LLooyyoollaa UUnniivveerrssiittyy CChhiiccaaggoo LLooyyoollaa eeCCoommmmoonnss Master's Theses Theses and Dissertations 1971 AAnnaaggrraamm SSoolluuttiioonn TTiimmeess:: AA FFuunnccttiioonn ooff BBiiggrraamm FFrreeqquueennccyy aanndd VVeerrssaattiilliittyy Gene Edward Topper Loyola University Chicago Follow this and additional works at: https://ecommons.luc.edu/luc_theses Part of the Psychology Commons RReeccoommmmeennddeedd CCiittaattiioonn Topper, Gene Edward, "Anagram Solution Times: A Function of Bigram Frequency and Versatility" (1971). Master's Theses. 2606. https://ecommons.luc.edu/luc_theses/2606 This Thesis is brought to you for free and open access by the Theses and Dissertations at Loyola eCommons. It has been accepted for inclusion in Master's Theses by an authorized administrator of Loyola eCommons. For more information, please contact [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License. Copyright © 1971 Gene Edward Topper LOYOLA UNIVERSITY ANAGRAM SOLUTION TIMES: A FUNCTION OF BIGRAM FREQUENCY AND VERSATILITY A THESIS SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree MASTER OF ARTS OF PSYCHOLOGY DEPART!.ffi~T BY GENE EDWARD TOPPER _JUNE, 1971 ANAGRAM SOLUTION TIMES: A FUNCTION OF BIGHAM FREQUENCY AND VERSATILITY Gene Topper Loyola University There are many variables that may affect the speed of anagram solution time. Mayzner and Tresselt (19.58: 1959; 19,62; 1963) in a myriad of anagram studies have laid down several basic factors which they consider es sential in the speed of solution. Solution word frequen cy of appearance in normal reading and speech affects re sponse rates, higher frequency words being solved at a higher rate than low frequency words. The frequency or "uniqueness" of a solution word has in these studies and numerous others proven to be an important and stable, if not superordinate factor in anagram solution. Early stud ies on anagram variables also revealed such obvious rela tionships as increasing word length and the requiring of more letter moves to solution results in longer solution times. More recent reseA.rch on variables of anagram solution have focused on the characteristics of the bigram and trigram constituents of the solution words. Any sequence of successive two-letter combinations in anagrams or their solution counterpart may be considered a bigram. Past Topper 2 studies on bigrams have used frequency counts taken froM the printed English language in a Manner of the Thorndike-Lorge (1944) word frequency count. These past studies focusing on the frequencies of successive bigrarns in both word SUM~ed and anagram have yielded more equivocal results than the word frequency relationships. Mayzner and Tresselt (1959; 1966) generally found. that high bigram frequency (BF) words and low anagr.a .m bigrarn totals facilitated solution. However, other studies including Dominowski and Duncan (1964) have not been able to consistently duplicate Mayzner and Tresselt's findings. As Dominowski (1967) suggests, "differences in problem difficulty produced by Manipulating BF (in ane.grams or solution words) have been small and unstable, suggesting the need for a new analysis of the problem." Johnson (1966) hypothesizes that S in "the process of anagram solution, generat·es words, tests them against the anagram letters, and that bigrams are used as a basis for word production." If it is true that § selects bigrams as a basis for word production in the solution process of ana- grams then the characteristics ofthe bigram used in this process becomes important in determining whether the anagram will be solved and in how much time the process will take. Dominowski (1967) outlines the basis for a need for a new approach of bigram classif1cBtion: "Ss production of bigrams must be somewhat re stricted by the letters of the anA.gram. The use of general bigram frequency takes no account of such a restriction, and a more appropriate mea sure may be developed." The impetus for the present study came from a consideration of the techniques and theory used in the cslculation of -~rr--. such frequ~ncy counts. It is proposed in this study that the bigram counts previously used are misleading and inappropriate in their use ns pr~dictors of eGse of anagram solution. The characteristics of the bigram in this study will be referred to bigrarn versatility as opposed to bigrarn fre RS quency. Bigram frequency counts, as is the case with word frequency counts, represent the relative frequency a partic ular bigram appears in the written English language. A high. bigram frequency might rt'lpresent the case of a bigram appear ing in a large number of words, in a few words which appear a large number of times, or a combination of the two. In contrast, a bigram with what will be called high versatility would indicate that the bigram appears in a large number of different words. As an example the bigram "of" has a high frequency due to its appearance as the word "of". The ver satility of the bigram of not ·be expected to be as woul~ high as its frequency since the word of can only be included once in the versatility count. Bigram versatility should be a better indicator of anagram solution ti.me than bigram frequency if §. uses the bigram to generate words And tests them with the letters in the anagram. The §. would only be expected to test a bi gram in an anagram once to see if it is a possible solution word. Thus the higher frequency bigrams with lower versa tilities should generate fewer potential solution words (less interference) than their high frequency high versatile counterparts. The study was designed to study the p~esent relationship between frequency and versatility and anagram solution times. J.opper Method MAterials.--Bigram versatilities were calculated from a sample of one-tenth of the words throughout the Thorndike Lorge word list of words of frequency one million and over. After a word was randomly selected from each block of 10 words each bigram in the word was recorded for its occurence. Table 1 shows the results of the d1Rtribution of the 12,344 bigrams recorded. Table 1 also shows the corresponding frequencies for the bi grams as found in Underwood and Schulz (1960). Both the frequency and versatility counts were arbi trarily divided into classes containing the highest, second highest, third highest, and lowest quartile values. It was calculated that bigrams with frequencies of 600 and higher were in the top quarter of the frequency distribution and will be referred to as group Fl. Table 2 shows the class limits of the first as well as the second, third, and fourth quarters (F2, F3, and F4) of the bigram frequency distribu- ti on. Insert Table 2 about here A versatility count of 36 and over was the calculated cri teria for the top quarter of the versatility distribution and will be referred to as group Vl. Table 2 shows group Vl and the second, third, and fourth quarters (V2, VJ, V4) class limits of the distribution of bigra.m versatilities. Each bigram was assigned an FV value according to its membership in each of the distributions. Table J insert Table._J_ about -here- - - -- ·-·-- - -· - - - - - -- - -- indicates the combined. FV value for each particular bigram. It is· on this basis of bigram classification that the present experiment was conducted. To make sure or at least increase the possibility that the Ss used tht'! bigraI!ls selected, the bigram under study for ' each anagram was indicated above its anagram with only its position remaining undisclosed. All anagram problems were constructed from five-letter words beginning with consonants, contained only one solution, and had no repeated letters. The anagrams differed slightly in terms of number and placement of consonants and vowels. The experiment was conducted with high frequency solution words, frequencies of Ao~ AA (Thorndike & Lorge, 1944). The experiment was ·also· replicated as close .as possible for low frequency words, frequencies ranging from 5-37 per mil- lion. All of the FV bigram were not used since co~binations bigrams were not found in all the cells. As would be ex pected no bigrBms were found in the F4Vl nor in the FlV4 condition. Other conditions WP.re eliminated when at leest two solution words could not be found containing bigraJ!J. ~ from the condition. For the high frequency solution words the bigram conditions used were the "normal" conditions FlVl, F2V2, FJVJ, plus conditions F2Vl, FlV2, FJV2, F2VJ, and FJV4. The F4 conditions had to be eliminated com- pletely due to insufficient word samples. The low fre- v solution words contA.inecl from conditions FlV2, qu~ncy b1/2'r~MS F2Vl, F2V3, and F3V2. When possible four anagrams from each condition were used. This enabled a sarriple frori each 'bigram condition to appear at each of thP four bigram positions (1-2, 2-3, 3-4, 4-5) in the solution word. No individual b1gram was used more than once in a condition. Other than the bigram under study the other thre~ bigrams of the solution words were always in the normal category. .A total of 36 words were used . in the experiment. Twenty-four of the words were high fre- quency solution words. Twelve words were used in the low solution word frequency condition. Table 4 lists all the stimulus materials for each condition. ·- - - - --- ..- Insert Table-4 about here All 36 solution words had medium to high solution word bigram totals, mean solbitot= 4,947. Anagram bigram totals (anbitots) were not calculated. These totals would be mis- leading since one of the bigrarns was correctly shown for each anagram. All of the anagrams were of the "hard" letter orders, requiring over two moves to solution. No bigram appeared in its correct sequential order in the anagram. Each anagram was typed individually on a 3 X 5 index card in a manner similar to that shown in Table 4. Design and Ss.--The 36 anagrams were split into two lists of 18 anagrams so that each of the 24 introductory psychology students from University received half the Loyol~ words froM each condition. The 24 §s each served in con- ditions FlVl, FlV2, F2Vl, F2V2, F2VJ, F3V2, FJVJ, F3V4 in the high Topper . 7 solution word frequency condition and in conditions FlV2, F2Vl, F2V3, and F3V2 in the low solution word frequency condition. The words in each list were randomly ordered. The §s were assigned to conditions in order of ap,earance at the labor atory. The order of the words in the lists were reversed for alternete Ss. Procedure.--Each § was run individually. Instructions included an example of an anagram. It was stressed that the bigram i'ndicated above the anagram could appear in a.ny po sition in the word. For each of the 36 anagrams a maximum of JO sec. was allowed. If § solved, he gave his answer orally and the solution time was recorded to the nearest tenth of a sec.; if§ failed to solve, was told the solution be ~e fore the next problem was presented. Results Each condition contsined bigrams under study at differ ent letter positions in the solution words. Dominowski (1968) showed thet the position of the bigram significant pr~se~ted ly affected response times. Positions 1-2 and 4-5 led to faster solution times than the middle positions 2-3 and 3-4. In'. the present experiment median times were calculated for each anagram. Medians were employed since there was an arti- ficial ceiling of )0 sec. for each anagram. The anagrams were divided into the four position groups and the mean of the median times for each groun (ns= 13, 6, 11, 6) were plotted as a function of position. The results as shown in Figure 1 - -- - ·-- - --- -- ·- - .. - . Fig. l about here Ins~rt -- - -· - - -··· ... V tJ f.JCJ.- ts reseMble those of Do~inowski. The 1-2 and 4-5 positions were almost identical and were associated with faster solution times than in the 2-3 and 3-4 positions. In comparing solut1on times across bigram conditions means of the median times for the words comprising each con dition were calculated. Figure 2 Insert Fig. 2 about here is a graphical representation of the trends in solution time with changing bigram frequency and versatility for the high, frequency solution words. The low frequency solution word conditions were not plotted due to a lack of sufficient data. Inspection of Figure 2 reveals a decrease in mean solution time across frequency groups, Fl-F2-FJ, in the V2 versatil- ity condition. Table 5 shows the mean of the means and mean of the median times for each condition. The fastest solution times for the high frequency solution words seen in the V2 condition also appear in the V2 condition in the low frequency solution word groups. An appropriate and valid dBta analysis was exceedingly difficult in the present experiment due to missing cells and the necessity of the use of median times. Solution times however were compared between the Vl and V2 conditions where a consistent trend in times appeared. In the high frequency solution word condition thP-re were significantly