Linear Models for Cell Means and Reciprocal within Cell Variances

Abstract

The analysis of variance, fixed effects model, is a method for studying the effects of changes in the levels of several factors on the mean of a random variable. It fits a linear model to the cell means under the assumption that all cells have a common variance. When this assumption does not hold, it may be possible to fit a linear model to the reciprocal cell variances. Two such models, differing in their treatment of the mean, are presented here. Both are mathematically tractable and either may be sufficient to explain the variance pattern.