The Analysis of Variance with Various Binomial Transformations

Abstract

The author gives a concise description of the maximum likelihood-probit method for analyzing quantal response data and shows how it conforms with the formal requirements for a meaningful analysis of variance. At the same time he criticizes the use of the angular, the square root and the logistic transformation on this kind of data. His objections are that these transformations are based on empirical arguments rather than theoretical, that their primary goal is to achieve uniformity of variance as an end in itself, and that they are not easier to compute than the probit method, as claimed by other authors. Following Fisher''s paper are a series of short comments by M. S. Bartlett, F. J. Anscombe, W. G. Cochran and Joseph Berkson, who are some of the authors referred to in the paper.