Analysis of variance and uncertainty analysis are analogous techniques for partitioning variability. In both analyses negative interaction terms due to negative covariance terms that appear when non-orthogonal predictor variables are allowed may occur. Uncertainties can be estimated directly from variances if the form of distribution is assumed. The decision as to which of the techniques to use depends partly on the properties of the criterion variable. Only uncertainty analysis may be used with a non-metric criterion. Since uncertainties are dimensionless (using no metric), however, uncertainty analysis has a generality which may make it useful even when variances can be computed.

Four different value laws are developed and tested by using them to predict the scale values of composite stimuli from the scale values of their components. These four laws are: an additive law, a square-root law, a logarithmic, and a negative exponential law. They are tried out on a set of food preferences by means of Pearson's Method of False Position. The negative exponential law of diminishing returns gave the best fit to the data but was not markedly better than any of the other laws.

A procedure is developed for computing optimum regression weights under the restriction that they be non-negative. The weights maximize, subject to the restrictions, the multiple correlation between several predictors and a criterion. A numerical example is provided.

Tables of the exact distributions of number of matches are given for small decks having the same number of cards in each suit. Several approximate distributions are considered for use with larger decks, and some indication of the goodness of the approximations is given.

It is shown that Estes' formula for the asymptotic behavior of a subject under conditions of partial reinforcement can be derived from the assumption that the subject is behaving rationally in a certain game-theoretic sense and attempting to minimax his regret. This result illustrates the need for specifying the frame of reference or set of the subject when using the assumption of rationality to predict his behavior.

At least four approaches have been used to estimate communalities that will leave an observed correlation matrix R Gramian and with minimum rank. It has long been known that the square of the observed multiple-correlation coefficient is a lower bound to any communality of a variable of R. This lower bound actually provides a “best possible” estimate in several senses. Furthermore, under certain conditions basic to the Spearman-Thurstone common-factor theory, the bound must equal the communality in the limit as the number of observed variables increases. Otherwise, this type of theory cannot hold for R.

A formula is developed for the correlation between a ranking (possibly including ties) and a dichotomy, with limits which are always ±1. This formula is shown to be equivalent both to Kendall's τ and Spearman's ρ.

When a new reference vector is chosen graphically from the plane of two old ones, its direction cosines as well as the projections of the tests on it are most easily computed by applying certain multipliers d and Sd to quantities which are already known. The nomogram quickly supplies d, after S has been read from the graph.

A method is provided for estimating the nonspurious correlation of a part of a test with the total test. Two cases are considered: one in which the actual subtest is parallel to the total test, the other in which the actual subtest is not parallel to the total test.

The variance of the number of mutual dyads in a sociometric situation where each member of a group chooses independently and at random is derived for unrestricted numbers of choices per group member, as well as for a fixed number of choices. The distribution of the number of mutuals is considered.