Investigation of the effects of a series of treatment conditions upon some social behaviors may require observation of a set of subjects which have been mutually paired, in round-robin fashion. Data arising from such experiments are difficult to analyze, partly because they do not fit neatly into standard designs. A paired compositions scaling model due to Bechtel is adapted to provide a linear model for such round-robin experiments. Both fixed and mixed versions of the model are considered and some results of a Monte Carlo study of the mixed model are reported. The model is applied to illustrative data from the field of physiological psychology.

A model is proposed for the description of ordinal test scores based on the definition of true score as expected rank. Derivations from the model are compared with results from clasiscal test theory as developed by Lord and Novick, in particular with respect to parallel tests and composites. An unbiased estimator of population true score from sample data is derived and its variance is shown to decrease with increasing sample size. Population reliability is shown to be analytically related to expected sample reliability, and methods of reliability estimation are discussed.

A selection of statistical problems commonly encountered in psychological or psychiatric research concerning correlation coefficients are re-evaluated in the light of recently developed simplifications in the forms of the distribution theory of the intraclass correlation coefficient (exact theory), of the product-moment correlation coefficient and of the Spearman rank correlation coefficient (approximate).

The theoretical and practical importance of a double undertaking is discussed: the development of learning and transfer taxonomies with psychometric relevance and the building of psychometric classificatory systems with implications for learning and instruction. Psychometric classifications of human performances are most often based on the covariation of individual differences. The model presented justifies the expectation that the transfer from learning one task to learning another is linearly dependent on the coefficient of intercorrelation between the two tasks when the coefficient is corrected for attenuation. Two studies so far have explicitly confirmed the main deductions from this model. Contrary to the predictions, however, the regression curves yielded negative intercepts. Two empirically testable explanations are offered, one of which would be in full accordance with the model, while the other would call for a further assumption.

A Bayesian procedure is given for estimation in unrestricted common factor analysis. A choice of the form of the prior distribution is justified. It is shown empirically that the procedure achieves its objective of avoiding inadmissible estimates of unique variances, and is reasonably insensitive to certain variations in the shape of the prior distribution.

This brief report provides a comparison of the Z-variance and Box-Scheffé tests for homogeneity of variance. Both procedures are relatively simple to perform and both may be readily utilized in complex, multifactor designs. The Z-variance test is not robust against non-normality; the Box-Scheffé test is robust against non-normality but is not nearly as powerful as the Z-variance test.

A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. The major characteristics of this approach are: (i) it does not require any grid refinement; (ii) the entire process of computation quickly converges to the acceptable level of accuracy, and (iii) the method employs specific sets of mesh points for specific variables, whereby it reduces the number of variables for the separable programming technique. Numerical examples were provided to illustrate the procedure.

It is argued that (1) the halo-model of Micko is probably too restrictive to fit empirical data, (2) the model misrepresents unrelated percepts as bipolar structures, (3) all variations will probably be interpreted as qualitative, (4) the model requires all dimensions to be bipolar, (5) interpretations of orthogonality of factors and of factor loadings become problematic, (6) the halo may be regarded as a sort of “surface variation,” (7) the common part of two percepts is inadequately defined, and (8) the opposite part of two percepts is neglected.

In some situations where reliability must be estimated it is impossible to divide the measuring instrument into more than two separately scoreable parts. When this is the case, the parts may be homogeneous in content but clearly unequal in length. The resultant scores will not be essentially τ-equivalent, and hence total test reliability cannot be satisfactorily estimated via Cronbach's coefficient alpha. Limitation on the number of parts rules out Kristof's three-part approach. A technique is developed for estimating reliability in such situations. The approach is shown to function very well when applied to five achievement tests.

The relationship between variables in applied and experimental research is often investigated by the use of extreme (i.e., upper and lower) groups. Earlier analytical work has demonstrated that the extreme groups procedure is more powerful than the standard correlational approach for some values of the correlation and extreme group size. The present article provides methods for using the covariance information that is usually discarded in the classical extreme groups approach. Essentially, then, the new procedure combines the extreme groups approach and the correlational approach. Consequently, it includes the advantages of each and is shown to be more powerful than either approach used alone.

Frender and Doubilet suggest that Bousfield’s ratio of repetitions (RR) is the best measure of clustering in free recall presently available. Conditioning only on the number of words recalled, they determine the mean of RR in the absence of clustering. In this note the null variance of RR is presented. This permits development of conservative significance tests based on the Cramér inequality.