Here we propose a new computational procedure for the number of factors in Principal Factor Analysis (PFA). The basic notion of our computational procedure is based upon that Thurstone-type,(1947) iterative PFA achieves a minimization of the offdiagonal residuals in a given correlation matrix on condition that the main-diagonal residuals are zeroes (Harman & Jones; 1966). The method is computationally a modification of Thurstone -type iterative PFA.
We assume the standard score of a test j, zj, and its variance as follows: (1) and (2)
Here, Fj, aji, Uj, and aj are the i-th common factor, the factor loading of test j on the i-th common factor, unique factor of test j, and the unique factor loading respectively. And we assume
(3) If 1<r<m, we have from (2) and (3)(4) And if m<s<n, we may have the following possi - bility in test j under s (5)(cf. Huttman; 1940).According to (5), we start with the estimation of total variance of at least one test. We perform our computation assuming that a given number of fac -tors under which the total variance of at least one test is defined or that it is unity. In every iteration, we set at unity the largest estimated test variance in the diagonal of a given correlation matrix, and perform computation under a given number of factors. Then, after all estimated test variances are stabilized, we compare each estimated test variance to its corresponding calculated test variance. When the former is equal to the latter, that is, the minimization of the sum of the squares of off-diagonal residuals (i. e., the minimization of the minres criterion of Harman and Jones (1966)) is achieved, we have at least one test whose total variance is defined perfectly under the number of factors.(5) indicates that the number of factors should not be adopted as the number of common factors m in the matrix, and that the greatest number of factors among all the numbers of factors under which each estimated test variance is greater than its corres - ponding calculated test variance should be the number of common factors m.
By using two illustrative hypothetical examples, we show that our method seems always to give the same number of factors as the assumed one. We apply the same rationale to empirical matrices and show that it is possible to classify empirical matrices into several types. And then we propose criteria concerning the number of factors each of which has its correspondence to a specific type by our classifica - tion. Finally, we discuss the estimation of commu - nalities in our method, and we suggest the use of Thurstone-type iterative PFA under the number of common factors m.

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Purpose:
We investigated achievements in each subject of many pupils and noticed the following two cases; the balancedachiever, whose achievements are well belanced in each subject, and the unbalancedachiever, whose achievements are excellent in special subjects but are on average or blow average in other subjects.
In this study, the indications and causes of those pupils are analyzed and investigated from the view points of their intelligence, achievements, learning habits, home environment, basic needs, and interests.
Method:
The subjects for this investigation were 385 pupils of junior high school. After the guidance of learning based on a certain teaching plan, the achievement tests were given to them. Pupils, whose achievement standard scores of 9 subjects were within-F-5 from the mean values, were classified as the balancedachievers (group B). The unbalancedachiever (group U) were devided into 4 groups: the literary-achiever group (group L), being excellent at Japanese, Social studies and English; the science-achiever group (group S) being excellent at mathematics and science; the technique-achiever group (group T), being excellent at music, art, health and physical education, and technique and home-making; and the literary and science-achiever grop (group LS), excellent Japanese, social study, English, mathematics, and science.
First, the standard-achievement tests of 9 subjects were given to pupils. Then, according to a certain experimental process, foundation tests and pretests prepared by teachers were given. And the guidance of learning was given for 8 weeks. Final tests and retention, tests were given, and pupils were classified into each experimental group by the retention tests.
Result:
The result can be summarized as follows: 1) 13 pupils in 385 belonged to group B.In group U, 12 belonged to group L, 12 belonged to group S, 4 belonged to group T, and 11 belonged to group LS: the total number of group U were 39. 2) Speaking of intelligence standard score, it was rather low in group B. Intelligence ranks were average and no difference could be found in group L, S, T and LS.
3) Comparing the average of retention tests of 9 subjects in each group, the achievement was low in group B. Achievement standard scores were from 48 to 58 in groUps L, S and T. They were rather high in group LS. About accomplishment score, it was negative, and achievement was lower than intelligence in group L. In group LS, it was positive and their intelligence was rather higher than their achievement.
4) Comparing the averages of retention tests classified by each order in each group, results are
as follows:
In group B, it was comparatively low in each subject. In group L, achievement was high in literary subjects, but it was especially low in science subjects. In group S, achievement was high in science subjects and not low in other subjects. In group T, it was generally low in every subjects except technique subjects, especially low in literary subjects. In group LS, it was high in all subjects except technique subjects and the a. chievement standard score was over 60.5) Collecting the tendencies of pupils' learning habits, home environments, basic needs and interests, etc. in this group, the results are as follows; (a) In group B, it is noticiable that learning habits and home evironments were bad. The will to achieve in study was low. About interests for school subjects, it was not definite but littfor science subjects.(b) In group L, learning habits were generally bad. Especially, learning plans and their utilizations, study skills and learning environments were bad. Home environments were generally bad, especially, equipments for children were deficient. Their interests in literary subjects were high and the achievement motives were high too.
(c) In group S, they generally had good home environment.

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As the electronic computers have been widely used, various -kinds of the aptitude diagnosis tests by the use of comoputers have been devised, but few of them are validated from the standpoint of psy -aology.
Generally, the norm of the diagnostic procedures of the aptitude test must have as its basis on the data of the criterion groups of the aptitude which the tests intend are to designed to measure. In view of this point, this study aims to investigate the best method of the aptitude diagnostic procedures, using two types of multivaliate analysis.
The subjects are 480 sudents of Tokyo Univer - sity who take specialization courses, including 117graduate students. They are divided into nine courses: law, economics, literature, education, mathematics and physics, engineering, architect, chemistry, medicine. In each of nine courses, there are at least 40 students, who are satisfied with the choice of their own specialization courses, whom we call criterion groups of aptitude for each courses. They answered the items of the aptitude test battery which consists of following subtests: i) personality test (14 scales), ii) interest test (8 scales), iii) ability test (5 scales), iv) rating scales of vocational interest (8 scales), v) the records of high school subjects (10 scales). In addition to these items, they rated the degree of satisfaction with their choices of their courses from five aspects.
Based upon these data, diagnostic procedure of the aptitude for nine courses are established by the method of multiple discriminant analysis and factor analysis.
The main results are as follows.
(1) By multiple discriminant analysis, four main factors are extracted, the meanings of which are as follows; i) natural science v. s. humanities, ii) architect v. s. medicine and chemistry, iii) business, iv) social welfare. Subjects of the nine courses are located in the Euclidian space with these dimensions.
Applying city block distance model (Atteneave1950) to this space, 76. 1 % of the criterion subjects are diagnosed to fit best to the courses they belong. When we compare the results of all the subjects with the degree of satisfaction, we find that no less than 90% of students who are satisfied, are diagnosed to fit well to their courses.Except for 14 students who are satisfied with the choice of their courses, but not diagnosed to lit well to their courses, the results of the diagnosis using multiple discriminant analysis are more valid than have been expected.
(2) The diagnoses by factor analysis are found to be inferior in its validity to that of discriminant analysis.
(3) In the diagnostic procedure, two kinds of the distance method are used. In case of discriminant analysis, city block distance models are better, but in case of factor analysis, Euclidian distance models (Togerson 1952) are better.
(4) The great difference is recognized between the factor structure of discriminant analysis and that of factor analysis.
(5) Further investigation is needed in order to construct the new forms of the test scales, or to develop the theory of aptitude diagnosis so that the results of the tests may do no harm to the testee.

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A series of experiments to get information about the functional levels of abstraction in verbalthinking have been made by asking a large number of children to find similarities between two things, e. g. an apple and an orange or among three things e. g. an apple, an orange and a grape.
The age of 648 subjects range from 6 to 13, of whom 323 were boys and 325 were girls. The results obtained by the cross-section method are as follows:
(1) There are four functional levels of abstraction, that is, wrong-and-no answer, perceptual abstraction, pre-conceptual abstraction, and conceptual abstraction in the order of the development of their ability of abstraction.
(2) Conceptual abstraction gains as the vge advances.
(3) Pre-conceptual abstraction gains till the age of 7 or 8 and declines after that.
(4) Perceptual abstraction declines as the child grows older.
(5) Fewer children give wrong answers or no answers as they grow older. Hardly any particular age dominates the sub-categories of wrong answers. There is no contradiction between the results obtained by the cross-section method and those obtained by the longitudinal method.
(6) A 6-year old child has been found capable of conceptual abstraction, while some of the 13- year old children have proved quite incapable of this.
(7) Abstraction among three things raises the functional levels more than abstraction between twothings.
(8) Contrary to the accepted view, abstraction among three things does not cause any greater difficulty than abstraction between two things.
The difficulty of abstraction among three things is due not to the larger number of material for chil-dren to abstract, but to the nature of materials themselves which may be very difficult to understand, to the complex quality of the whole structure consisting of many parts or to the unfamiliarity on the part of children with the objects set before them

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This study aims to find out a basic index of personality by'the Experimental Diagnostic Method instead of using'the paper test. In this investigation, we att: empted to see whether there are any differences between the blind, the deaf, and the normal in terms of the expressional pattern of mental energy. For it seems that the differences of the expressional pattern depend on the differences of individual personality or temperament.
Purpose and method:
The first purpose is to measure as many objective aspects as we can of personal tempo with tapping and to examine their reliability. In this experiment, nine measures, that is Comfortable speed (S), Maximal speed (Max), Fluctuation of S (S·SD), Tapping pressure in S (P), Fluctuation of P (P·SD), S × P (E), S: Max (com/max), Expansion of tapping points (W), Height of tapping (H), were established. The second purpose is to devise a method for the description of the personal tempopattern with tapping and then, to compare the differences in the patterns of the blind, of the deaf, and of the normal. For this description, we used the factorial structure as the basic model of the per - sonal tempo-pattern.
Results:
The mainresults were as follows;
(1) Nine measures used here were somewhat reliable and indicated effectively individual differences. Above all, it was remarkable that the tapping pressure (P) corresponded well to the GSR process.
(2) Clear differences in the personal tempo-pattern with tapping among the groups were disting -uished and these differences were also statistically significant. Especially, did the deaf differ from the others, that is, the pattern of the deaf was in sharp contrast with the normal, and the blind was intermediate between them.
These differences will be an important clue for diagnosing the personality of the handicapped, if we can find out the psychological meaning of the main factors, such as SPEED and POWER, of the personal tempo with tapping.

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