Volume IV of The American Solider presents the first complete account of the scale analysis approach of Guttman and the latent structure approach of Lazarsfeld to the problem of attitude measurement. This review has been prepared for the purpose of providing an expository account of the models proposed by Guttman and Lazarsfeld, together with an indication of the places which call for additional clarification and research.

An extension of Dwyer's “square root” method has been made to the problem of selecting a minimum set of variables in a multiple regression problem. The square root method of selection differs from the Wherry-Doolittle method primarily in that (1) the computations required are more compact, (2) an F ratio criterion is used which leads to the selection of fewer variables. The method provides solutions for the problems of test selection, item analysis, analysis of variance with disproportionate frequencies, and other problems requiring the rejection of superfluous variables. In a subsequent article a worked example will be given, and the square root and Wherry-Doolittle methods compared.

Most indexes of item validity and difficulty vary systematically with changes in the mean and variance of the group. Formulas are presented showing how certain item parameters will vary with these alterations in group mean and variance. Item parameters are also suggested which should remain invariant under such changes. These parameters are developed under two different assumptions: first, the assumption that the total distribution of the item ability variable is normal, and, second, that the distribution of the item ability variable for each array of the explicit selection variable is normal.

A general formula (α) of which a special case is the Kuder-Richardson coefficient of equivalence is shown to be the mean of all split-half coefficients resulting from different splittings of a test. α is therefore an estimate of the correlation between two random samples of items from a universe of items like those in the test. α is found to be an appropriate index of equivalence and, except for very short tests, of the first-factor concentration in the test. Tests divisible into distinct subtests should be so divided before using the formula. The index \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\bar r_{ij} $$\end{document}, derived from α, is shown to be an index of inter-item homogeneity. Comparison is made to the Guttman and Loevinger approaches. Parallel split coefficients are shown to be unnecessary for tests of common types. In designing tests, maximum interpretability of scores is obtained by increasing the first-factor concentration in any separately-scored subtest and avoiding substantial group-factor clusters within a subtest. Scalability is not a requisite.

Formulas are developed for estimating a point-biserial r or a tetrachoric r from an obtained phi coefficient. The estimate of a tetrachoric r, which is called rϕ, is shown to be equivalent to that obtained from first-order use of the tetrachoric r series. A tabulation is made of corrections needed to make rϕ equivalent numerically to the tetrachoric r. In spite of its greater generality than estimates of tetrachoric r by previous methods, there are limitations, which are pointed out.