The problem of combining abilities of group members to maximize the performance of the group as a whole is examined in terms of redundancy in task assignments. In particular, ways of distributing a given number of items of information among a given number of individuals to obtain the maximum probability of each item being recalled by at least one individual are studied. It is shown that there exists an optimal distribution scheme which is independent of the amount of material originally given, the size of the group, and individual differences in ability.

Two alternative formulas, based upon the analysis of variance, are given for Tryon's general form for the reliability coefficient.

A modification of the Gram-Schmidt process yields an easily constructed orthogonal transformation matrix which may be used to rotate a centroid, principal axis, or maximum likelihood factor matrix in a manner such that one of the new axes has predetermined direction. The procedure is illustrated by rotating a centroid factor matrix into an abbreviated bifactor matrix, the general factor being defined as the centroid of a specified subgroup of reasoning tests.

An exposition of a calculus for empirical classes (CEC), one of the few attempts by logicians to deal with the problem of constructs and indicators, is presented. The CEC provides the groundwork for a formal structure for the situation in which individuals have a degree of membership in various classes rather than having either membership or nonmembership—a situation nearly always true in empirical research. The CEC is presented and its relation to various social science concepts is mentioned. An application of the CEC model to latent structure analysis (LSA) suggests alternatives to the local independence assumption including one called the local scale assumption, which has a close relation to a Guttman scale.

Formulas are given for a descriptive statistic related to the fourfold-point correlation but having always-attainable limits ±1.

Mood's likelihood ratio test is generally considered an unreliable x2 approximation in 2 × 2 contingency tables containing expected cell frequencies less than five. Probability values were computed for 60 such tables as part of an item analysis for two 30-item alternate forms of a measure. The rank orders of the items, from best to worst differentiators, as determined separately by Mood's test and by Fisher's exact test correlated .97 for one form and .96 for the other.

A technique is presented that differs from the previous one in that the use of variance terms is eliminated from the computations; thus some formulas are simplified. A rationale for the improved method is presented.

The K-R (21) formula can be derived without recourse to the undesirable assumption that the test items are all indistinguishable.

Two nomographs are presented for estimating item validity indices identical in value to those obtained from Flanagan 's table and to those obtained from Davis' chart. Experience has shown that the use of the nomographs results in the saving of a significant amount of time with no loss in accuracy. The nomographs also provide a method of quick conversion between the familiar coefficients and the Davis indices, which are less familiar but which offer greater flexibility.

There are occasions in psychological research where it is desirable to have available sets of variables with arbitrary intercorrelations. A quite simple procedure is described for generating pairs of such variables.

The Tryon-Kaiser solution for the communalities is reviewed. Numerical investigation suggests that the procedure is applicable if and only if the correlation matrix has unique minimum rank communalities. This implies that this approach to the communality problem is not general enough to be of practical use.

When scaling a large number of stimuli from comparative judgments, considerable savings in time and labor may be realized if stimuli are presented in triad form rather than in pairs. If, for N stimuli, the proper configuration of triads can be assembled so that all possible pairs appear once, the paired judgment matrix may be reproduced with one-third fewer judgments and two-thirds fewer presentations than would be required with complete pairing. A simple procedure is described for enumerating triad configurations for which N is an odd multiple of three.