Selection of a Model for a Two-Factor Analysis of Variance

Abstract

There are three models for a two-factor analysis of variance, Model I (effects fixed), Model II (effects random) and Model III (mixed). In Model I main effects and interaction effects may always be estimated, but the results of the analysis may not be generalized to any effects other than those represented in the study. If there is a significant interaction in Model II, neither main effects nor interaction effects may be meaningfully estimated, but the results of the analysis may be generalized to the populations of which the main effects are random samples. Empirical evidence suggests application of Model I procedures to Model II data can produce results comparable to those obtained by “proper” usage of Model I methods.