A model for a score based on an interview is presented which identifies the effect due to the subject, to the manner in which the interviewer tends to conduct his interviews, to the criteria he tends to use in scoring subjects' responses, to the compromises he tends to adopt between the demands of interviewing and those of scoring, and to chance errors. A suggested experimental design calls for each of K investigators to interview a different sample of N subjects, but for all investigators to score each subject. The drawing of inferences when interest is only in the K participants in the reliability study is considered, and a numerical example is given.

Data are reported which show the statistical relation between the sample and population characteristic vectors of correlation matrices with squared multiple correlations as communality estimates. Sampling fluctuations were found to relate only to differences in the square roots of characteristic roots and to sample size. A principle for determining the number of factors to rotate and interpret after rotation is suggested.

A method of estimating the parameters of the normal ogive model for dichotomously scored item-responses by maximum likelihood is demonstrated. Although the procedure requires numerical integration in order to evaluate the likelihood equations, a computer implemented Newton-Raphson solution is shown to be straightforward in other respects. Empirical tests of the procedure show that the resulting estimates are very similar to those based on a conventional analysis of item “difficulties” and first factor loadings obtained from the matrix of tetrachoric correlation coefficients. Problems of testing the fit of the model, and of obtaining invariant parameters are discussed.

A model for direct multidimensional ratio scaling is presented, based on the concepts “common” and “difference” of the “halos” of two percepts. Measures of halos and their differences are proportional to lengths of corresponding percept vectors and their distance in subjective space. Ekman type scaling judgements are assumed to reflect the ratio measure of the common/measure of the standard's halo. The model is supposed to yield results that are in line with the results of distance models of multidimensional ratio scaling since negative scalar products of percept vectors are admitted.

The quartimax and varimax algorithms for orthogonal rotation attempt to maximize particular simplicity criteria by a sequence of two-factor rotations. Derivations of these algorithms have been fairly complex. A simple general theory for obtaining “two factor at a time” algorithms for any polynomial simplicity criteria satisfying a natural symmetry condition is presented. It is shown that the degree of any symmetric criterion must be a multiple of four. A basic fourth degree algorithm, which is applicable to all symmetric fourth degree criteria, is derived and applied using a variety of criteria. When used with the quartimax and varimax criteria the algorithm is mathematically identical to the standard algorithms for these criteria. A basic eighth degree algorithm is also obtained and applied using a variety of eighth degree criteria. In general the problem of writing a basic algorithm for all symmetric criteria of any specified degree reduces to the problem of maximizing a trigonometric polynomial of degree one-fourth that of the criteria.

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 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.

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.