The basic models of signal detection theory involve the parametric measure, d′, generally interpreted as a detectability index. Given two observers, one might wish to know whether their detectability indices are equal or unequal. Gourevitch and Galanter (1967) proposed a large sample statistical test that could be used to test the hypothesis of equal d′ values. In this paper, their large two sample test is extended to a K-sample detection test. If the null hypothesis d1′ = d2′ = ... = dK′ is rejected, one can employ the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences. In addition, it is shown how one can use the Gourevitch and Galanter statistics to test d′ = 0 for a single individual.

A method is introduced for oblique rotation to a pattern target matrix specified in advance. The target matrix may have all or only some of its elements specified. Values are estimated by means of a general procedure for minimization with equality constraints. Results are shown using data from Harman and Browne.

A model is presented for factor analysing scores on a set of psychological tests administered as both pre- and postmeasures in a study of change. The model assumes that the same factors underlie the tests on each occasion, but that factor scores as well as factor loadings may change between occasions. Factors are defined to be orthogonal between as well as within occasions. A two-stage least squares procedure for fitting the model is described, and generally provides a unique rotation solution for the factors on each occasion.

If the discriminal distributions of signal-detectability theory evolve in time according to a normal Markov process, they can be characterized by Brownian motion generalized with a constant bias determined by signal strength. If the process is stopped at the first occurrence of a preset criterion displacement, the resulting latency distribution provides a model for the central component of simple reaction time. Discussed are properties of the distribution which should be useful in obtaining experimental predictions from neural-counting assumptions, and in relating reaction times to basic variables of the theory of signal-detectability.

A least squares method is presented for fitting a given matrix A to another given matrix B under choice of an unknown rotation, an unknown translation, and an unknown central dilation. The procedure may be useful to investigators who wish to compare results obtained with nonmetric scaling techniques across samples or who wish to compare such results with those obtained by conventional factor analytic techniques on the same sample.

For the case of two or more groups of variables (batteries), generalizations on three common factor models, the Equal Residual Variances model, the Image model of Jöreskog, and the Canonical Factor Analysis model, are described and illustrated with empirical examples.

Three methods for selecting a few predictors from the many available are described and compared with respect to shrinkage in cross-validation. From 2 to 6 predictors were selected from the 15 available in 100 samples ranging in size from 25 to 200. An iterative method was found to select predictors with slightly, but consistently, higher cross-validities than the popularly used stepwise method. A gradient method was found to equal the performance of the stepwise method only in the larger samples and for the largest predictor subsets.