and the LF word. Over the 17 pairs, 13 different classes of objects were .55. represented; trees, musical instruments, vegetables, and birds were represented twice each (the two EXPERIMENT I I I pairs for each of these latter four categories began I n Exp. I I the task was rather difficult; with different letters and differed in length of words). the mean number of words given was small in The 17 HF words ranged in frequency from 3 per million to AA; the median frequency was 22. comparison to the total possible. So in Exp. The LF words ranged in frequency from 1 to 19; I I I another set of pairs of words was used, a the median was 5. set that pilot work indicated would elicit Conditions. There were four groups, differentiated more responses. on the basis of the word or words that Ss were to Experiment I I I was also designed to ob- emit. tain certain other kinds of information. The In Group E (either), S could give either the HF following question was asked: When S is re- or the LF word for each item. After a word was quired to guess a w o r d from a pair of words, emitted, or after 60 sec had elapsed with no response, E gave S the next item; thus, Group E is a replicaone of them of higher T-L frequency than tion, with the new items, of Exp. II. the other, will the probability of guessing one In Group L (low frequency), E gave S the HF of the pair change if S is told the other word? word /or each pair (see Procedure), leaving S If S is told one of the two possible words just with only the LF word remaining to be guessed as he starts trying to think of a word that (though S would not know that this was the case). will meet the specifications given him, then Group H (high frequency) is the opposite of Group he no longer has a choice, since only one word L. Group H Ss were given the LF word of each pair, and thus had only the HF word left to be remains to be guessed. Also, knowing one of guessed. In Group B (both), Ss were asked to give the words might either facilitate or inhibit two words (i.e., both the LF and HF words) for guessing the other. If such a transfer occurs, each item. Subjects. There were 30 Ss, students from introit may vary depending on whether S is given
438
DUNCAN
ductory psychology classes, in each of the four groups. Students were assigned to groups in turn. Procedure. After E and S h a d sat down facing each other across a table, E gave the general instructions for all groups. These were to the effect that S was to guess words that were n a m e s of objects, a n d that E would give S the class of object (such as Animals, or P a r t of the Body), the n u m b e r of letters in the word, a n d the first letter. Groups L a n d H were also told they would be given an example of a word t h a t fit the specifications. Group B was given the general instructions a n d told that they were to think of two words that fit the specifications. In Groups E, L, a n d H, Ss were allowed 60 see per item. T h e Ss in Group B were allowed 2 rain per item. It is recognized t h a t these Ss were free to take either more than or less than 1 min to think of one word, thereby leaving less than or more t h a n 1 rain to think of another word. T h e data will suggest that this was probably not a serious problem. A different h a p h a z a r d order of presentation of the 17 items was used for each S.
Results Table 2 shows the mean number of words (HF, LF, or both) given by the four groups. Among the groups, three comparisons of H F and LF means can be made: within Group E, between Groups L and H, and within Group B. In all three cases the H F mean was significantly higher than the LF mean. Within Group E, the t (related measures) between the means was 7.68. Between Groups L and H, t (independent measures) was 5.83. Within Group B, t (related measures) was 11.12. As expected, the items used in Exp. III were easier than those used in Exp. II, as suggested by higher means in Group E for both HF and LF words in Exp. III, while the advantage of H F over LF words is, if anything, greater in Exp. III. Comparisons across groups may be made TABLE 2 MEAN NUMBER OF HIGH-FREQUENCY AND OF Low-FREQUENCY WORDS GIVEN BY EACtI GROUP m ExP. III Group E L H B
HF
OM
8.80
A1
9.60 11.63
.43 .28
LF
~
3.83 6.33
.31 .36
7.27
.34
to determine if the different methods of eliciting HF and/or LF words did in fact produce differences in mean number of words emitted. The H F means will be considered first. Comparison of H F means of Group E, H, and B yielded F(2,87) ~ 14.71, p ~ .01. The difference between the H F means of Groups E and H is not significant (t ---- 1.48) ; thus, giving S the LF word in Group H, leaving only the H F word to be guessed, did not increase the number of H F words. However, the procedure used with Group B did increase the number of H F words. The H F mean for Group B is significantly higher than the HF means for Group E (t = 5.25) and for Group H (t z 3 . 7 7 ) . The mean (11.63) for Group B is, of course, based both on those items where the first response was an H F word, plus those items where S, after giving an LF word as his first response, managed to give the H F word as a second response. An H F mean for Group B that should not be greatly different from the means of Groups E and H would be the mean of first responses only. This H F mean for Group B was 9.73, and it does not differ significantly from Group E (t z 1.83) or from Group H (t z .25). Thus, an increased total number of H F words was obtained only by allowing another guess (Group B) on those items where the first response was an LF word. It may also be noted that although the experimental procedure permitted Ss in Group B up to 2 rain. (vs. 1 rain in all other groups) to think, this did not increase the number of HF words that were first responses. The F(2,87) for the three LF means was 27.72, p ( .01. Comparison of Groups E and L yields t z 5.25; thus, giving the Group L Ss the H F words, leaving only the LF words to be guessed, significantly increased the number of LF words emited. Group B also produced significantly more LF words than Group E (t z 7.23), and Group L (t ~ 1.97). If the Group B mean is reduced by including only those LF words that were the first responses (Mean z 4 . 1 7 ) , then Groups B and E do
WORD FREQUENCY AND THINKING
not differ ( t - - . 7 4 ) , but now Group L is significantly higher than Group B (t - - 4.36). Comparison of Groups E and B revealed that the interaction of groups with frequency was not significant (F less than 1.0). The preceding analyses of the H F and LF means yield the following conclusions: (a) no procedure significantly increased the number of H F words given as first responses; (b) giving Ss the H F words (Group L) significantly increased the number of LF words thought of as first responses; (c) when Ss were allowed to attempt a second response (Group B), both the numbers of H F and of LF words guessed were significantly increased. So far, the words emitted have simply been classed as HF or LF, and the results have been analyzed in terms of numbers of such words in each class. Since the mean number emitted, shown in Table 2, was less in every case than the number possible (17 H F and 17 LF), it is of interest to examine the actual T-L frequencies of the words that were emitted. The mean T-L frequency of the 17 H F words was 28.71. The H F words emitted by Groups E, H, and B had mean T-L frequencies of 34.05, 34.72, and 32.07 respectively. The standard errors of these three means were 1.68, 1.54, and 1.36, respectively; thus, in all cases the sample (HF words emitted) mean frequencies were higher than the population mean frequency by t's of at least 2.4 (even though in Group B, the mean number of H F words emitted, 11.63, is 68% of the available words). The mean T-L frequency of the 17 LF words was 6.47. The mean frequencies of the LF words emitted by Groups,'E, L, and B, were 7.76, 8.27, and. 7.73, with standard errors of .51, .37, and .34, respectively. Thus the LF words emitted also tended, by t's of at least 2.5, to be those of higher frequencies. DISCUSSION
Mayzner and Tresselt (1958) found that solution time of anagrams varied as a func-
439
tion of the Thorndike-Lorge frequency of the solution words, a result which has been confirmed by O'Connell and Duncan (1961). Mayzner and Tresselt suggested that the anagram stimulus generates implicit responses by S, and that words of higher frequency in S's past experience should occur earlier among the implicit responses. This notion that order of occurrence of words should vary directly with word frequency is what Und~rwood and Schulz (1960) called the spew hypothesis. The spew hypothesis, as applied to problem solving, may be considered to be a part of response-hierarchy theory, a more general approach to problem solving that has been discussed elsewhere (Duncan, 1959; Maltzman, 1955). Briefly, a problem is assumed to elicit several responses varying in habit strength, a response hierarchy. The order of responses in the hierarchy will be determined by a number of variables, e.g., recency, set, frequency, etc. The spew hypothesis refers only to the frequency variable. Applied to the present study, the spew hypothesis seems adequate to account, in part, for the main findings. In all three experiments, the instructions restricted, to varying degrees, the response space or word population that S had to search. However, S was still free to make a number of implicit responses while searching. If it can be assumed that implicit words of higher T-L frequencies occur either earlier, or in greater numbers, or both, as compared to lower-frequency words, then one may say that if the solution to a problem is a high-frequency word, the probability of occurrence of the solution is increased. At the same time, it is worth noting that the spew hypothesis, if true, only a~sures that some high-frequency words will occur prior to low-frequency words. In a problemsolving situation, where the number of responses acceptable as solutions may be limited to a few or only one, S's implicit responses may be in accord with spew, but still
440
DUNCAN
not include the solution response. In the present Exp. I every S failed to give a word to at least one, and usually to several, of the items, even though all the items included one or more high frequency words. In Group H of Exp. I I I , only one of two words was allowed as the solution for each item. Since the lower-frequency word of each pair was given to these Ss, only the higher-frequency word remained to be guessed. Some of these words were also of high absolute frequency; even so, not all of them were guessed. These were failed problems. Thus, the spew hypothesis alone cannot account for the fact that some one-solution problems will not be solved even if the solutions are high-frequency words. It also cannot account for the fact that with multiple-solution problems, some of the solutions will be low-frequency words, even when high-frequency words are available and acceptable. The spew hypothesis may be limited by inadequate sampling. When S samples words in attempting to think of a solution word., the sample apparently includes more high-frequency words than low-frequency words, but probably does not include all possible high- or low-frequency words in the population specified by the problem stimuli. Thus, it is suggested that when S is trying to think of a word, a combination of sampling and spew determine that (a) only part of the words, of high or of low frequency, that might occur do occur, and, (b) of those words that do occur, high-frequency words occur earlier and in greater number than low-frequency words. Finally, it is worth noting that the tendency to emit words of higher frequency (relative to some other words) held in general throughout the entire range of absolute frequency. This is suggested in part by the data in Table 1. Another indication comes from Exp.
I I and I I I . In these experiments, all of the following numerical differences were found (regardless of whether one or two words were available to be guessed): (a) the higherfrequency word of a pair of words was emitted more often than the lower-frequency word, (b) among the higher-frequency words that were emitted, more of them were words with absolute frequencies above the median frequency of their own distribution than below the median, (c) in those cases where the lower-frequency word of a pair was emitted, more of such words had absolute frequencies above the median frequency of their own distribution than below the median. REFERENCES
DOMINOWSKI, R. L., ANn DUI~CAZ%C. P. Anagram solving as a function of bigram frequency. J. verb. Learn. verb. Behav., 1964, 3, 321-325. DU~CCAN,C. P. Recent research on human problem solving. Psyehol. Bull., 1959, 56, 397-429. MALTZMAN,I. Thinking: From a behavioristic point of view. Psyehol. Rev., 1955, 62, 275-286. MAYZNER, M. S., AND TRESSELT, M. E. Anagram
solution times: a function of letter order and word frequency. J. exp. Psychol., 1958, 56, 376379. MAYZNER, M. S., AND TRESSELT, M. E. Anagram solution times: a function of transition probabilities. J. Psychol., 1959, 47, 117-126. O'CONNELL, E. J., JR., ANn DUNCAN, C. P. Anagram solving as a function of letter spacing. Psychol. Rep., 1961, 8, 117-118. RHINE, R. J. The relation of achievement in problem solving to rate and kind of hypotheses produced. J. exp. Psychol., 1959, 57, 253-256.
TERAOKA, T. Effects of letter-orders and material words on the anagram solution. ]ap. J. Psychol., 1959, 30, 253-263. TI-IORNDIKE,E. L., ANDLORGE,I. The teacher's word book o/ 30,000 words. New York: Teachers Coll., Columbia Univer. Press, 1944. UNDERWOOD, B. J., AND SCHULZ, R. W. Meaninglulness and verbal learning. Chicago: Lippincott, 1960. (Received January 25, 1965)