This paper discusses the item selection problem when the item responses follow a linear multiple factor model. Because of this restrictive assumption, not too unrealistic in situations such as mental testing, it is possible to select optimal sets of items without going through all possible combinations. A method proposed by Elfving to accomplish this is analyzed and then demonstrated through the use of two illustrations. The common and often used procedure of observing the magnitude of the correlation coefficient as an index in item selection is shown to have some merit in the single-factor case.

Beginning with sets of arbitrary elements, concepts of distance and betweenness of sets are defined. Since betweenness as defined is not transitive, an investigation is made of the conditions which ensure desirable regularity. It is found that a straight line or linear array of sets is a generalization of nested sets (Guttman scales). Close relationships among the notions of distance, betweenness, and linear arrays are demonstrated. Parallel and perpendicular arrays, dimensions, and multidimensional spaces are characterized.

The logistic function is proposed as an alternative to the integrated normal function when estimating parameters of test items. The logistic curve is described; an iterative method for finding maximum likelihood estimates of its parameters is given, and an example of its use is presented.

The factor analysis model and Lazarsfeld's latent structure scheme for analyzing dichotomous attributes are derived to show how the latter model avoids three knotty problems in factor analysis: communality estimation, rotation, and curvilinearity. Then the latent structure model is generalized into latent profile analysis for the study of interrelations among quantitative measures. Four latent profile examples are presented and discussed in terms of their limitations and the problems of latent metric and dimensionality thereby raised. The possibility of treating higher order empirical relations in a manner paralleling their various uses in the latent structure model is indicated.

A class of strategies is defined, each member of which possesses a certain plausibility. If a subject follows any strategy in this class in a two-choice learning experiment of the type dealt with by the Estes model, the subject's long-run behavior will be the same as that predicted by the Estes model.

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

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.

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.