A battery of pencil-and-paper tests is commonly used for predicting a single criterion. If the score on each test is the number of correct answers, the composite battery score would normally be the sum of the weighted test scores, where the weights are the raw score regression weights. Knowing the reliability of each test, it is possible to alter the lengths of the tests in a manner such that the weights will all be equal. The composite battery score would then simply be the total number of items answered correctly and scoring would be greatly simplified. Such simplification is particularly desirable where the volume of testing is large. Section I of the article outlines the procedure for altering the lengths of the tests, and Section II gives a proof of the method.

A method of exhaustion has been described for calculating regression coefficients. This method dispenses with the solution of simultaneous equations but utilizes a process of successive extraction in obtaining β's, where each successive β is maximized. This procedure permits the worker to discard as he goes along those weights which are deemed unsatisfactory for purposes of prediction. The β coefficients and the R in a problem involving a criterion and six independent variables were calculated in sixty minutes. The R's obtained by this method are smaller than those yielded by the Doolittle technique, but in problems which have been considered this discrepancy has not exceeded .05.

A person can be openly friendly, or hostile, or war-weary. Depth-psychology has shown that the underlying mood is also important. In the present theory the independent variable is time, and the dependent variables are the numbers of persons in different warmoods in two opposing nations. The rate of conversion of persons from one mood to another is taken to be proportional both to the number of susceptible persons and to the number of influencing persons, as in Kermack and McKendrick's theory of epidemics of cholera (15). This formulation leads to a set of differential equations nearly but not quite like those whereby Volterra (41) described the interaction between predator and prey among fish. Here the constants are fitted to the history of the First World War. The gregarious motive to follow a fashion of either peace or war is formulated as an amendment.

Data originally analyzed by Charles H. Goodman on the MacQuarrie Test for Mechanical Ability are subjected to the principal axes factoring method. The maximum variance was extracted with three factors. Rotation to an oblique simple structure yielded a factor pattern which satisfies the simple structure concept more adequately than the orthogonal factor matrix, thus leading to greater clarity of interpretation of the factors.

Factorial analysis begins with an n × n correlation matrix R, whose principal diagonal entries are unknown. If the common test space of the battery is under investigation, the communality of each test is entered in the appropriate diagonal cell. This value is the portion of the test's variance shared with others in the battery. The communalities must be so estimated that R will maintain the rank determined by its side entries, after the former have been inserted. Previous methods of estimating the communalities have involved a certain arbitrariness, since they depended on selecting test subgroups or parts of the data in R. A theory is presented showing that this difficulty can be avoided in principle. In its present form, the theory is not offered as a practical computing procedure. The basis of the new method lies in the Cayley-Hamilton theorem: Any square matrix satisfies its own characteristic equation.

Methods of correcting for continuity in tests of significance of the difference between correlated proportions are presented. These corrections should increase the range of usefulness of the formulas developed by McNemar (1).