The proposal is made to consider a paired-associate item as becoming conditioned to its correct response in all-or-none fashion, and that prior to this conditioning event the subject guesses responses at random to an unlearned item. These simple assumptions enable the derivation of an extensive number of predictions about paired-associate learning. The predictions compare very favorably with the results of an experiment discussed below.

A modification of stimulus sampling theory is presented. The restriction that each stimulus element is conditioned to one and only one response is replaced with the notion of a scale of conditioning for each element. This variation provides a context in which such variables as reward magnitude and motivation can be viewed as determiners of behavior. Some experimental results on multiple response problems also have a natural interpretation in terms of these ideas.

A theory of cue learning, which gives rise to a system of recurrent events in Feller's sense, is analyzed mathematically. The distribution of total errors and sampling distribution of mean errors are derived, and the learning curve is investigated. Maximum likelihood estimates of parameters and sampling variances of those estimates are derived. Likelihood ratio tests of the usual null hypotheses and approximate tests of goodness of fit of substantive hypotheses are developed. The distinguishing characteristic of these tests is that they are concerned with meaningful parameters of the learning process.

Experimenters in psychology frequently investigate the relationship between two variables by selecting extreme groups on the first measure and comparing their mean scores on the second. This paper considers the efficacy of this procedure from the criterion of the power of the statistical tests. Optimal cutting points for the extreme groups are defined, and the power of the difference approach is compared to that of significance tests for the productmoment correlation coefficient.

Factorial transformation is viewed as an estimation problem in which the usual assumption of homogeneously distributed error cannot be applied, but may be replaced by a principle of maximum kurtosis. This leads to quartimax in the orthogonal case, and to “oblimax” in the oblique case. Oblimax is readily programmable, and typically provides results similar to those of subjective rotation. However, oblimax may encounter special difficulty in data which do not determine a simple structure, or which have been imprecisely factored.

A method is proposed whereby the distribution of stimuli and subjects can be derived directly from the subjects' rankings of the stimuli. The solution for four stimuli is presented with examples and suggestions for the solution of problems involving more stimuli. The model is intuitively attractive and is likely to prove useful when direct solutions for larger number of stimuli are available.

Probability matching is shown to be a property of a broad class of models of binary choice behavior.