Statistics in a Nutshell

Chapter 13. Extensions of Analysis of Variance

In Chapter 12, you learned about the general linear model and its applications in linear regression and one-way Analysis of Variance (ANOVA). In the algebraic derivation of the general linear model, from an analysis of the two-dimensional number plane, the possible extension to the multidimensional case was alluded to. Factorial ANOVA involves the use of models that include more than one independent variable, while Multivariate ANOVA (or MANOVA) uses models with multiple dependent variables.

In this chapter, you will learn about more of these complex ANOVA designs, including two-way and three-way factorial ANOVA, and MANOVA for at least two dependent variables. Issues surrounding the use of factorial and nonfactorial designs, and the Analysis of Covariance (ANCOVA), will be covered, while in Chapter 14, corresponding multidimensional extensions to linear regression will be covered.

Realistically, most ANOVA designs are typically factorial, and at least two-way, depending on your field of interest. In addition, during model building based around groups, it may become apparent that there is a confound influencing variation in the dependent variable as observed. For example, a test of athletic performance between two schools is confounded if one happens to be a specialist athletics school, with twice as many contact sport hours as the second school. The number of contact sport hours is thus considered a covariate, and ANCOVA allows an adjustment ...