Open Access
February 2005 Analysis of variance—why it is more important than ever
Andrew Gelman
Ann. Statist. 33(1): 1-53 (February 2005). DOI: 10.1214/009053604000001048


Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a hierarchical analysis that automatically gives the correct ANOVA comparisons even in complex scenarios. The inferences for all means and variances are performed under a model with a separate batch of effects for each row of the ANOVA table.

We connect to classical ANOVA by working with finite-sample variance components: fixed and random effects models are characterized by inferences about existing levels of a factor and new levels, respectively. We also introduce a new graphical display showing inferences about the standard deviations of each batch of effects.

We illustrate with two examples from our applied data analysis, first illustrating the usefulness of our hierarchical computations and displays, and second showing how the ideas of ANOVA are helpful in understanding a previously fit hierarchical model.


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Andrew Gelman. "Analysis of variance—why it is more important than ever." Ann. Statist. 33 (1) 1 - 53, February 2005.


Published: February 2005
First available in Project Euclid: 8 April 2005

zbMATH: 1064.62082
MathSciNet: MR2157795
Digital Object Identifier: 10.1214/009053604000001048

Primary: 62F15 , 62J05 , 62J07 , 62J10 , 62J12

Keywords: ANOVA , Bayesian inference , fixed effects , hierarchical model , Linear regression , multilevel model , random effects , variance components

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 1 • February 2005
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