Problems in applying the analysis of variance are discussed. Emphasis is placed on using the technique to understand the data. The scale of the dependent variable is important for the analysis. Crossed and nested categories must be recognized. The error terms in the analysis depend on whether the classes of each independent variable are (1) all out of a few or (2) a few out of many. To simplify the analysis, mean squares should be aggregated with their error term when they are less than twice its size. An illustrative example is discussed in detail.

The varimax solution for Thurstone's classic Primary Mental Abilities study is presented. Comparisons between the factors of Thurstone's original subjectively rotated factor pattern, Zimmerman's subjectively revised solution, Wrigley, Saunders, and Neuhaus' quartimax results, and the present varimax factor matrix are made by finding correlations between factors defined by these four solutions. It is pointed out that any possible ultimate merit of the varimax solution should be based on its psychological meaningfulness and on the rationale of the varimax criterion—not on its relationship to the other studies.

A quantitative model for the behavior of albino rats in choice-making situations is presented. The model, which is based upon a cognitive conceptualization of the learning process, is shown to yield predictions which are equivalent to those produced by the linear operator stochastic models at the asymptotic limit but which differ from these during early trials in the learning situation.

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically into n/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomes n/2 is contradictory to Guttman's contention that the minimal rank is n − 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.

Some extensions of the existing determinantal methods for solving the accounting equations in latent class analysis are presented. These extensions cover more cases than previous methods, give rise to new sufficient conditions for identifiability of the latent class model, and give insight into the necessity of various sufficient conditions for identifiability. These implications to the identifiability problem are discussed.

A modification of the quartimax computation for factor rotation is described in which a hypothesized factor pattern is given to the machine along with the data. The machine uses the pattern to select the subset of variables to which it will attend when rotating in a given plane, in order to find an orthogonal solution which closely fits the hypothesis. The program also provides a measure of the goodness of this fit. The program can utilize pattern matrices that reflect only partial hypotheses as to the nature of the factors, as well as those that specify highly determined simple structure.

Deuel's rotational method for factor analysis is translated from vector algebra to matrix algebra. A computational example is presented using Deuel's nomogram.