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.

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.

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 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.

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 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.

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.

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.

(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.

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.

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 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.

For the point distribution model of Lazarsfeld's latent structure analysis, the general matrix equation is stated which relates the manifest data in the form of joint occurrence matrices to the latent parameters. The relationship of the item responses and these joint occurrence matrices is also indicated in matrix form. A general solution for the latent parameters is then presented, which is based on the notion of factoring two joint occurrence matrices. The solution is valid under certain conditions which will usually be fulfilled. The solution assumes that estimates are available for the elements in the joint occurrence matrices with recurring subscripts, analogous to item communality or reliability. Some alternative methods of obtaining these estimates are discussed. Finally a fictitious 3-class, 8-item example is presented in detail.

Twenty years have now elapsed since Professor Thurstone’s ingenuity pulled the factor problem out of its tetrad difference quagmire. Most of us have watched Thurstone’s brain-child grow. One might say that the fledgling was so precocious as to reach maturity during the first ten years of its life. Its development was fostered not only by Thurstone but also by the resistance it encountered. Indeed, even as an infant, it was forced to throw aside its swaddling clothes in order to kick back at the Spearmans, the Tryons, the Anastasis, and others who sometimes rightly, ofttimes wrongly, pointed a finger at supposed imperfections. The youngster weathered more or less successfully the many storms it had stirred up, and by the end of its tenth year of life had in the hands of Thurstone made significant contributions and was ready for the sober coming-of-age evaluation of its strengths and weaknesses by Dael Wolfle. We suspect that the facts of life pointed out by Wolfle had already been whispered to the growing adolescent by none other than Thurstone himself.

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.

A battery of 46 tests was given to 237 college men. A factor analysis using the Thurstone technique revealed eight clearly interpretable first-order factors, one dubious factor, and a residual factor. The factors were interpreted as induction, deduction, flexibility of closure, speed of closure, space, verbal comprehension, word fluency, and number. Four second-order factors were abstracted from the matrix of first-order correlations. The presence of induction, deduction, and flexibility of closure on the first second-order factor, interpreted as an analytic factor, confirmed previous indications of relationships between the reasoning and closure factors. A second bipolar factor is interpreted as a speed of association factor. The third factor is interpreted as facility in handling meaningful verbal materials—perhaps an ability to do abstract thinking. The fourth factor is possibly a second-order closure factor—perhaps an ability to do concrete thinking.

Non-spurious methods are needed for estimating the coefficient of equivalence for speeded tests from single-trial data. Spuriousness in a split-half estimate depends on three conditions; the split-half method may be used if any of these is demonstrated to be absent. A lower-bounds formula, rc, is developed. An empirical trial of this coefficient and other bounds proposed by Gulliksen demonstrates that, for moderately speeded tests, the coefficient of equivalence can be determined approximately from single-trial data. It is proposed that the degree to which tests are speeded be investigated explicitly, and an index τ is advanced to define this concept.