# What is “ANOVA”?

Wikipedia says:

Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). In ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

In one way or two way ANOVA, (which are the types of ANOVA I have seen), the input variable $X$ is categorical, whose value represents the group of the sample.

in The Elements of Statistical Learning: Data Mining, Inference, and Prediction. by Trevor Hastie, Robert Tibshirani, and Jerome Friedman, ANOVA seems to be a way of modeling $E(Y|X)$ as sum of functions of various number of components of $X$. It doesn't relate to variance or partition of variance into some form. $X$ is not necessarily categorical either and may be continuous valued. Or am I missing something? Thanks!

• Please give a reference for your extracted material, as a courtesy both to readers and to the original authors. – Nick Cox Jul 2 '13 at 18:57
• I have given a link to the reference to the book ESL – Tim Jul 2 '13 at 19:00
• At the risk of adding even more confusion, I would suggest trying to read ANOVA – Why It Is More Important Than Ever by Andrew Gelman. – Gala Jul 2 '13 at 19:17
• Good reference. I was thinking ANOVA paper: was it Speed, was it Gelman? Answer: Both. – Nick Cox Jul 2 '13 at 19:31