This is a continuation of a paper in the previous issue of Psychometrika (Sept., 1948, pp. 147-174) in which some historical facts about the First World War were expressed in mathematical form. The present introduction is intended to make the sequel readable by a person who has never seen Part I. This can perhaps just be done; although for ease, clarity, and conviction a prior study of Part I is strongly to be recommended. The independent variable is t, the time.

A test of the significance of a row or column agent in an analysis of variance may be expressed in the form of correlation between the agent and the variate. A test of the significance of interaction variance may be expressed in the form of correlation between the agents. These expressions are principally of theoretical interest in that the degree of significance in an F test or the value of a correlation coefficient may be controlled at will, or inadvertently, within certain limits.

Outlined is the method used at present by the Educational Testing Service for computing intercorrelations from basic summations. This procedure is adapted to the use of high speed calculators in performing the calculations, and much of its value lies in the complete system of checks that is a part of the method. Besides the correlations that are the object of the procedure, covariances, means, standard deviations, and the number of cases are also recorded on the completed form to be available for further statistical steps.

Ignorance concerning the standard error of individual factor loadings and their differences has been a major obstacle to the proper interpretation of factorial results. The effects of three types of experimental error (selection of variables, selection of subjects and selection of scores) are here reported. In order to handle the errors of rotation systematically, it has been necessary to introduce a new semi-analytical criterion for the attainment of simple structure. Variability in results which may theoretically be eliminated is discussed under the heading of non-essential error.

This article offers a new nomogram for the tetrachoric correlation coefficient, together with a correcting table. The development of the nomogram is described and directions for its use are included.

In order to raise the predictive efficiency of its college entrance test battery, the Educational Testing Service is working on the development of non-academic measures to supplement the standard aptitude and achievement examinations. A test of difficult number series problems was set up to measure persistence by tempting the students to give up early; the students were informed that some of the problems had no solution, and that full credit would be received by so marking them. This test was tried out and found to have some correlation with grades, while having no correlation with the other tests. Adding this test to the battery showed an appreciable rise in the battery's multiple correlation with grades.

A worksheet simplifying the calculation of tetrachoric correlation coefficients and their standard errors is presented for use with Hayes' percentage difference method.