It is assumed that a scale of true scores on a function exists and that the probability of answering an item correctly is a curve of the type of the integral of the normal curve. The product moment correlation between the test score and true score is derived for a normal distribution of subjects and a test composed of equivalent items. Numerical examples demonstrate that the maximum correlation between test scores and true scores occurs for a one hundred item test when the point correlation between items is less than three tenths.

A factorial analysis was made of a small battery of twelve anthropometric measurements. The correlations can be accounted for by four factors in a simple structure. This small battery has been used by the author for teaching purposes. Several of these factors seem to be meaningful, but their acceptance must depend on more comprehensive studies of body measurements with a larger number of measurements.

Formulas are presented for triserial correlation, quadriserial correlation, etc., and for serial correlation in general. These formulas are based on well-known procedures outlined by Kelley, Peters and Van Voorhis, and others, and involve Pearson's correction for “broad categories.” The formula for biserial correlation also may be developed following these procedures. The assumptions underlying serial correlation are that the segmented variable is basically continuous and normally distributed, and that all the segments which together would form a whole normal distribution are present.

Twenty-one reagents were rated on a pleasantness scale by 182 subjects. The tetrachoric correlation coefficients were determined for the variables. The correlation matrix thus obtained was subjected to a Thurstone analysis which gave rise to a 6-dimensional structure. Two of these were not clear-cut, and the last one appeared to be a residual factor. One factor, the benzene-ketone, revealed the chemical property of unsaturation and the physiological quality of possible trigeminal stimulation. The other two factors were marked by the presence of oxygen and nitrogen, respectively, and were tentatively labelled as a plant factor and an animal factor accordingly. The intercorrelations of the primaries are high.

When one knows in advance the minimum percentage difference which will be of practical interest in an investigation, principles of economy suggest the desirability of an accurate estimate of the size of the sample to be used. Charts are presented which eliminate any computation where the two groups involved are to be equal. A table is included for the case where one group will be from one to three times the size of the other. The charts are also useful for determining whether or not obtained differences are statistically significant at the 5 per cent or the 1 per cent level.

A simple method of making orthogonal rotations by projecting coordinates from one plot to another is presented. An easily constructed apparatus for rapid and accurate work is described in detail. By the technique proposed 12 to 15 rotations of pairs of axes involving 20 test variables can be completed per hour by a practiced technician.

This article proposes a new descriptive statistic related to the second order parabola in the same manner in which the familiar correlation coefficient is related to the regression coefficient. The parabolic r describes in standard terms simultaneously the general trend of the regression and the extent and nature of its curvilinearity, and is relatively easy to compute and easy to communicate. Formulas for its standard error and its limits are derived and it is applied to a number of regressions.