Rate of addition was studied as a function of difficulty as measured by problem length. The hypothesis was tested that the rate of addition would decline as a function of the logarithm of the number of addition operations per problem. The test material required the rapid addition of single columns of digits ranging from two to twenty-five digits in length. Rate of uncorrected addition declined as a power function of problem length and the rate of correct addition declined as an exponential function of length. Results indicated that subjects who varied in age and mental status could be differentiated according to the parameters defining the curves of addition rate as a function of length.

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 mechanical model is described for illustrating changes in the configuration of points when the reference axes are rotated obliquely and the values of the orthogonal projections of the points on the reference axes are maintained constant. This type of transformation is important in factor analysis.

A description is given of a diagram (available separately) for computing biserial or point biserial correlation coefficients. The diagram is maximally useful where large numbers of coefficients are to be calculated in test item analysis. The diagram is entered with the mean criterion score of the group passing the item and the proportion of correct answers to the item.

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.