Hypotheses presented in a previous paper conceive of an individual's position on an attitude scale as represented by a mean position (status score) and a sigma (dispersion score). The testing of these hypotheses requires a determination of these two scores for each individual. A rationale is presented here for the determination of these two scores for an individual from his forced choice responses to pairs of items of nearly equal scale value.

On the basis of the assumption that distributions of scores on psychological functions are generated by a finite number of equally probable factors, a method is presented which yields the number of factors and their probability p. The statistics β1 and β2 are used for this purpose. An experiment utilizing a code-transcription test is described in which the method was employed to analyze performance at several stages in the learning process. n was found to be 10 for the first 2 minutes of practice and 19 for the second 2 minutes. For the third, fourth, and fifth 2-minute periods, no value could be obtained owing to the pronounced leptokurtosis of the distributions. The first 3 periods of practice, when lumped together, gave an n of 33. It is suggested that the method offers a means of comparing the variability and “complexity” of otherwise non-comparable psychological functions. The use of the method as an instrument of investigation in the field of factor analysis is described.

A method of computing ΣX, ΣX2, ΣXY and higher moments on IBM equipment is described. The basic method is that of successively summary punching, collating a variable number of blank cards behind these summary cards, gang-punching the data from the summary cards into the blank cards, and totalling the entries on these summary cards. The method appears to have several advantages over those previously described, especially if coded data are used.

Professor Godfrey Thomson, in a communication to this laboratory, has drawn our attention to certain computational and editorial errors in a recent publication on the effects of selection in factor analysis. The purpose of this note is to rectify these errors. In so doing, we wish to express our gratitude to Professor Thomson for preventing their prepetuation.

Since the particular tables under consideration appear also in Chapter XIX, “The Effects of Selection,” of and are identical with those of, the material presented in this note is equally applicable to both publications. These tables were numbered identically in both and may be referred to non-differentially. In order to facilitate the exposition in this note, the numbers assigned to each of the corrected tables and figure correspond to the analogous tables and figure of the original publications.

There appears to be a gap in published computational techniques inasmuch as nowhere in the literature nor in textbooks can one find a model to be followed in computing the numerous zero-order correlation coefficients for a correlation matrix. The purpose of this paper is to present, by means of an illustration, such a model. The model consists of two computational matrices, matrix one being the Summation Matrix and matrix two the Computational Matrix. The entries on these matrices are arranged so as to facilitate the future computations.

An abac is computed which gives the probability that at least q% of the whole population will be included in the range of a random sample of given size. Applications are suggested for testing homogeneity of a sampling from a given population.

This paper discusses and compares the methods of attitude scale construction of Thurstone (method of equal-appearing intervals), Likert (method of summated ratings), and Guttman (method of scale analysis), with special emphasis on the latter as one of the most recent and significant contributions to the field. Despite a certain lack of methodological precision, scale analysis provides a means of evaluating the uni-dimensionality of a set of items. If the criteria for uni-dimensionality are met, the interpretation of rank-order scores is made unambiguous, and efficiency of prediction from the set of items is maximized. The Guttman technique, however, provides no satisfactory means of selecting the original set of items for scale analysis. Preliminary studies indicated that both the Likert and the Thurstone methods tend to select scalable sets of items and that their functions in this respect are complementary. A method of combining the Likert and Thurstone methods in order to yield a highly scalable set of items is outlined. Sets of 14 items selected by the method have, in the two cases where the technique has been tried, yielded very satisfactory scalability.