An analysis of Guttman's simplex

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically inton/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomesn/2 is contradictory to Guttman's contention that the minimal rank isn — 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.Prepared under Contract 816(02) between the Office of Naval Research and Washington University and presented in part at a meeting of the Southern Society for Philosophy and Psychology, St. Louis, Missouri, March 27, 1959. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

Statistical simulation on microcomputers

The statistical simulation program DATASIM is designed to conduct large-scale sampling experiments on microcomputers. Monte Carlo procedures are used to investigate the Type I and Type II error rates for statistical tests when one or more assumptions are systematically violated-assumptions, for example, regarding normality, homogeneity of variance or covariance, mini-mum expected cell frequencies, and the like. In the present paper, we report several initial tests of the data-generating algorithms employed by DATASIM. The results indicate that the uniform and standard normal deviate generators perform satisfactorily. Furthermore, Kolmogorov-Smirnov tests show that the sampling distributions ofz, t, F, χ², andr generated by DATASIM simulations follow the appropriate theoretical distributions. Finally, estimates of Type I error rates obtained by DATASIM under various patterns of violations of assumptions are in close agreement with the results of previous analytical and empirical studies; These converging lines of evidence suggest that DATASIM may well prove to be a reliable and productive tool for conducting statistical simulation research.