A computer program is described that is designed to reconstruct the metric configuration of a set of points in Euclidean space on the basis of essentially nonmetric information about that configuration. A minimum set of Cartesian coordinates for the points is determined when the only available information specifies for each pair of those points—not the distance between them—but some unknown, fixed monotonic function of that distance. The program is proposed as a tool for reductively analyzing several types of psychological data, particularly measures of interstimulus similarity or confusability, by making explicit the multidimensional structure underlying such data.

A statistical model for verbal learning is presented and tested against experimental data. The model describes a Markov process with a realizable absorbing state, allowing complete learning on some finite trial as well as imperfect retention prior to this trial.

A least-squares solution for scaling the variables of a Guttman simplex is developed. The procedure yields a ratio scale, two varieties of interval scale, and orders the variables. A measure of the goodness of fit of the scale to the data is suggested. An example of the application of the method is given. The problem of non-positive correlations is discussed.

The choice model considered by Luce in an earlier work is stated in terms of unobservable parameters. In this paper a consequence of the model, involving only observables, is shown to be equivalent to the model.

A modification of Hotelling’s iteration method of factor analysis is presented which is much more rapid and almost as accurate. At any stage of the approximation for a factor vector its major product moment reduces the rank of the residual matrix by precisely one. Each approximation to an eigenvalue is larger than the preceding one. By observing the decline in these increments one can often stop the iterations at early stages without serious loss. If subsequent rotational procedures are used, the method gives practically the same results as the more exact methods and in a small fraction of the time.

A method for generating sample and population score matrices and sample correlation matrices from a given population correlation matrix is developed. An example giving the desired matrices for a population Guttman simplex correlation matrix is presented.

The Mueller-Urban method of fitting the normal ogive is derived, and the inadequacies of its inherent assumptions are discussed. This and the unweighted least squares method are compared to the maximum likelihood solution which is shown to be very close to the “ideal” least squares solution. As an empirical demonstration of the superiority of the maximum likelihood solution, random ogives are fitted by all three methods and they are compared on the basis of the expected values and the standard errors of the estimates. It is concluded that the maximum likelihood solution is uniformly superior to the others in all respects.

After proving a special case of a theorem stated by Eckart and Young, namely, that an oblique transformation G is the product of two different orthogonal transformations and an intervening diagonal, this note shows that the best fitting orthogonal approximation to G is obtained simply by replacing the intervening diagonal by the identity matrix. This result is shown to be identical with two earlier orthogonalizing procedures when G is of full rank. A multiplicity of solutions is shown for the case of a singular G.

Abacs approximating the product-moment correlation for both explicit and implicit selection are presented. These abacs give accuracy to within .01 of the corresponding analytic estimate.

A general formulation of the latent structure principle is suggested, from which it is possible to derive Lazarsfeld’s accounting equations in their most general form. The basic equations of Gibson’s latent profile model can thence be derived in a single step.