The problem of choosing the correct additive constant to convert relative interstimulus distances to absolute interstimulus distances in multidimensional scaling is investigated. An artificial numerical example is constructed, and various trial values of the constant are inserted to demonstrate the effect on the multidimensional map of making a variety of incorrect choices. Finally, a general solution to the problem, suggested by Dr. Ledyard R Tucker, is presented; each of the computational steps in this solution is set down for easy reference.

A technique is presented for obtaining a rapid estimate of reliability between judges, with special reference to qualitative judgments. It is shown that reliability and discrimination are independent and that estimates of both are needed. A method of obtaining an independent estimate of multi-judge discrimination is developed. It is shown that the size of item-samples is specified by the latter method. Tests of significance for both reliability and discrimination are described.

Speeded and unspeeded tests of vocabulary, spatial relations, and arithmetic reasoning were factorially analyzed, together with certain reference tests and academic grades. Lawley's maximum likelihood method was used, the computations being carried out on the Whirlwind electronic computer. Four different speed factors were isolated, together with a second-order general speed factor. Consistent small positive correlations between the academic grades and the speed factors were found.

For the case of a single criterion a method is already available for determining the optimal distribution of testing time for a battery of predictors, assuming that intercorrelation, validity, and reliability data are available for predictors of arbitrary lengths. In this article a modification and generalization of the method is presented for the case of differential prediction involving a number of criterion variables. A numerical example is given to illustrate the method, after which the mathematical rationale is outlined.

A method of estimating the regression of gains upon initial scores is suggested and compared with two other methods which have been used in recent investigations.

A method of Guttman scalogram analysis is presented that does not involve sorting and rearranging the entries in the item response matrix. The method requires dichotomous items. Formulas are presented for estimating the reproducibility of the scale and estimating the expected value of the chance reproducibility. An index of consistency is suggested for evaluating the reproducibility. An illustrative example is presented in detail. The logical basis of the method is discussed. Finally, several methods are suggested for dealing with non-dichotomous items.

A method for computing the transformation matrix for Carroll's analytic simple structure (1) is presented. The procedure involves successively finding the smallest latent root and associated vector of symmetric matrices.