Thurstone's Case V of the method of paired comparisons assumes equal standard deviations of sensations corresponding to stimuli and zero correlations between pairs of stimuli sensations. It is shown that the assumption of zero correlations can be relaxed to an assumption of equal correlations between pairs with no change in method. Further the usual approach to the method of paired comparisons Case V is shown to lead to a least squares estimate of the stimulus positions on the sensation scale.

The correlations among the thirteen personality scores yielded by the Guilford schedule for factors STDCR, and the Guilford-Martin schedules for factors GAMIN, and O, Ag, and Co, as reported by Lovell, were factored by the centroid method. The purpose was to see how many factors were represented by the thirteen scores; therefore the test reliabilities were used in the diagonal cells. It was found that the scores represent not more than nine linearly independent factors. The orthogonal factor matrix was rotated to oblique simple structure. Seven of the oblique factors were given tentative interpretation. Two factors were regarded as residual factors because of the small variance which they represent. The seven factors have been named Active, Vigorous, Impulsive, Dominant, Stable, Sociable, and Reflective.

The conventional scoring formula to “correct for guessing” is derived and is compared with a regression method for scoring which has been recently proposed by Hamilton. It is shown that the usual formula, S = R – W/(n−1), yields a close approximation (correct within one point) to the maximum-likelihood estimate of an individual's “true score” on the test, if we assume that the individual “knows” or “does not know” the answer to each item, that guessing at unknown items is random, and that success at guessing is governed by the binomial law. It is also shown that the usual scoring formula yields an unbiased estimate of the individual's “true score,” when the true score is defined as the mean score over an indefinitely large number of independent attempts at the test or at equivalent (parallel) tests.

The problem considered is the use of a set of measurements on an individual to decide from which of several populations he has been drawn. It is assumed that in each population there is a probability distribution of the measurements. Principles for choosing the rule of classification are based on costs of misclassification. Optimum procedures are derived in general terms. If the measurements are normally distributed, the procedures use one discriminant function in the case of two populations and several discriminant functions in the cases of more populations. The numerical example given involves three normal populations.

The relationship between Horst's method of successive residuals and Gengerelli's method of exhaustion is demonstrated by transforming both methods into L notation. The L notation form is much more efficient computationally.

Typical selection or classification testing programs should provide for improvement of the predictive efficiency of the test battery. Such provision calls for the administration of experimental tests along with the operational battery administration and follow-up analysis to determine the value of the experimental material. It is possible to determine without waiting for criterion data what the validity of the experimental test must be in order to improve the battery validity. The method together with the proof is presented.

A comparison of the Wherry-Gaylord iterative factor analysis procedure and the Thurstone multiple-group analysis of sub-tests shows that the two methods result in the same factors. The Wherry-Gaylord method has the advantage of giving factor loadings for items. The number of iterations needed can be reduced by doing a factor analysis of sub-tests, re-grouping sub-tests according to factors, and using each group as a starting point for iterations.

The proof of the existence of “g” is more than a methodological problem and concerns the very core of psychological theory. The principles of noegenesis should be identified experimentally before a final opinion can be rendered about “g.” Many general factors isolated in different studies are not necessarily “g.” In the present study a second-order unrotated general factor has been identified by using Thurstone's method. It seems possible to identify this factor with “g.” In the first order, factors that seem to represent the first and second principles of noegenesis have been found. The existence of synthetic and analytic activities and their interplay in intellectual performances is indicated. The relation of likeness is of great interest in explaining cognitive abilities and is isolated both as a first and second order factor. For the final identification of factors the search should be conducted beyond the elementary listing of tests. The dynamic aspects underlying factors are more meaningful than their simple description. The second order gives indications that allow for a better interpretation of fundamental psychological activities.

(1) A new descriptive parameter for tests, the standard length, is defined and related to reliability, correlation, and validity by means of simplified versions of known formulas. (2) The standard error of measurement is found to be related in simple fashion to the amount of information in a test in the sense of R. A. Fisher. The amount of information is computable as the test length divided by the standard length of the test. (3) The invariant properties of the standard length of a test under changes in length are discussed and proved. Similar results for the correlation coefficient corrected for attenuation and the index of validity are indicated.

As an analytical tool the negative binomial distribution may have wide applications in the psychological field. The estimation of its parameters is demonstrated to be often inefficient when fitting by the method of moments. This causes possibly true hypotheses to be rejected. Formulas for the efficiency of the moment method and solution of the likelihood equations are derived. Efficiency graphs and detailed tables for the \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda (r,\hat p)$$\end{document} function reduce the maximum-likelihood method to a minimum of computational labour. Practical applications of the ease and power of the M.L. procedure are given.

The ratio of item validity to item-total correlation can be used to select items which will tend to yield the maximum correlation with a criterion. Items to be retained are identified by comparing the ratio for each item with the validity of the original test. Further improvement of the validity in the experimental sample can be obtained by adding items to or removing items from the selected nucleus, according to recomputed ratios involving the correlations of the items with the nucleus and evaluated by means of a revised cut-off point. With slight variations, the method may be used for interest and personality tests as well as for aptitude material. The principal advantage over previous methods is that for any cycle of the analysis an exact cut-off point is provided.