One of the most difficult parts of multiple-factor analysis for the student to learn is the rotation of the coordinate axes to simple structure. The complete graphical methods have been the most dependable. The work of interpreting these diagrams is not only tedious but it requires the development of a skill that many otherwise competent students are unable to master. The writer has tried many times to develop an analytical method which would eliminate the graphical methods of successive approximation. The method to be described here seems at last to be successful and practically feasible. It is equally applicable to unimodal and bimodal hyperplanes so that no restrictive assumptions need to be made about the positive or negative signs of the factorial components.

A generalized method for collecting data on interstimulus similarity is presented and its special cases evaluated by use of information theory. A method of analyzing the data by the Unfolding Technique is presented which permits the study of the latent attribute structure underlying the similarity of stimuli for a single individual.

In descriptive factor analysis, the factor matrix is merely an alternate mode of expression of the meaning expressed by the correlation matrix. In inferential factor analysis, the factor matrix expresses material inferred from the correlation matrix but not contained in the correlation matrix. A major problem has been whether or not the latter type is possible. Granit's color cone study is interpreted as a factor study in the hope of showing that inferential factor analysis actually exists. It is argued that proof of these and other points in factor theory can be accomplished only by logical analysis.

A simple algebraic proof of a theorem defining the optimal solution to the personnel classification problem is given. If a set of constants, one for each job, are known, the theorem indicates that each individual should be classified by adding the constants to the estimates of the individual's productivity in the several jobs and selecting the job for which the resulting sum is highest.

This paper reports on the third of a series of four experiments using similar concepts and methods for objective personality measurement, and overlapping test batteries. One hundred students were measured with 115 tests. The scores were correlated and factored by a re-iterated multiple group centroid method. The 17 factors thus obtained were rotated toward a clear simple structure. The relation of the rotated factors to earlier ones is indicated, but no extensive interpretation is attempted.

This paper describes the construction of a new item analysis table for the high-low-27-per-cent group method. The table provides a ready means of translating the observed proportions of success in the two extreme groups (pH, pL) into measures of item difficulty and item discrimination (p, Δ, and r). The tabled values of both the difficulty index, p, and the discrimination index, r, have been derived from Karl Pearson's tables of the normal bivariate surface.

Scores obtained at eight different stages of practice on the Complex Coordination Test together with scores on 18 reference tests were subjected to a Thurstone Centroid Factor Analysis. Nine meaningful factors were identified in the experimental battery. The results indicated considerable, but systematic, changes in the factor structure of the Complex Coordination Test as practice on the task was continued. The test became less complex (factorially) as practice was continued. Moreover, there was a change in the nature of the factors contributing variance at early and later stages of practice. Implications of the findings are related to certain problems of learning theory, psychomotor test development, and criterion analysis.

The purpose of this article is to show that a relationship can be established between Osgood and Suci's D based on raw scores and scores obtained from factor analysis data without equalizing the means and variances of each individual's set of scores.

An electronic computer with large capacity memory, and employing binary numbers, is ideally suited for large-scale item analysis. The adaptation and use of one computer, SWAC, is described.