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.

The problem of determining linear functions for two sets of variables so as to maximize the correlation between the two functions has been solved by Hotelling. This article presents a more efficient computational solution for the case of two sets of variables and a generalized solution for any number of sets. Applications are discussed and a numerical example is included to demonstrate the solution for more than two sets.

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.

The selection of one of several stimuli as most similar to a reference stimulus is assumed to satisfy a choice axiom that permits assigning ratio scale values to each variable-reference stimuli pair. The logarithm of this scale is treated as a distance measure, leading to the following testable conclusions about the pairwise choice probabilities as the reference stimulus is varied. First, the plot is a symmetrically truncated ogive with horizontal tails. Second, if two pairs of choice stimuli have the same midpoint, the ogive of one pair is part of the ogive of the other. In terms of this model, the hysteresis and midpoint displacement effects in the method of bisection are discussed, and relations with Coombs' unfolding techniques are explored.

Continuous analogues of the finite linear and stimulus sampling theories are developed for non-determinate reinforcement schedules. Closed-form expressions are derived for the asymptotic response distribution and certain sequential statistics. Computations for a target experiment are given to illustrate the character of the theoretical results.

By virtue of certain modifications in the Law of Comparative Judgment, equations are developed which (i) permit the construction of a joint scale of individuals and items, as in the case of attitude measurement, directly from their pair-comparison preferences, and (ii) take into account the variable of laterality which is significant for the construction of group preference scales.

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.

Two linear operator models are presented for a class of learning situations in which the response is on a numerical scale and the subject is given the magnitude of his error on some or all of the trials. Theoretical expressions are developed for sequential dependencies, mean learning curves, variances, and covariances, which permit a number of tests of goodness of fit.

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.

From a theoretical point of view, paired comparisons and the law of comparative judgment provide an excellent approach to the problem of psychological measurement. However, if a reasonably large number of stimuli are to be investigated, paired comparisons become extremely time-consuming and fatiguing to the subjects. A balanced incomplete block design, requiring multiple rank order judgments for each subject, provides an efficient experimental method for obtaining paired comparisons judgments. Features of the analysis proposed for this design are discussed in detail. A program for the analysis is available for the IBM 650 electronic computer.

Certainly the most interesting tool that science employs in its perpetual pursuit of knowledge is the scientist, with his enthusiasms, egoisms, and prejudices, his inevitable unconscious attitudinal orientation in the consensus of contemporary opinion, which we call the Zeitgeist. One wonders what science would be like if automation could take over completely. Are there mechanical equivalents for jealousy and pride and pigheadedness and insight, and those other interacting personal forces that contribute to contemporary truth in the scientific field?

Fechner never tried to found psychophysics or a new experimental psychology. He was, in his own estimation in those last forty-five years of his life, a philosopher, fighting what he regarded as the crass materialism of his day, the Nachtansicht or “night view,” as he called it, and promoting the faith that mind and soul are the ultimates of reality, the Tagesansicht or “day view.” This favoring of the clear philosophical vision in the day view as opposed to the materialistic darkness of the night view is Fechner’s panpsychism, a faith that seems mystical to most modern scientists, partly because the German word Seele does not distinguish between mind and soul, between that which compares the sensory intensities of two lifted weights and whatever it is that persists after the body’s death.

Note is taken of four related sources of confusion as to the usefulness of Thurstone's factor analysis model and of their resolutions. One resolution uses Tucker's distinction between exploratory and confirmatory analyses. Eight analyses of two sets of data demonstrate the procedures and results of a confirmatory study with statistical tests of some, but not all, relevant hypotheses in an investigation of the stability (invariance) hypothesis. The empirical results provide estimates, as substitutes for unavailable sampling formulations, of effects of variation in diagonal values, in method of factoring, and in samples of cases. Implications of these results are discussed.

Fechner’s work [12] was motivated by an interest in the mind-body problem concentrating particularly upon the question, “What is the relationship between the measurable characteristics of the physical stimulation and the subjective characteristics of the sensations produced?” Some of Fechner’s work was devoted to experiments in areas where the physical measurements that can be made on the object are not functionally related to the psychological characteristics.

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 stochastic model is proposed to account for the behavior of subjects in recognition tasks in which stimuli are presented, one at a time, in a protracted sequence. The basic assumption is that the memory trace resulting from the presentation of a particular stimulus not only fades away during the presentation of subsequent stimuli but also “diffuses” in such a way as to become decreasingly stimulus specific. An account is thereby provided for both (a) the increase in the probability of false recognition with the total number of stimulus presentations and (b) the departure of curves of forgetting from the previously proposed simple exponential decay functions. An expression for the amount of information carried along when the number of stimulus presentations becomes large is then derived for subjects who conform with the model.