The latent structure model considered here postulates that a population of individuals can be divided into m classes such that each class is “homogeneous” in the sense that for the individuals in the class the responses to N dichotomous items or questions are statistically independent. A method is given for deducing the proportions of the population in each latent class and the probabilities of positive responses to each item for individuals in each class from knowledge of the probabilities of positive responses for individuals from the population as a whole. For estimation of the latent parameters on the basis of a sample, it is proposed that the same method of analysis be applied to the observed data. The method has the advantages of avoiding implicitly defined and unobservable quantities, and of using relatively simple computational procedures of conventional matrix algebra, but it has the disadvantages of using only a part of the available information and of using that part asymmetrically.

The personnel classification problem is identified mathematically with other problems in the social and biological sciences. This mathematical problem is shown to be a special case of the general mathematical problem of linear programming. It is proposed here that the personnel classification problem may be solved directly by methods particularly appropriate to it as well as by the simplex method, which is a standard method for solving the general linear programming problem. The method of optimal regions is derived and illustrated in this paper.

It is first demonstrated that Aitken's selection formulas are equivalent to a linear transformation in the factor space. On this basis the Thomson-Ledermann theorem concerning the invariance of the number of common factors under selection, and a theorem concerning the invariance of factor loadings under selection are derived. A mathematical proof of the results of Thurstone, which are concerned with the invariance of simple structure under selection, is given. The paper provides a conclusive answer to the question, considered by Thurstone and Thomson, whether a multivariate selection is always reducible to successive univariate selections.

The square root method for the solution of a set of simultaneous linear equations or the reduction of a matrix has been known for some time under a variety of names. Because of its usefulness in statistical work, especially in factor analysis, the square root method is presented in general terms and an example given. Several independently developed “multiple group methods” for factor analysis are compared and synthesized. Their fundamental concepts are set forth and an appropriate system of notation developed. Detailed computational procedures are outlined, and the square root method is emphasized as a computing aid in multiple group analysis.

A solution for Case III of the Law of Comparative Judgment, modeled after Thurstone's solution for Case IV but eliminating the restrictive assumption of relatively equal discriminal dispersions, is developed.

Assuming chance to be fully operative, the predicted effect of chance success on test validity when answer options are supplied depends on the number of options, the difficulty of the test and the variance of test scores. Predicted validity values are compared with empirical validity values in an experiment which used the same mathematics test items with and without answer options.

This article reports a second-order factor analysis of the 13 interpretable first-order factors of Adkins and Lyerly based on 66 variables for 200 Army men. The approach to simple structure for 6 second-order factors was unusually good. Loadings of the original 66 variables on the second-order factors were also obtained. Five of the factors are tentatively interpreted as Precision in Formation and Use of Verbal Concepts, General Verbal Fluency, Visualizing Spatial Constancy During Movement, Speed in Analysis, and Flexibility in Analysis.

Attempts to develop improved methods of selecting a panel of judges for psychometric work are presented. The applications reported are in the sensory field and are limited to the assumption of a unidimensional ability underlying the judgments in question. Some aspects of cost efficiency are also considered.