In experiments dealing with the rigidity or the mental set, anagram series have been occasionally used in problem solving situations. Usually, such a series contains a certain fixed cue for the solution; e.g., a fixed letter-order is used through the series, or every word has the same kind of meaning. Although anagrams are useful as experimental materials from various points of view, subject's performance clearly depends on the difficulty of the letter-orders and that of the words used. So it is necessary to control these two kinds of difficulty in order to make the use of anagrams effective. To serve this purpose, this paper mainly intended to inquire into factors determining these two kinds of difficulty and to investigate interactions between them.
Materials used were simple anagrams made from 120 common four-letter nouns in Japanese by permuting letters of each word in all possible orders except the basic order (abcd) and the reverse (dcba) (Table 1, 2). Thus the total number of anagrams used in this experiment was 120×22 and each of them was performed by nine junior high school students who served as subjects. Each subject was given a series composed of 120 anagrams in which all 22 letter-orders appeared randomly. These anagrams were presented one after another, for 10 seconds each, and the subject was instructed to find the original word of each anagram in the series one after another.
Main results were as follows:
1) The order of the scores of relative difficulty from the most difficult to the least difficult of 22 letter-orders, as shown in Table 2, was approximately the same for different words. The variance of scores among letter-orders was not uniform, and appeared to have a curved regression on the score of the word.
2) As factors determining the relative difficulty of a letter-order, the “direction”, “interval” and “position” of three different bonds in each letter-order were considered. The ‘bond’ means the pair of adjacent letters in the basic order. By the analysis of these factors the relative difficulty of a letter-order was shown to depend upon the deviation from the basic order. In order to indicate the deviation uniquely, an index, D=1-r², was adopted. r was the Pearsonean correlation coefficient between the order in question and the basic order when each letter was given the ordinal number in the basic order. It was found that letter-orders were arranged in approximately the same order in terms of the values of this index as they were in terms of the scores of relative difficulty. So it seems plausible that the relative difficulty of any letter-order, irrespective of the number of letters, can be predicted to some extent from the value of this index.
3) The order of relative difficulty of 120 words, as shown in Table 1, was approximately the same for different letter-orders. In addition to the familiarity of the words, redundancy was taken into consideration as one of the factors determining the relative difficulty of words.
4) In order to detect the interactions between the letter-orders and the words, a simple two-factor model was used. Anagrams whose scores of relative difficulty differ significantly from the theoretical values calculated from the model were checked.
These results should be useful when those anagrams are used as experimental materials.

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