The derivation of multiple and partial regression statistics from uniqueness-augmented factor loadings, presented in the literature for orthogonal factor solutions, is generalized to oblique solutions. A mathematical rationale for the general case, without restriction to uncorrelated factors, is presented. Use of the general formulation is illustrated with a two-factor, seven-variable example.

Implications of random error of measurement for the sensitivity of the F test of differences between means are elaborated. By considering the mathematical models appropriate to design situations involving true and fallible measures, it is shown how measurement error decreases the sensitivity of a test of significance. A method of reducing such loss of sensitivity is described and recommended for general practice.

Consideration is given to determination of parameters of a functional relation between two variables by the means of factor analysis techniques. If the function can be separated into a sum of products of functions of the individual parameters and corresponding functions of the independent variable, particular values of the functions of the parameters and of the functions of the independent variables might be found by factor analysis. Otherwise approximate solutions may be determined. These solutions may represent important results from experimental investigations.

A stochastic process applicable to the learning behavior of an individual subject is discussed. The process describes both the response times and the sequence of choices obtained from a situation involving two alternatives. Parameter estimates and techniques for assessing goodness of fit are considered.

Consistency in paired comparison data is defined. Two types of inconsistency which may arise are defined. Computational formulas for these types of inconsistency are derived, and examples illustrating the use of these formulas are presented.

A method of deriving from the item score matrix all the usual statistics describing the performance on a test of a group of examinees is given. Since this matrix usually is not actually written out, but is implicit in a set of punched cards, a method of working from a more compact matrix F is described. A numerical example is presented. Applications and advantages of the method are cited, as compared with that of recording only the examinees' test scores and the item difficulties.

A disposition index, DI, which provides information about each possible placement to be considered in a personnel classification situation is discussed. The index is readily computed by machine methods and can be used by counselors required to make assignments. The use of the disposition index provides an adequate approximation to optimal solutions obtained by other methods.

A method of studying the problem of correction for guessing and other problems associated with behavior in the test situation is described and an illustrative example presented. As far as the writers are aware this method of approach is novel but, at the same time, it covers many of the practical and theoretical points raised by other writers as reviewed in the introduction.

A method of measuring function fluctuation is suggested and an appropriate test of significance is indicated. The proposed method is compared with bi-factor analysis and with some other suggested methods of measuring function fluctuation.

Derivations are presented relating the length of a test to its weight in a composite. Tests of varying length are constructed so that their weights will be of predetermined magnitudes, and the results compared with expectations. Weighting schemes involving standard deviations of raw scores and of true scores are compared. An important secondary derivation is presented from which it is possible to estimate test reliability knowing only the relative length of a test, its shortened form, and the standard deviation of each.