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Experimental Aging Research: An International Journal Devoted to the Scientific Study of the Aging Process Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uear20
Determinants of anagram problem solution in adulthood Bert Hayslip Jr.
a
a
Department of Psychology, Hood College, Frederick, Maryland, 21701 Version of record first published: 27 Sep 2007.
To cite this article: Bert Hayslip Jr. (1977): Determinants of anagram problem solution in adulthood, Experimental Aging Research: An International Journal Devoted to the Scientific Study of the Aging Process, 3:2, 147-163 To link to this article: http://dx.doi.org/10.1080/03610737708257095
PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/termsand-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
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DETERMINANTS OF ANAGRAM PROBLEM SOLUTION IN ADULTHOOD BERT HAYSLIP, JR. DeGratment of Psychology Hood College Frederick, Maryland 21701
Hayslip B. Determinants of anagram problem solution in adulthood. Experimental Aging Research, 1977,3, (Z), 147-163. An evaluation of the indices proposed in the literature regarding measures of anagram difficulty was made by asking three groups (ages 17-26, 39-51, 59-76) of adults ( n = 54) to solve a list of 30 anagrams. Results indicated that only two of these indices (ThorndikeLorge and Bigram Rank measures) significantly predicted frequency of solution in samples beyond college age. I t was also found that the cognitive variable mediating the effects of these indices in middle aged and elderly subjects was crystallized ability, suggesting an experiential basis for the effects of both task and organismic variables as determinants of anagram problem solving in adulthood. T h e role of fluid ability as a mediator of problem solution in the young received limited support.
DETERMINANTS OF ANAGRAM SOLUTION I N ADULTHOOD In contrast to most types of traditional learning and problem solving tasks finding decrements in performance with increased age (Arenkrg, 1973; Botwinick, 1973), no such decrements have been obtained in adulthood with the anagram task (Hayslip & Sterns, Note 1). As an experimental problem, the anagram task has been the subject of a great deal of research over the past 20 years. Johnson (1966) has reviewed much of this research dealing with the determinants of anagram solution: anagram and solution word variables, anagram-word relationships, and temporal factors. Numerous other investigators have linked a wide variety *of factors,
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i. e., imagery (Jablonski & Mueller, 1972), set and practice effects (Gavurin, 1973; Johnson, 1966), and individual differences in cognition (Gavurin, 1967; Johnson, 1966; Mendelsohn & Griswold, 1966; Mendelsohn, Griswold & Anderson, 1966; Mendelsohn & Covington, 1972; Mendelsohn & Lindholm, 1972) to anagram solution. Mayzner and Tresselt (1958, 1959, 1962, 1963, 1966), Mayzner, Tresselt and Helback (1964) and Tresselt and Mayzner (1965, 1966) have established a relationship between the following factors and anagram solution times: a) digram frequency of the anagrun, b) digram frequency of the solution word, c) the ThorndikeLorge (1944) frequency count, d) word length, e) number of letters moves and f ) multiple solutions. Mayzner and Tresselt have concluded low transitional probality (TP) anagrams and the high TP solution words to be solved most quickly. Others, however, (e.9. Dominowski & Duncan, 1964; Dominowski, Note 3; Warren & Thompson, 1969) have been unable to replicate these findings. Much effort seems to have gone into developing a satisfactory measure for assessing anagram difficulty. Mayzner and Tresselt (1965) have revised the Underwood-Schultz (1960) tables for calculating digram T P values, taking into account word length and letter position within word. Gavurin and DeVito (1973) have compared these two measures of difficulty, in addition to Thorndike-Lorge frequency count, as predictors of frequency of anagram solution. The Thorndike-Lorge index was found to be unrelated lio problem dolutjon. Both Underwood-Schultz and MayznerTresselt systems for calculating digram frequencies however, produced comparable results with one exception (anagram TP) . The authors suggested a TPD (digram transitional probability differtnce between anagram and solution word), index as an alternative, more sensitive measure of anagram difficulty. Topper, Macey and Solso (1973) and Solso, Topper and Macey (1973) have suggested biagram versatility (BV), as measured by the number of different words in which a digram appeared, as an index of anagram solving. Silvestri and Gavurin (1972) have reported a more refined measure: the “transition probability ratio” of each correct solution word digram to all of the possible alternate digrams formed with the same
Downloaded by [McGill University Library] at 10:20 10 April 2013
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initial letter. Most recently, Mendelsohn and O’Brien (1974) have offered still another measure of anagram problem solving which significantly predicted anagram solution, using a comprcmise meaSure incorporating both response latency and item success/failure. This index was similar to an anagram-related measure proposed by Dominowski (Note 3) (rank of bigram within the set of all bigrams with the same initial letter). This was termed a solution word bigram rank measure, based on the relative frequencies of “correct” (comprising the solution word) to “incorrect” bigrams within the pool of bigrams defined by the letters made from the anagram, rather than by the absolute frequencies of the correct bigram. This bigram rank measure also took both word length and letter position into account. With the exception of a few studies (Dominowski & Duncan, 1964; Gavurin & DeVito, 1973; Mendekohn & Griswold, 1966; Mendelsohn & O’Brien, 1974; Pinckney, 1965, Silvestri & Gavurin, 1972; Stacknik, 1963), most anagram research has utilized item response latency as a dependent variable- Furthermore, no published research on anagram solving has employed samples of other than college age. With the comparatively recent thrust of the study of adulthood and aging (Baltes & Goulet, 1970), it would seem desirable to extend/replicate the research on the determinants of anagram difficulty using samples beyond early adulthood. This study first seeks to assess the relative efficiency of the above proposed indices of anagram difficulty in predicting frequency of anagram solution in three adult samples varying in age. Such information about the most predictive index of anagram difficulty could thus be applied to experimental research dealing with subjects beyond late adolescence or young adulthood.
A second objective of the present study is to incorporate the above findings into the literature dealing with anagram solvingability relationships. Most research to date has implicated t,he role of verbal ability in determining anagram performance (Gavurin, 1967; Johnson, 1966; Mendelsohn, e t al., 1966, 1972). Most recently, Hayslip and Sterns (Note 1) found that with increased age, the role of crystallized ability (Gc) relative to that of fluid (Gf) intelligence increased (Horn, 1968, 1970) as a correlate of anagram
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solving. No evaluation of the relationships between intelligence and the above indices of anagram difficulty as determinants of solution frequency was made, however. Accordingly, the present study a,lso represents an additional analysis of the Hayslip and Sterns (Note 1) data dealing with anagram solving-ability relations in adulthood, to incorporate differential measures of anagram difficulty. Both Hunter (1959) and Johnson (1966) have viewed anagram problem solving in two phases: 1) letter rearrangement and 2) comparison with stored word models. Mendelsohn and O’Brien (1974) suggested that solution is comprised of 1) a hypothesis formation phase followed by 2) a phase in which the subject moves from partial reorganizations of the anagram to the production of whole words or solutions. One might, on the basis of the above literature, propose that different task variables (indices of difficulty) and subject variables (Gf and Gc) may interact differently with increased age to account for anagram problem solution. On the basis of the nature of each ability factor (Horn, 1968, 1970) one may speculate that Gf may represent or mediate this letter rearrangement (hypothesis formation) phase, Gc reflecting the acquisition of experientially determined stored word models in the anagram solving proces. Thus, the present study seeks to examine what has thus far been treated experimen%ally (indices of anagram difficulty), and link it to cognition (crystallized and fluid ability) within a developmental context.
METHOD Three groups (7% = 54) of subjects varying in age (17-26, 3951, 59-76) were tested individually on the anagram task, as part of a more comprehensive battery of ability and problem solving tasks (see Hayslip & Sterns, Note 1). Equal numbers of males and females comprised each age group. The young adult group was comprised of both college and noncollege people, employed at a local utility firm, hourly city em-
Downloaded by [McGill University Library] at 10:20 10 April 2013
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ployees, and undergraduate college students at varying points in their education. Middle aged subjects consisted of individuals employed at a local utility company, city and county government staff personnel, university staff personnel and residents of a low income government sponsored apartment complex. Older adults were sampled from local community groups such as AARP (American Association of Retired Persons), RSVP (Retired Senior Volunteer Persons), or residents of a Metropolitan Housing Authority older adult apartment building. Subjects all willingly participated and were free of obvious visual and auditory defects that would hamper their performance. and all were er,gaged in Community living.
Materials and Procedure Thirty anagrams, each consisting of five letters, were listed on a sheet of paper. Ten anagrams were “easy”, ten were of medium difficulty, and ten were “difficult”, as determined by normative solution times (Tresselt & Mayzner, 1966). Each item had been listed by these authors as having only one solution. Each subject was informed of the nature of the anagram task, and was given five practice problems, with explanations of solution, prior to the test list. This list consisted of the anagram typed in capital Ietters separated by a space, with blanks t o the right of each. Subjects were instructed to write their solutions down without the use of any notes, to work at a comfortable pace, and not to spend an excessive amount of time on any one item. An effort was made to insure that no notes were used throughout. Subjects were given a maximum of thirty minutes to complete the list (they were not told this fact). In all but one case, subjects had finished work at the conclusion of the allotted time limit. The dependent variable was number of correct solutions, rather than time to solution/item. Botwinick (1966, 1973), Canestrari (1963) and Eisdorfer (1968) have all demonstrated the unsuitability of the use of any temporal performance measure f o r the elderly, emphasizing the roles of cautiousness and overarousal in hindering an accurate assessment of their performance (see also Arenberg, 1973).
Downloaded by [McGill University Library] at 10:20 10 April 2013
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HAYSLIP
Spearman Rho correlations were employed to assess the relative value of each index of anagram difficulty in predicting solution frequency. Spearman Rho rather than Pearson T was employed due to the small ( N = 30) number of paired observations, and so that direct comparisons between the ThorndikeLorge and other measures could be made. Corrections for large numbers of tied ranks were used where necessary (Siegel, 1956). The indices assessed were: 1) transition probability ratio (Silvestri & Gavurin, 1972), 2) bigram TP counts for the anagram according to Mayzner and Tresslet (1965), 3) Mayzner-Tresselt TP counts for the solution word, 4) bigram versatility (BV) (Topper, et ul., 1973) for the anagram, 5) BV counts for the solution word, 6) ThorndikeLorge (1944) solution word class frequency, 7) TPD index (transition probability difference between anagram and solution word) (Gavurin & DeVito, 1973) computed from both the MayznerTresselt and Underwood-Schultz tables, 8) Underwood-Shultz TP counts for both anagram and solution word, 9) bigram rank index (Mendelsohn & O’Brien, 1974), and 10) summed letter frequency of the solution word (Cohen, 1968; Johnson, 1966) as calculated from both the Mayzner-Tresselt and Underwood-Schultz tables.
Results und Discussion
It should be noted that a great many (129) correlations were computed between an anagram’s rank on an index of difficulty, frequency of solution by age (Table 1)’ and the developmental relationship between Gf, Gc and solution/nonsolution of that anagram (Table 2). Given this consideration, one would expect a certain number of significant relationships to occur on the basis of chance alone. To test this hypothesis, since 1) the number of correlations was large, 2) p was close to 0 or 1, and 3) NPQ exceeded 9 (Siegel, 1956), the approximation to the normal distribution by the binomial distribution (Edwards, 1954; Siegel, 1956) was utilized. With p = .05 (probability of finding a given number or more of significant correlations by chance), x = 29 (number of significant correlations in the present study), and N = 129 (total number of correlations computed in the present study), the obtained z value was +2.82 (p-c.005). This indicates that in the present
ANAGRAM PERFORMANCE
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study, the number of significant correlations (29) obtained was significantly (pioraZsciences. New York: hfcGraw-Hill, 1956. SILVESTRI, P. J., & GAVURIN, E. I. Anagram solving and relative solution-word transition probability. Perceptunl and Alotor Skills. 1972. ( 3 5 ) . 3 3 8 . SOLSO,R. L., TOPFER, G. E., & MACEY,W. 13. Anagam solution ar a function of bigram 1,ersatility. Journal of Experirnentnl Psychology, 1973. ( 100 ) 259-762. STACKNIK, T. Transitionnl probability in anagram solution in a group settin2. Journol of Psychology, 1963, ( 5 5 ) , 259-261. TIIORNDIKE, E. L., ?: LORGE,I. A Teccha’s wordbook of 30.000iisords. hTew York: Columbia University Tencher’s Collcge, Burearl of Publication, 1944. TOPPER, G . E., R ~ A C E Y ,I f ? ,H., & SOLSO,R . L. Bigram versatility and bigrani frequency. Behavioral Research Methodology and Instrumentation, 1973, ( 5 1, 51- 53. TRESSELT,M . E., & MAYZNER, RI. S. Anagram solution times: A function of inindividual differences in stored digram frequencies. Journal of Experimental Psychology, 1965, ( 7 0 ) , 606-610. MAYZNER, M. S. Normative solution times for a sample of 134 solution words. Psychonomic Monograph Supplements, 1965, (1 ), 293-298. UNDERWOOD, B. J., & SCHULTZ, €3. W. Meaningfulness and verbal learning.. Chicago: Lippincott, 1960. WARREN,A. W., 8i THOMPSON, 111. J. Anagram solution as a function of transition probabilities and solution word frequency. Psychonomic Science, 1969, (171,
TRESSELT, M. E., &
333-334. Received January 7, 1977; accepted January 28, 1977.
Experimental Aging Research: An International Journal Devoted to the Scientific Study of the Aging Process Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uear20
Determinants of anagram problem solution in adulthood Bert Hayslip Jr.
a
a
Department of Psychology, Hood College, Frederick, Maryland, 21701 Version of record first published: 27 Sep 2007.
To cite this article: Bert Hayslip Jr. (1977): Determinants of anagram problem solution in adulthood, Experimental Aging Research: An International Journal Devoted to the Scientific Study of the Aging Process, 3:2, 147-163 To link to this article: http://dx.doi.org/10.1080/03610737708257095
PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/termsand-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
147
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DETERMINANTS OF ANAGRAM PROBLEM SOLUTION IN ADULTHOOD BERT HAYSLIP, JR. DeGratment of Psychology Hood College Frederick, Maryland 21701
Hayslip B. Determinants of anagram problem solution in adulthood. Experimental Aging Research, 1977,3, (Z), 147-163. An evaluation of the indices proposed in the literature regarding measures of anagram difficulty was made by asking three groups (ages 17-26, 39-51, 59-76) of adults ( n = 54) to solve a list of 30 anagrams. Results indicated that only two of these indices (ThorndikeLorge and Bigram Rank measures) significantly predicted frequency of solution in samples beyond college age. I t was also found that the cognitive variable mediating the effects of these indices in middle aged and elderly subjects was crystallized ability, suggesting an experiential basis for the effects of both task and organismic variables as determinants of anagram problem solving in adulthood. T h e role of fluid ability as a mediator of problem solution in the young received limited support.
DETERMINANTS OF ANAGRAM SOLUTION I N ADULTHOOD In contrast to most types of traditional learning and problem solving tasks finding decrements in performance with increased age (Arenkrg, 1973; Botwinick, 1973), no such decrements have been obtained in adulthood with the anagram task (Hayslip & Sterns, Note 1). As an experimental problem, the anagram task has been the subject of a great deal of research over the past 20 years. Johnson (1966) has reviewed much of this research dealing with the determinants of anagram solution: anagram and solution word variables, anagram-word relationships, and temporal factors. Numerous other investigators have linked a wide variety *of factors,
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HAYSLIP
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i. e., imagery (Jablonski & Mueller, 1972), set and practice effects (Gavurin, 1973; Johnson, 1966), and individual differences in cognition (Gavurin, 1967; Johnson, 1966; Mendelsohn & Griswold, 1966; Mendelsohn, Griswold & Anderson, 1966; Mendelsohn & Covington, 1972; Mendelsohn & Lindholm, 1972) to anagram solution. Mayzner and Tresselt (1958, 1959, 1962, 1963, 1966), Mayzner, Tresselt and Helback (1964) and Tresselt and Mayzner (1965, 1966) have established a relationship between the following factors and anagram solution times: a) digram frequency of the anagrun, b) digram frequency of the solution word, c) the ThorndikeLorge (1944) frequency count, d) word length, e) number of letters moves and f ) multiple solutions. Mayzner and Tresselt have concluded low transitional probality (TP) anagrams and the high TP solution words to be solved most quickly. Others, however, (e.9. Dominowski & Duncan, 1964; Dominowski, Note 3; Warren & Thompson, 1969) have been unable to replicate these findings. Much effort seems to have gone into developing a satisfactory measure for assessing anagram difficulty. Mayzner and Tresselt (1965) have revised the Underwood-Schultz (1960) tables for calculating digram T P values, taking into account word length and letter position within word. Gavurin and DeVito (1973) have compared these two measures of difficulty, in addition to Thorndike-Lorge frequency count, as predictors of frequency of anagram solution. The Thorndike-Lorge index was found to be unrelated lio problem dolutjon. Both Underwood-Schultz and MayznerTresselt systems for calculating digram frequencies however, produced comparable results with one exception (anagram TP) . The authors suggested a TPD (digram transitional probability differtnce between anagram and solution word), index as an alternative, more sensitive measure of anagram difficulty. Topper, Macey and Solso (1973) and Solso, Topper and Macey (1973) have suggested biagram versatility (BV), as measured by the number of different words in which a digram appeared, as an index of anagram solving. Silvestri and Gavurin (1972) have reported a more refined measure: the “transition probability ratio” of each correct solution word digram to all of the possible alternate digrams formed with the same
Downloaded by [McGill University Library] at 10:20 10 April 2013
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initial letter. Most recently, Mendelsohn and O’Brien (1974) have offered still another measure of anagram problem solving which significantly predicted anagram solution, using a comprcmise meaSure incorporating both response latency and item success/failure. This index was similar to an anagram-related measure proposed by Dominowski (Note 3) (rank of bigram within the set of all bigrams with the same initial letter). This was termed a solution word bigram rank measure, based on the relative frequencies of “correct” (comprising the solution word) to “incorrect” bigrams within the pool of bigrams defined by the letters made from the anagram, rather than by the absolute frequencies of the correct bigram. This bigram rank measure also took both word length and letter position into account. With the exception of a few studies (Dominowski & Duncan, 1964; Gavurin & DeVito, 1973; Mendekohn & Griswold, 1966; Mendelsohn & O’Brien, 1974; Pinckney, 1965, Silvestri & Gavurin, 1972; Stacknik, 1963), most anagram research has utilized item response latency as a dependent variable- Furthermore, no published research on anagram solving has employed samples of other than college age. With the comparatively recent thrust of the study of adulthood and aging (Baltes & Goulet, 1970), it would seem desirable to extend/replicate the research on the determinants of anagram difficulty using samples beyond early adulthood. This study first seeks to assess the relative efficiency of the above proposed indices of anagram difficulty in predicting frequency of anagram solution in three adult samples varying in age. Such information about the most predictive index of anagram difficulty could thus be applied to experimental research dealing with subjects beyond late adolescence or young adulthood.
A second objective of the present study is to incorporate the above findings into the literature dealing with anagram solvingability relationships. Most research to date has implicated t,he role of verbal ability in determining anagram performance (Gavurin, 1967; Johnson, 1966; Mendelsohn, e t al., 1966, 1972). Most recently, Hayslip and Sterns (Note 1) found that with increased age, the role of crystallized ability (Gc) relative to that of fluid (Gf) intelligence increased (Horn, 1968, 1970) as a correlate of anagram
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solving. No evaluation of the relationships between intelligence and the above indices of anagram difficulty as determinants of solution frequency was made, however. Accordingly, the present study a,lso represents an additional analysis of the Hayslip and Sterns (Note 1) data dealing with anagram solving-ability relations in adulthood, to incorporate differential measures of anagram difficulty. Both Hunter (1959) and Johnson (1966) have viewed anagram problem solving in two phases: 1) letter rearrangement and 2) comparison with stored word models. Mendelsohn and O’Brien (1974) suggested that solution is comprised of 1) a hypothesis formation phase followed by 2) a phase in which the subject moves from partial reorganizations of the anagram to the production of whole words or solutions. One might, on the basis of the above literature, propose that different task variables (indices of difficulty) and subject variables (Gf and Gc) may interact differently with increased age to account for anagram problem solution. On the basis of the nature of each ability factor (Horn, 1968, 1970) one may speculate that Gf may represent or mediate this letter rearrangement (hypothesis formation) phase, Gc reflecting the acquisition of experientially determined stored word models in the anagram solving proces. Thus, the present study seeks to examine what has thus far been treated experimen%ally (indices of anagram difficulty), and link it to cognition (crystallized and fluid ability) within a developmental context.
METHOD Three groups (7% = 54) of subjects varying in age (17-26, 3951, 59-76) were tested individually on the anagram task, as part of a more comprehensive battery of ability and problem solving tasks (see Hayslip & Sterns, Note 1). Equal numbers of males and females comprised each age group. The young adult group was comprised of both college and noncollege people, employed at a local utility firm, hourly city em-
Downloaded by [McGill University Library] at 10:20 10 April 2013
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ployees, and undergraduate college students at varying points in their education. Middle aged subjects consisted of individuals employed at a local utility company, city and county government staff personnel, university staff personnel and residents of a low income government sponsored apartment complex. Older adults were sampled from local community groups such as AARP (American Association of Retired Persons), RSVP (Retired Senior Volunteer Persons), or residents of a Metropolitan Housing Authority older adult apartment building. Subjects all willingly participated and were free of obvious visual and auditory defects that would hamper their performance. and all were er,gaged in Community living.
Materials and Procedure Thirty anagrams, each consisting of five letters, were listed on a sheet of paper. Ten anagrams were “easy”, ten were of medium difficulty, and ten were “difficult”, as determined by normative solution times (Tresselt & Mayzner, 1966). Each item had been listed by these authors as having only one solution. Each subject was informed of the nature of the anagram task, and was given five practice problems, with explanations of solution, prior to the test list. This list consisted of the anagram typed in capital Ietters separated by a space, with blanks t o the right of each. Subjects were instructed to write their solutions down without the use of any notes, to work at a comfortable pace, and not to spend an excessive amount of time on any one item. An effort was made to insure that no notes were used throughout. Subjects were given a maximum of thirty minutes to complete the list (they were not told this fact). In all but one case, subjects had finished work at the conclusion of the allotted time limit. The dependent variable was number of correct solutions, rather than time to solution/item. Botwinick (1966, 1973), Canestrari (1963) and Eisdorfer (1968) have all demonstrated the unsuitability of the use of any temporal performance measure f o r the elderly, emphasizing the roles of cautiousness and overarousal in hindering an accurate assessment of their performance (see also Arenberg, 1973).
Downloaded by [McGill University Library] at 10:20 10 April 2013
152
HAYSLIP
Spearman Rho correlations were employed to assess the relative value of each index of anagram difficulty in predicting solution frequency. Spearman Rho rather than Pearson T was employed due to the small ( N = 30) number of paired observations, and so that direct comparisons between the ThorndikeLorge and other measures could be made. Corrections for large numbers of tied ranks were used where necessary (Siegel, 1956). The indices assessed were: 1) transition probability ratio (Silvestri & Gavurin, 1972), 2) bigram TP counts for the anagram according to Mayzner and Tresslet (1965), 3) Mayzner-Tresselt TP counts for the solution word, 4) bigram versatility (BV) (Topper, et ul., 1973) for the anagram, 5) BV counts for the solution word, 6) ThorndikeLorge (1944) solution word class frequency, 7) TPD index (transition probability difference between anagram and solution word) (Gavurin & DeVito, 1973) computed from both the MayznerTresselt and Underwood-Schultz tables, 8) Underwood-Shultz TP counts for both anagram and solution word, 9) bigram rank index (Mendelsohn & O’Brien, 1974), and 10) summed letter frequency of the solution word (Cohen, 1968; Johnson, 1966) as calculated from both the Mayzner-Tresselt and Underwood-Schultz tables.
Results und Discussion
It should be noted that a great many (129) correlations were computed between an anagram’s rank on an index of difficulty, frequency of solution by age (Table 1)’ and the developmental relationship between Gf, Gc and solution/nonsolution of that anagram (Table 2). Given this consideration, one would expect a certain number of significant relationships to occur on the basis of chance alone. To test this hypothesis, since 1) the number of correlations was large, 2) p was close to 0 or 1, and 3) NPQ exceeded 9 (Siegel, 1956), the approximation to the normal distribution by the binomial distribution (Edwards, 1954; Siegel, 1956) was utilized. With p = .05 (probability of finding a given number or more of significant correlations by chance), x = 29 (number of significant correlations in the present study), and N = 129 (total number of correlations computed in the present study), the obtained z value was +2.82 (p-c.005). This indicates that in the present
ANAGRAM PERFORMANCE
153
study, the number of significant correlations (29) obtained was significantly (pioraZsciences. New York: hfcGraw-Hill, 1956. SILVESTRI, P. J., & GAVURIN, E. I. Anagram solving and relative solution-word transition probability. Perceptunl and Alotor Skills. 1972. ( 3 5 ) . 3 3 8 . SOLSO,R. L., TOPFER, G. E., & MACEY,W. 13. Anagam solution ar a function of bigram 1,ersatility. Journal of Experirnentnl Psychology, 1973. ( 100 ) 259-762. STACKNIK, T. Transitionnl probability in anagram solution in a group settin2. Journol of Psychology, 1963, ( 5 5 ) , 259-261. TIIORNDIKE, E. L., ?: LORGE,I. A Teccha’s wordbook of 30.000iisords. hTew York: Columbia University Tencher’s Collcge, Burearl of Publication, 1944. TOPPER, G . E., R ~ A C E Y ,I f ? ,H., & SOLSO,R . L. Bigram versatility and bigrani frequency. Behavioral Research Methodology and Instrumentation, 1973, ( 5 1, 51- 53. TRESSELT,M . E., & MAYZNER, RI. S. Anagram solution times: A function of inindividual differences in stored digram frequencies. Journal of Experimental Psychology, 1965, ( 7 0 ) , 606-610. MAYZNER, M. S. Normative solution times for a sample of 134 solution words. Psychonomic Monograph Supplements, 1965, (1 ), 293-298. UNDERWOOD, B. J., & SCHULTZ, €3. W. Meaningfulness and verbal learning.. Chicago: Lippincott, 1960. WARREN,A. W., 8i THOMPSON, 111. J. Anagram solution as a function of transition probabilities and solution word frequency. Psychonomic Science, 1969, (171,
TRESSELT, M. E., &
333-334. Received January 7, 1977; accepted January 28, 1977.
