A critical appraisal of the analysis of variance for two-way classifications

This paper discusses two reasons for invalidity of analysis of variance, namely heterogeneous variance and heterogeneous correlation. Textbook examples of data in two classifications are presented in which these failures of validating assumptions were not recognised and which led to analyses which were seriously in error. Both forms of heterogeneity result in a residual mean square in the usual analysis of variance being made up of heterogeneous components; the difficulty is overcome by partitioning the mean square and using the component appropriate to the hypothesis to be tested and the contrast to be estimated.