ABSTRACT
This discussion of variance components begins with the usual one-way ANOVA model.But before launching into that discourse, the reader should notice that this problem looks very easy from a purely theoretical viewpoint. There are just three parameters to estimate: an overall mean, a variance parameter for groups/treatments/varieties, and the usual noise variance. This simplicity belies the fact that variance component problems are indeed quite difficult. As the analysis of the one-way model will indicate, while the balanced case remains somewhat straightforward, the unbalanced case becomes surprisingly complicated, permitting only limited analysis before deferring to the general case. Moreover, the focus of our attention has changed from a mean or linear parameter to a variance-and variances are so much harder to estimate than means. As a result, the presentation here consists of much of the analysis that can be done with the one-way and two-way models, before giving up and deferring to the general case in Section 8.4. The important special case of the split plot is undertaken in Section 8.5, followed by estimation of the random effects in Section 8.6.
