Linear Models and Time-Series Analysis

2Fixed Effects ANOVA Models

Having established the basics of the linear model in Chapter 1, this chapter provides an introduction to one of the most important workhorses of applied statistics, the analysis of variance, or ANOVA, concentrating on the basics of fixed effects models. Section 2.1 explains the notions of fixed and random effects. Section 2.2 illustrates the analysis in the case of two groups, resulting in the usual ‐test for significant differences between the means of two populations. This is extended in Section 2.3 to the case with two groups and ignored block effects, which is a special case of the two‐way ANOVA. It also shows the relevance of the doubly noncentral distribution and the usefulness of being able to calculate its c.d.f. quickly via a saddlepoint approximation.

A core part of this chapter is Section 2.4 , providing the details of the (always Gaussian) one‐way ANOVA model, and also the use of the SAS system for conducting the calculations with data. Section 2.5 extends this to the two‐way ANOVA, with emphasis on rigorous derivation of the relevant distribution theory, and the use of (Matlab, but notably) SAS to perform the required calculations.

This chapter, and Chapter 3 on random effects models, are far from a complete treatment of ANOVA and designed ...