A procedure for maximizing selective efficiency is developed for application to situations in which it is desired to select from a single group of applicants for several possible assignments. The problem of comparable units for the several criteria whose values must be compared to each other for differential assignment purposes is discussed. It is demonstrated that, assuming linear regressions, maximal selection is obtained if individuals in any given assignment are differentiated from those rejected according to critical rejection scores on the multiple weighted sum of the predictors and from another possible assignment by critical difference scores which are merely the differences between the two critical rejection scores. Since the relationships just indicated give no way of determining the magnitude of the critical scores required to select the required number of persons for each assignment, a successive approximation procedure for accomplishing this purpose has been devised and a computational example is worked out.

Ordinary product-moment correlation and regression methods are frequently not immediately applicable to qualitative data, whereas multiserial r, point-multiserial r, and multiserial eta can be easily applied. The multiserial r is rejected for prediction since it tells us only what the correlation might be if certain assumptions were true and if we could measure what is not now measured. The point-multiserial r and multiserial eta are identical when the number of categories is two but differ when it is three or greater. The multiserial eta is identical with the product-moment r when categories are assigned scale values equal to their means on the continuous variable. With three or more categories, the point-multiserial r, which assumes linearity with equal step intervals, is always lower than the multiserial eta, which forces linearity by adoption of unequal step intervals based upon difference in criterion attainment. While the multiserial eta expends one degree of freedom with the weighting of each category, this is known and correctable, whereas the vague partial loss of degrees of freedom due to the ordering of categories in the point-multiserial is not correctable.

A description is given of diagrams (available separately) for computing tetrachoric correlation coefficients. The diagrams are entered with “per cent of combined groups above dividing point” and difference between groups in their per cents above the dividing point.

A new method of test selection, which attempts to combine the merits of the Toops L-Method with those of the Wherry-Doolittle Method, is presented. It results in integral (unit if desired) positive and/or negative (optional) weights. This flexibility makes the method applicable to all kinds of material and for both selecting items for tests and tests for batteries. An explicit solution of one test construction problem is presented. Necessary changes in method for the solution of five other types of test construction problem are presented. A few cautions are provided for potential users.

Correlation data on nine reading tests originally analyzed by Frederick B. Davis by the principal axes method are reanalyzed by Spearman's uni-dimensional method. It is concluded that a single common factor (reading ability) accounts for the correlations among the tests with residuals remarkably small in view of the fact that the tests were designed to test nine supposedly different skills. Three of the tests showed additional specific variance not attributable to the common factor.