The Use of the Square Root Transformation and Analysis of Variance with Contagious Distributions1

Abstract

The possibility of bias and the power of the analysis of variance and related tests were investigated in an hypothetical expt. for the case in which the data follow a contagious distribution and are transformed by adding 1/2 and extracting the square root before applying the analysis. The transformation introduces a bias but in reasonable cases this bias is not sufficient to invalidate the analysis. The type of distribution and possible effects of treatments may result in such a great generalized error term that the analysis has very little power to detect rather large differences in means that may occur. At least until more powerful tests are available for such cases, analysis of variance of the transformed data may be a satisfactory guide for the experimenter if not too much reliance is placed on the results.