The relations of abilities, as measured by Thurstone's Tests for Primary Mental Abilities, to activity preferences, as measured by Kuder's Preference Record, are investigated for a population of 512 university freshmen. Ability profiles for contrasted groups on each preference scale reveal relatively slight overlapping between the two sets of measures, although the apparent trends are reasonable. The Pearson inter-correlation coefficients of all pairs of measures involved were determined. Implications of the findings in relation to theory and to educational and vocational guidance are indicated.

In the application of the analysis of variance to data obtained in educational methods experiments which involve several classes of several schools, one assumption is that of homogeneity in the variances of pupil scores from school to school. It is shown that such variances on representative educational achievement tests are heterogeneous. The effects of this heterogeneity upon the F-tests of significance commonly employed in methods experiments are investigated by comparing the actual distribution of F values for a large number of “experiments” involving marked heterogeneity with a theoretical distribution based on the assumption of homogeneity. Although the findings, which vary somewhat with the type of variance ratio, are not entirely conclusive, they apparently demonstrate that departure from homogeneity does not invalidate the use of the customary F-tests for evaluating results of the typical methods experiment.

An analytic technique for the study of trait variability is presented. An expression for the average variance from test to test and an expression for the variance of these variances are derived in terms of the number of tests and the intercorrelations between them, and limiting cases are examined. The question of the true relationship between the nature of the distribution of test scores in a sample of N persons and the nature of the distribution of n traits in a single individual is discussed, and other problems are introduced.

It is noted that the average inter-item correlation, which represents the internal consistency of a test, yields a unique estimate of test reliability. A close approximation to this average is given by a formula which requires the correlation of each item with the total score and the standard deviation of each item. The formula is especially useful in those instances where the number of items is small and where the variation in item sigmas should not be neglected.

A machine to expedite matrix multiplication has been developed by modifying the International Business Machines Corporation scoring machine. The principles and operation of the machine are described, and time and accuracy estimates are indicated.

The problem in multiple correlation work of nonsense results attributable to linear dependence of variables, which has been discussed by Ragnar Frisch in relation to economic data, is presented from the standpoint of its significance in psychological research. It is shown that a symmetric correlation determinant with unity in the diagonal cells can vanish only when there is a first-order or partial correlation of unity between one pair of the variables. On the basis of this result, it is argued that the problem should be expected to cause less difficulty in the field of psychology than in economics and that psychologists should be able to avoid the pitfall by bringing to bear their knowledge of the variables with which they are working.

An attempt is made to define and treat analytically the concept of individual freedom in a society. Two possible definitions are briefly discussed. One takes as a measure of freedom the ratio (w0 − w)w0, where w0 is the maximum amount of work that a person can physically perform per unit time and w is the amount of work which he has actually to perform per unit time in a given society. The other definition takes as a measure of freedom that fraction of an individual's time during which he can indulge in any activity of his own choice without interfering with other individuals. Expressions are derived by way of illustration, giving the individual freedom in terms of other parameters which characterize the social structure.

The Kuder-Richardson reliability coefficient is derived in a manner independent of that originally given. Various alternative forms applicable to special situations are exhibited with the purpose of making them available to others interested in using this formula. A simplification in computation is suggested for use with a calculating machine.