A multivariate analysis based on transmitted information is presented. It is shown that sample transmitted information provides a simple method for measuring and testing association in multi-dimensional contingency tables. Relations with analysis of variance are pointed out, and statistical tests are described.

A least squares solution has been presented for the Law of Categorical Judgment and the Method of Successive Intervals, which is formally equivalent to Horst's solution for the matrix of incomplete data. A simplified approximation which is recommended for use with any matrix of complete data is also given. A procedure, analogous to that originally devised by Thurstone and presented by Saffir, is outlined for the typical experimental matrix of incomplete data. It is essentially a “point and slope” method of fitting a straight line which comes rather directly from the least squares solution.

A rationale and a procedure for constructing questionnaire keys so as to minimize the effect of distortion or faking by the respondents is developed. This rationale is based on the supposition that suppressor items can be identified to reduce distortion in, and thus add to, the validity of questionnaire keys. The procedure is designed primarily for application to the construction of forced choice items.

The results of an empirical test of the efficicacy of the forced choice pairing procedure developed as a consequence of this rationale are presented. A key based on forced choice pairs developed by this procedure gave a validity of .33; a second key based on forced choice pairs developed by more conventional procedures gave a validity of .23.

Let R be any correlation matrix of order n, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrix U2 such that G = R − U2 is Gramian and of minimum rank r. Let s1 be the number of latent roots of R which are greater than or equal to unity. Then it is proved here that r ≥ s1. Two further lower bounds to r are also established that are better than s1. Simple computing procedures are shown for all three lower bounds that avoid any calculations of latent roots. It is proved further that there are many cases where the rank of all diagonal-free submatrices in R is small, but the minimum rank r for a Gramian G is nevertheless very large compared with n. Heuristic criteria are given for testing the hypothesis that a finite r exists for the infinite universe of content from which the sample of n observed variables is selected; in many cases, the Spearman-Thurstone type of multiple common-factor structure cannot hold.

This note revises the figures in the original article concerning the accuracy of the tetrachoric estimates involved. These estimates are better than previously noted and are very satisfactory. Some minor known errors in the original article are also noted.