This paper explores certain problems which arise within the context of the theory of generalizability put forward by Cornbach, Rajaratnam, and Gleser. In particular, a formal explication of their theory for the single observation is given, and the various coefficients of generalizability which they define are related to the estimation of universe scores.

A least squares method for approximating a given symmetric matrix B by another matrix B which is orthogonally similar to a second given matrix A is derived and then generalized to nonsymmetric (but square) A and B. A possible application to ordering problems is discussed.

Usually, an iterative procedure based on two-dimensional rotations is employed to find the varimax solution in factor analysis. A matrix is given where this procedure does not yield the maximum value of the varimax criterion. However, random orthogonal transformations of some matrices and subsequent varimax-rotation using the iterative procedure seem to indicate that usually no local maxima exist.

This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essentially a two-way analysis of variance model which requires that the matrix of interaction parameters be decomposed by using factor analytic techniques. Problems of judging statistical significance are discussed; and an illustrative example is presented.

Ogilvie and Creelman have recently attempted to develop maximum likelihood estimates of the parameters of signal-detection theory from the data of yes-no ROC curves. Their method involved the assumption of a logistic distribution rather than the normal distribution in order to make the mathematics more tractable. The present paper presents a method of obtaining maximum likelihood estimates of these parameters using the assumption of underlying normal distributions.