This paper is a presentation of an essential part of the sampling theory of the error variance and the standard error of measurement. An experimental assumption is that several equivalent tests with equal variances are available. These may be either final forms of the same test or obtained by dividing one test into several parts. The simple model of independent and normally distributed errors of measurement with zero mean is employed. No assumption is made about the form of the distributions of true and observed scores. This implies unrestricted freedom in defining the population. First, maximum-likelihood estimators of the error variance and the standard error of measurement are obtained, their sampling distributions given, and their properties investigated. Then unbiased estimators are defined and their distributions derived. The accuracy of estimation is given special consideration from various points of view. Next, rigorous statistical tests are developed to test hypotheses about error variances on the basis of one and two samples. Also the construction of confidence intervals is treated. Finally, Bartlett's test of homogeneity of variances is used to provide a multi-sample test of equality of error variances.

A general formulation of the power law is presented which has two special features: (1) negative exponents are admissible; and (2) the log law is a special limiting case. Estimation procedures, which provide joint estimates of the exponent and the absolute threshold, are derived for the direct ratio scaling methods. A solution is provided for the averaging problem for ratio production and bisection scaling, two methods generating observations on the physical scale, and Monte Carlo methods are used to evaluate the resulting estimators.

The defects of the least-squares or multiple-regression equation approach to estimating orthogonal factors are discussed and transformations of the beta weights are derived which remove these defects with minimum loss in correlations between estimators and true factor scores.

A set of definitions leading to an axiom set which makes possible distinction between two or more forms of lexicographic choice is offered. It is shown that, by treating value as quantized and only taking a finite number of levels for each attribute of a multi-attribute choice situation, lexicographic evaluation might be subsumed under more familiar forms of choice model. Special cases and implications are discussed.

Improved estimation procedures are suggested and a more complete distribution theory is presented for Restle's Cue Learning Model.

The problem of detecting emergent social structure in small groups is examined in terms of establishing a baseline or expected structure. The standard proposed here is equalitarianism; that is to say, every member is equally likely to interact with every other member. Using information theory, a formal statement of the equalitarian argument is possible. In addition to detecting a deviation by a single group, the structural tendency of several groups assigned to some experimental condition is discussed. This technique is designed for the preliminary analysis of structure; it deals only with the general character of the total structure.

Solutions for simple structure obtained from empirical data through the use of the Oblimax, Quartimax, and Varimax procedures are matched with independently determined graphic solutions for the same data. The relative merits of the two analytic orthogonal solutions (Quartimax and Varimax) are discussed. Factors of employee morale are interpreted.

The biserial correlation between an item and the total test of which the item is a part tends to be misleadingly high when used in item analysis, since the item is included in the total test. Two formulas with correction for this overlap are derived and compared with Zubin's and Guilford's formulas. One of the new coefficients is invariant to test length.