A simulation program examining the use of ratios as raw variables in analyses of variance

An interactive, BASIC-PLUS, simulation program is described for performing a large number of multivariate analyses in accord with, or in violation of, known underlying models. Using a PDP 11/40 computer, random numbers are generated and converted into bivariate normal observations X and Y. These data are then analyzed according to three models. The three analyses are: (1) a standard analysis of variance ignoring the concomitant variable; (2) an analysis of covariance; (3) an analysis of variance on the ratio Y/X. The program can be used to examine the effect of performing multivariate analyses on data transformed into ratios. The utility of the program is the simplicity with which one can alter the underlying models and/or the mathematical relationships between X and Y. Output provides comparisons between models by accumulating rejections and other statistics on critical F-values for each model.