The likelihood-ratio significance test is derived for the hypothesis that after correction for attenuation two variables have a perfect correlation in the population from which the sample is drawn.

Consideration is given mathematical problems arising in two learning theories—one developed by Bush and Mosteller, the other developed by Estes. The theory of Bush and Mosteller leads to a class of Markov processes which have been studied in considerable detail (see [1] and [7]). The Estes model can be treated as a Markov chain, i.e., a Markov process with a finite number of states. For an important class of special cases, it is shown that the Bush-Mosteller model is, in a sense, a limiting form of the Estes model. The limiting probability distributions are derived for the cases treated in both models.

The problem of estimation in the method of successive categories is reconsidered and a new least squares solution is obtained. An empirical comparison of this solution with Gulliksen's solution is presented.

The communality of a variable represents the degree of its generality across n − 1 behaviors. Domain-sampling principles provide a fundamental conception and definition of the communality. This definition may be alternatively stated in eight different ways. Three definitions lead to precise formulas that determine the true value of the communality: (i) from the k necessary and sufficient dimensions derived by iterated factoring, (ii) from the n − 1 remaining variable-domains, and (iii) from k′ multiple clusters of the n variables. Seven definitions provide approximation formulas: (i) one from the k dimensions as initially factored, (ii) one from the n − 1 remaining variables, and (iii) five from a single cluster. Rank of the matrix is not a desiratum in some definitions. Using an example designed by Guilford to illustrate multiple-factor analysis, applications of the formulas based on the three precise definitions recover the true communalities, and five approximation formulas each gives values closer than the ad hoc estimates usually employed in factor analysis.

The proposed quantitative description of maze learning rests on the assumption that two independent processes are involved: (i) a discovery process based on trial-and-error search for the correct response, (ii) a fixation process equivalent to that observed in serial learning. The model leads to predictions that are consistent with the available experimental data. In particular, the number of trials required for fixation is independent of the number of alternatives at each choice point (and hence independent of the number of bits of information contained in each correct response).

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.

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.

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 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.