ANOVA：Why It Is More Important than Ever

Abstract

What is Anova? Econometricians see it as an uninteresting special case of linear regression. Bayesians see it as an inflexible classical method. Instructors see it as one of the hardest topics to teach, especially in its more elaborate forms such as split-plot analysis. We believe, however, that the ideas of Anova are useful in many applications of statistics. We consider these topics: - Is Anova obsolete? - A hierarchical regression example where you add a predictor and the variance goes up - Using Bayesian hierarchical modeling to do Anova automatically - The three different and contradictory definitions of fixed and random effects - Degrees of freedom, R-squared, etc. - Computational challenges - Applications in sample surveys, psychometrics