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.

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.

The seven analysis-of-variance mean squares for an unreplicated three-way classification may be written as linear combinations of a mean variance and three mean covariances. Formulas are presented for computing the mean variances and mean covariances from linear combinations of mean squares. The relevance of these formulas for assessing rater biases and trait independence is discussed, a numerical example is provided, and proposed extensions are briefly noted.

The appearance of a statistical paper in a symposium honoring the founding of psychophysies was surely to have been expected. These two disciplines had their modern beginnings in about the same period of time and the well-known founders of each made at least some contributions in the other. Karl Pearson’s research on the personal equation is still a good example of painstaking psychophysical experimentation. Indeed much of his statistical reputation rests on techniques he developed to analyze this data. Fifty years ago Urban published, in a psychological journal, the final form of the Müller-Urban weights. Twenty years later biologists rediscovered Urban’s weights and now use them routinely. Spearman, too, contributed to both fields.

The occasion of a symposium to honor Fechner on the centennial of the publication of his Elemente der Psychophysik (1] has provided an excuse to review the Fechnerian legacy and to ask what perversity in the nature of science or the Zeitgeist has made it possible for Fechner’s concept of error to persist for a hundred years and grow famous. The central feature of this legacy is the notion that the jnd (just noticeable difference) can serve as a unit for the measurement of sensation. Since the jnd is really a measure of the uncertainty, dispersion, or variability among a set of judgments, this proposition makes residual “noise” the yardstick of sensory magnitude–a notion as curious as it seems improbable. Why did this conception survive its inventor, and why did it become, under Thurstone's expert guidance, the foundation of psychological measurement applied to subjective values and attitudes? Thurstone’s Case V in which he assumes equal discriminal dispersions (equal subjective variabilities) matches in effect the Fechnerian assumption that all jnds are subjectively equal.

Within the model of isotonic space, a principle is presented which generalizes the unfolding technique to the multidimensional case. The availability of exhaustive configurational solutions given complete data is pointed out. Finally three criteria are suggested for the choice of a particular solution from among the set of all solutions, which are applicable in the case either of complete or incomplete data.

This paper describes a relationship between the variance-covariance matrix of test items and Woodbury's concept of the standard length of a test. An index of item-test relationship is described in standard length terms. The sum of these indices for the items in a test is equal to the square of Jackson's coefficient of sensitivity.

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

Maximum likelihood estimates of item parameters of a scholastic aptitude test were computed using the normal and logistic models. The goodness of fit of ogives specified by the pairs of item parameters to the observed data was determined for all items. While negligible differences in the limen values were found, differences in item discrimination indices indicated that interpretation of these indices requires separate frames of reference. The empirical results showed the logistic model to be a useful alternative to the normal model in item analysis.

A cosine function is suggested to approximate the normal distribution as a device for simplifying algebraic manipulations of the latter. Numerical evaluations remain straightforward and employ only the commonly available trigonometric tables. A method of visual curve fitting requiring only an oscilloscope is also described.

We are gathered today to commemorate the completion of the first quarter of a century of the Society’s history, and I consider it no small honor to have been selected to address this distinguished group on this memorable occasion. When Dr. Charles Wrigley, Chairman of the Program Committee, extended the invitation, he expressed the hope that I would review the history of the formation of the Society and discuss something of its achievements to date. Today I shall only highlight the early history of the organization, since in my Presidential Address in September 1941 a rather full history was presented.

Several types of new developments in statistical behavior theory deserve attention: (i) attempts at relatively direct empirical tests of basic axioms; (ii) the application of models that survive these tests for purposes of data reduction and analysis; (iii) the extension of extant models, or elaborations of them, to new empirical problems; and (iv) the introduction of new models based primarily on abstract mathematical considerations. The last two of these “new developments” have been well represented in recent books [3, 11]; the first two will be illustrated in the following sections.