Thurstone's Method Research Articles

Determining a simple structure when loadings for certain tests are known

A rigorous and an approximate solution are found for the problem: Given a primary trait matrix forn tests andr 1 traits, and a matrix for the samen tests andr 2 reference axes, to discover the transformation which will transform the second matrix into the first, or primary trait matrix. Formulas for determining the limits of the effect of using the approximate solution are presented. The method is applied to a set of twenty hypothetical tests, defined by their loadings on four orthogonal primary traits. After factoring the inter-correlations of these variables by Thurstone's centroid method, approximating the diagonals, the original hypothetical matrix is reproduced with a root mean square discrepancy of .014 by assuming as known the primary trait loadings of only the first eight tests. The method is applied to the results of factoring two batteries of 14 tests, having 8 tests in common, to give the factor loadings of the two batteries on the same reference axes. The method provides a means of comparing directly and quantitatively the results of two different factor studies, provided they have tests in common, and of testing the stability of simple structure under changes in the battery. The relations of the method here developed to certain problems in multiple correlation are shown.

The common factors in fifty-two mental tests

An analysis by Thurstone's centroid method of the intercorrelations of fifty-two tests was carried to ten factors. Included were tests of social intelligence, Philip's attention tests, and Seashore's tests of musical ability. After rotation of axes, the most important factors appeared to pertain to operations conventionally alluded to by the following terms: verbal facility; spatial ability; numerical ability; attention; musical ability; and memory (or memory span). The social intelligence tests proved to be mainly tests of the verbal factor. A factorial sex difference was indicated by the superiority of men in tests of spatial ability.

The multiple factor theory in terms of common elements

With the mechanism of common elements we designed numerous sets of variates correlated with each other in a known manner and also correlated with the primary and specific factors in the same predetermined fashion. To the correlations from theoretical populations, and also from experimental samples, Thurstone's centroid method of factoring was applied. The resulting centroid co-ordinates were rotated to yield the test vectors. These vectors were close approximations to the theoretical and sample correlations.

The multiple factor theory in terms of common elements

With the mechanism of common elements we designed numerous sets of variates correlated with each other in a known manner and also correlated with the primary and specific factors in the same predetermined fashion. To the correlations from theoretical populations, and also from experimental samples, Thurstone's centroid method of factoring was applied. The resulting centroid co-ordinates were rotated to yield the test vectors. These vectors were close approximations to the theoretical and sample correlations.

A comparison of the thurstone method of multiple factors with the hotelling method of principal components

The factors found by the Hotelling method of principal components present the same necessity for rotation as those found by the Thurstone method of multiple factors.

The scaling of practice data

It is shown that in certain cases practice data approximately meet the assumptions involved in Thurstone's method of absolute scaling. An application of the method was accordingly made in the case of four test performances practiced for 39 days by a group of 56 subjects. The manner in which the practice data were scaled is described by using the data on practice in anagrams as an illustration. Scaling had little effect upon the correlations between initial and final score, but produced marked changes in the apparent effect of practice upon individual differences and in the correlations between initial score and gain.

A factor analysis of certain neurotic symptoms

In an attempt to investigate the concept of neurotic tendency thirty-nine of the forty-two most discriminative items in the Thurstone Neurotic Inventory were administered as a questionnaire to a group of five hundred male college students. An analysis of the table of intercorrelations by Thurstone's centroid method showed that eight factors were sufficient to account for the observed intercorrelations with negligible residuals. The eight centroid factors were then transformed into a simple structure. It is concluded that a single trait of neurotic tendency cannot be postulated and tentative hypotheses are formed as to the nature of the primary traits revealed by the analysis.

The relation between results obtainable with raw and corrected correlation coefficients in multiple factor analysis

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.

Measuring specific attitudes toward the social rights of the negro.

The scores made on Forms A and B of the Hinckley scale of attitude toward the negro are not exactly comparable when given at the same sitting to a group that is strongly opposed to social intermixture with the race. The more advanced students in the groups studied are more liberal in their attitude toward the rights of the negro than the freshmen. The results of this experiment show that this group of southern students are much more liberal toward the economic, the political, and the educational rights of the negro than toward social intermixture with the race. Results also seem to show the possibility of developing by the Thurstone method of equal-appearing intervals a battery of comparable scales of attitude which will make possible an analysis of specific attitude variables toward the social rights of the negro. (PsycINFO Database Record (c) 2006 APA, all rights reserved)

An Application of Thurstone's Method of Factor Analysis to Practice Series

An Application of Thurstone's Method of Factor Analysis to Practice Series

Some comments on Professor Thurstone's method of determining the scale values of test items.

Some comments on Professor Thurstone's method of determining the scale values of test items.

Thurstone's method of study of the learning curve.

Thurstone's method of study of the learning curve.