A model of individual differences in pair comparisons is developed, assuming the affective values to have a quasi-simplex structure. Procedures for fitting the model to data are suggested. An empirical example is given for one of the procedures.

Experiments in short-term memory usually collect binary data and pool the results of several subjects. The observed pooled proportion of recall is then transformed by the angular transformation to stabilize the variance. In this paper the variance of the transformed proportion is derived and a simple test statistic is obtained to check the validity of the binomial model. Some numerical comparisons for selected poolings are made.

A theorem is presented relating the squared multiple correlation of each measure in a battery with the other measures to the unique generalized inverse of the correlation matrix. This theorem is independent of the rank of the correlation matrix and may be utilized for singular correlation matrices. A coefficient is presented which indicates whether the squared multiple correlation is unity or not. Note that not all measures necessarily have unit squared multiple correlations with the other measures when the correlation matrix is singular. Some suggestions for computations are given for simultaneous determination of squared multiple correlations for all measures.

The rank test Rn of Cronholm and Revusky [1965] in effect doubles the number of comparisons carried out in the Mann-Whitney test between “Treated” and “Control” subjects chosen from a single group of n and triples the asymptotic Pitman efficiency against shift alternatives by using a series of n – 1 subexperiments. However, the full series can be too costly or time-consuming. It is shown that j appropriately chosen subexperiments will permit one to make at least j/(j + 1) of the number of comparisons possible under Rn, with large sample efficiency of j/(j + 2) relative to Rn against shift alternatives and small sample efficiency greater than that, j = 2, 3, …, n − 2. The resulting test criterion is a sum of j independent Mann-Whitney test statistics. Its null distribution is tabulated for n ≤ 10 and small sample efficiency comparisons are carried out for n = 10.

The asymptotic distributions of response probabilities in the Audley-Jonckheere learning model, as applied to the two-choice learning situation, are described for (1) the experimenter-controlled events model, (2) the subject-controlled events model, and (3) the experimenter-subject-controlled events model.

It seems intuitively compelling to many investigators that measurements, on the same subjects by different methods, purportedly of the same given trait are somehow better evidenced to be mutually valid measurements of that trait to the degree that they are intercorrelated. It is similarly compelling that measurements on the same subjects of purportedly different and uncorrelated traits are somehow better evidenced to be valid measurements to the degree that they are not intercorrelated. Further, a demonstration of hetero-method mono-trait intercorrelation (convergence) jointly with one of hetero-method, or preferably mono-method, hetero-trait independence (discrimination) is more compelling than either single demonstration alone [see Campbell & Fiske, 1959]. I hope to show in what follows that this intuition is misleading unless certain rather demanding prerequisites are satisfied. Then I hope to show that contrary demonstrations are generally too indecisive to consitute validity disconfirmations. Finally, I shall consider some issues in the practical use of the indecisive multitrait-multimethod data.

The “longitudinal factor analysis” model, which uniquely resolves factors from two occasions of data representing the same persons measured on the same test battery, is shown to be derivable by application of canonical correlation procedures to factor scores. Interpreted in this light, it is suggested that, in attaining its objective, “longitudinal factor analysis” maximizes temporal stability of factor scores—an emphasis which may be warranted for some types of change but not for others.

Given the complete set R of rank orders derived from some configuration of n stimulus points in r dimensions in accordance with the unfolding model, a stimulus configuration which generates just these orders will be described as a solution for R. The space is assumed to be Euclidean. Necessary and sufficient conditions are determined for a nondegenerate configuration to be a solution for R. The geometrical conditions which are necessary and sufficient to determine the subset of pairs of opposite orders are also identified and constitute the constraint system for the ordinal vector model.