A method of pattern analysis is presented for the case of dichotomous items and a quantitative criterion. This “configural scale” has maximum validity in the least squares sense. A technique for computing the configural scale as a polynomial function of the item scores is given. Tests of significance are outlined for such questions as: Is there a linear or non-linear relation between the quantitative criterion and the item scores? Does the addition of certain items to the test increase the validity of the configural scale? Are all the items in the configural scale fully effective?

A method is presented for converting the scores on one form of a test to those on another form of the same test. The method is particularly applicable to the case where each form has been administered to a different group and the only link between the two forms is a subset of items common to both. The proposed method, called the item method of conversion, has been applied to several tests for which other methods of conversion are available for comparison. The necessary data are limited to tests for which the total score is the criterion for item analyses. The method gives highly satisfactory results for all the tests to which it has been applied, particularly when the two groups are rather different, in which case the delta method (a different item method) is inappropriate.

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.

When an information processing system is faced with an excess of input information the task of selecting the items which are to get immediate processing is frequently assigned to a human being. A quantitative measure of the extent to which a man avoids random activity during such filtering operations is derived in terms of two parameters (normalized overload and correct proportion of selections) which are determined from experimentally available quantities. This coherence measure may be used for studies of random behavior, comparison of rules for selecting items, and perhaps prediction of human performance at filtering tasks.

An expression for the expected variance of the sampling errors for the validities of a set of correlated items that is computationally feasible when the number of items is large is developed. Since the item difficulties are assumed to be constant, the estimate must be applied to pools or sub-pools of items reasonably homogeneous with respect to difficulty.

This study reveals the usefulness of multiple correlation techniques in estimating the relative importance of different aspects of a tracking task in the operator's tracking behavior. The technique is applied to a compensatory tracking task with a position control.

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.

In contrast to Thurstone's Law of Comparative Judgment, a model in which a comparison pair and its complement are assumed to give rise to two different distributions of differences is considered. The consequences of this revised model on scaling problems is developed.

A method of rotating a set of orthogonal axes into a reference frame on which loadings are as nearly proportional to a predetermined set of weights as possible is presented. The method, an approximate algebraic solution, often requires some additional graphical refinement but eliminates most of the rotations involved in usual graphical solutions. Its primary value is speed and ease of calculation, involving only one matrix multiplication and solution of a simple formula to determine the rotation cosines.

For the purpose of extracting factors from matrices, it is proved that a certain formula is both necessary and sufficient. In factor analysis, the formula may be applied either to the correlation matrix, or directly to the score matrix (assuming the communality problem is solved). As many factors as desired can be extracted in one operation. Having such a compact formulation is useful for teaching as well as computing purposes, since it includes all techniques of factor extraction as special cases.

A formula is developed for measuring the gambling response-set or utility for risk in objective tests in which the testees are apprised of the application of a correction for guessing. Some implications of this measure for test theory and construction are discussed briefly.

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.

The use of binomial coefficients in place of factorials to shorten the calculation of exact probabilities for 2 × 2 and 2 × r contingency tables is discussed. A useful set of inequalities for estimating the cumulative probabilities in the tail of the distribution from the probability of a single table is given. A table of binomial coefficients with four significant places and n through 60 is provided.

A simplified re-derivation of the formula underlying the rule is presented, followed by a derivation of the comparable rule for the unitrectangular distribution, which turns out to be a 33-per cent rule. Critical comments are offered concerning two assumptions: normality of the score distribution and equality of mean standard errors of measurement in the high and low groups.

A model for the acquisition of responses in an anticipatory rote serial learning situation is presented. The model is developed in detail for the case of a long intertrial interval and employed to fit data where the list length is varied from 8 to 18 words. Application of the model to the case of a short intertrial interval is considered; some predictions are derived and checked against experimental data.

The tau coefficient is defined, and a computational procedure for tied ranks is described. The procedure maintains continuous computational checks, saves labor, and particularly facilitates the use of tau with large samples. It is also shown how tau correlation may be applied to Q-sorts with any shape of forced distribution or with unforced distributions.

By interchanging persons and items, iterative inverse factor analysis provides a relatively inexpensive way of clustering persons according to their patterns of response to the items. In addition to permitting the clustering of large numbers of persons, the technique enables one to determine the bases for such clustering. The items of behavior used can be heterogeneous in content and form.