Some of the methodologies that have become standard tools in psychometrics suffer from neglect. They are taken too much for granted and are not given the attention that seems appropriate to the important role they play in research advances. I propose to make some suggestions which may, in a modest way, assist in alleviating this difficulty. In a very general way I would like to suggest that effort expended in examining a variety of restatements of a methodological problem may lead to new methodologies of real value.

The concepts of differential prediction and multiple absolute prediction were developed in earlier papers [2, 3]. Methods for determining optimal distribution of testing time for each type of prediction are available [4, 5] and are appropriate for use provided that no altered time allotment approaches zero. In this article the methods developed in [4, 5] are extended to include cases where the altered time allotment for one or more tests may approach zero. The procedures developed are illustrated by numerical examples, after which the mathematical rationales are provided.

A mathematical model is developed in an attempt to relate errors in multiple stimulus-response situations to psychological inter-stimulus and inter response distances. The fundamental assumptions are (a) that the stimulus and response confusions go on independently of each other, (b) that the probability of a stimulus confusion is an exponential decay function of the psychological distance between the stimuli, and (c) that the probability of a response confusion is an exponential decay function of the psychological distance between the responses. The problem of the operational definition of psychological distance is considered in some detail.

For continuous distributions associated with dichotomous item scores, the proportion of common-factor variance in the test, H2, may be expressed as a function of intercorrelations among items. H2 is somewhat larger than the coefficient a except when the items have only one common factor and its loadings are restricted in value. The dichotomous item scores themselves are shown not to have a factor structure, precluding direct interpretation of the Kuder-Richardson coefficient, rK-R, in terms of factorial properties. The value of rK-R is equal to that of a coefficient of equivalence, H2Φ, when the mean item variance associated with common factors equals the mean interitem covariance. An empirical study with synthetic test data from populations of varying factorial structure showed that the four parameters mentioned may be adequately estimated from dichotomous data.

A method based on configural analysis has been given whereby test scoring techniques can be evaluated to see if they have optimal validity. Configural analysis has also been used to show how three well known item scoring techniques, multiple regression, total score, and multiple cut-off, imply (for optimal validity) certain conditions on the answer pattern means. The method is illustrated by a worked example.

A model is proposed to predict the performance on a compound stimulus as a function of the performance on the component stimuli in a two-choice situation. Data from a learning task are used to evaluate the model.

Using two distinct models, several formulas for obtaining separate set and content components of a test score have been derived. Comparisons among the methods are made algebraically and through their application to a set of test data apparently affected by response sets.

A number of methods for increasing test homogeneity by item selection are discussed. Exact selection conditions which will maximize obtained homogeneity as measured by KR - 20 and KR - 21 are derived, and an application is given. Since they require only item count data, the selection conditions are economical to apply.