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2010 | OriginalPaper | Chapter
2. The Analysis of Variance (ANOVA)
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Abstract
While the linear regression of Chapter 1 goes back to the nineteenth century, the Analysis of Variance of this chapter dates from the twentieth century, in applied work by Fisher motivated by agricultural problems (see §2.6). We begin this chapter with some necessary preliminaries, on the special distributions of Statistics needed for small-sample theory: the chi-square distributions χ2(n) (§2.1), the Fisher F-distributions F(m, n) (§2.3), and the independence of normal sample means and sample variances (§2.5). We shall generalise linear regression to multiple regression in Chapters 3 and 4 – which use the Analysis of Variance of this chapter – and unify regression and Analysis of Variance in Chapter 5 on Analysis of Covariance.