Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space of r dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individual's preference orderings will yield a space of r + 1 dimensions with the original r-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.

This paper studies asymptotic properties of Luce's beta model. Asymptotic results are given for the two-operator and four-operator cases of contingent and noncontingent reinforcement.

Likelihood ratio tests have been proposed by Wilks for testing the hypothesis of equal means, variances, and covariances (Hmvc) and the hypothesis of equal variances and covariances (Hvc) in a p-variate normal distribution. Using exact distributions of the appropriate likelihood ratio statistics, tables of the .05 and .01 points of these distributions are constructed for p = 4, 5, 6, 7 and sample size n = 25 (5) 60 (10) 100. A correction factor is recommended for larger n. Two numerical examples illustrate use of the tables. A nonparametric test is proposed for Hmvc when the multivariate parent population is known to be non-normal.

In the two-choice situation, the Wald sequential probability ratio decision procedure is applied to relate the mean and variance of the decision times, for each alternative separately, to the error rates and the ratio of the frequencies of presentation of the alternatives. For situations involving more than two choices, a fixed sample decision procedure (selection of the alternative with highest likelihood) is examined, and the relation is found between the decision time (or size of sample), the error rate, and the number of alternatives.

A distinction is made between reliability data and decision data. Each of these sets of data may be matched or independent, depending on whether the same instruments (tests, judges, etc.) are applied to every individual in the group or the instruments to be applied to each individual are selected independently for him. Reliability formulas are developed (for both single observations and for composites of k observations) for the case where reliability data are matched but decision data are independent. Formulas previously reported in the literature are inappropriate for this case.

A model for signal detectability suggested by Luce is extended to situations in which the observer is uncertain of some important characteristic of the signal, such as frequency. By making a single assumption concerning the observer's covert response behavior, two solutions are obtained corresponding to qualitatively different behavior. Decrements in detectability and in recognition with uncertainty are shown to be particular functions of discriminability and detectability of the stimuli in other situations. Relevant experimental data are considered.

A matching procedure is proposed by which a judge may use the same items in different matches. The K items in one group most likely to include the correct match with each item in the other are selected. Inclusion of the correct match among the K items chosen is defined as a success. The distribution of the number of successes is discussed. Tables are presented showing the number of successes needed for significance for various values of K and of N, the number of items in each group.

A general critical analysis of the median tests proposed by Wilson for certain analysis of variance hypotheses is presented. Specifically, discrepancies between the purported and actual approximate distributions of some of the test statistics are noted. Validity and power of the resulting tests are discussed.

The weakness in the usual application of the Fisher method of combining probabilities is pointed out and a supplementary method is suggested.