One-Way ANOVA

Abstract

In this and following chapters, we apply the general theory of linear models to various special cases. This chapter considers the analysis of the one-way ANOVA model. A one-way ANOVA model can be written $${y_{ij}} = \mu + {\alpha _i} + {e_{ij}}\quad i = 1, \ldots ,t,\quad j = 1, \ldots ,{n_i}$$ (1) where E(e ij ) = 0, Var(e ij ) = σ 2, and Cov(e ij , e i′ j′) = 0 when (i, j) ≠ (i′, j′). For finding tests and confidence intervals, the e ij ’s are assumed to have a multivariate normal distribution.