A distinction is drawn between the method of principal components developed by Hotelling and the common factor analysis discussed in psychological literature both from the point of view of stochastic models involved and problems of statistical inference. The appropriate statistical techniques are briefly reviewed in the first case and detailed in the second. A new method of analysis called the canonical factor analysis, explaining the correlations between rather than the variances of the measurements, is developed. This analysis furnishes one out of a number of possible solutions to the maximum likelihood equations of Lawley. It admits an iterative procedure for estimating the factor loadings and also for constructing the likelihood criterion useful in testing a specified hypothesis on the number of factors and in determining a lower confidence limit to the number of factors.

New formulas are developed to give lower bounds to the reliability of a test, whether or not all respondents attempt all items. The formulas apply in particular, then, to completed tests, pure speed tests, pure power tests, and any mixture of speed and power. For the case of completed tests, the formulas give the same answer as certain standard ones; for noncompleted tests the formulas give a correct answer where previous standard formulas are inappropriate. The formulas hold both in the sense of retest reliability and of parallel tests.

It is postulated that occurrence of a conditioned response depends on recurrence of one of a finite number of specific vigilance reactions. Number of trial on which a conditioned response occurs is shown to be a sufficient statistic for estimating the number of such vigilance reactions. The hypothesis is tested by noting whether numbers of trials on which conditioned responses occur fall within confidence intervals determined on the basis of a selected sufficient statistic. Applications of the model to psychological research are suggested.

A study by Shaw (7) some twenty years ago is frequently cited by social scientists to support the generalization that groups are superior to individuals in problem-solving. Shaw suggests that personal interaction within the group is responsible for the superior performance of groups. This article re-examines her data in the light of two models which propose that the difference in quality of solution between group and individual performance is solely a matter of ability. It is shown that Shaw's data may be considered to have been an outcome of behavior postulated by the models. Since Shaw's observations relate to a special population and to special kinds of problems, the proposed models may not be appropriate under differing experimental conditions. In fact, Lorge et al. (4) have indicated that experimental demonstration of the superiority of groups over individuals in problem-solving depends not only on the kind of group but also on the kind of problem to be solved. In addition, the diversity of transfer of training for groups and for individuals is considered.

In principle it is possible to design automata to display any explicitly described behavior. The McCulloch-Pitts “neuron” is a convenient elementary component for the control mechanisms of automata. Previously described techniques permit the design of an automaton which would arbitrarily well simulate human behavior. The difficulty of producing such a design lies primarily in formulating an explicit description of the required behavior. The control mechanism of such an automaton would be of very great logical complexity. Its mode of operation probably would not resemble that of a human brain. The brain is more plausibly represented by stochastic models as proposed by Hebb. Such models can more easily be designed or understood by reason of lesser logical complexity. A method of computational investigation of the functioning of such stochastic models is described. Several extremely simple models have been investigated. One is shown to have properties suggestive of learning ability.