Two-way analysis of variance: Difference between revisions

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{{expert-subject needed|statistics |date=January 2012}}

In [[statistics]], the '''two-way [[analysis of variance]] (ANOVA)''' is an extension of the [[One-way analysis of variance|one-way ANOVA]] that examines the influence of two different [[Categorical variable|categorical]] [[independent variables]] on one [[Continuous function|continuous]] [[dependent variable]]. The two-way ANOVA not only aims at assessing the [[main effect]] of each independent variable but also if there is any [[Interaction (statistics)|interaction]] between them.

==History==

In 1925, [[Ronald Fisher]] mentions the two-way ANOVA in his celebrated book from 1925, ''[[Statistical Methods for Research Workers]]'' (chapters 7 and 8). In 1934, [[Frank Yates]] published procedures for the unbalanced case.<ref>{{cite journal |last=Yates |first=Frank |date=March 1934 |title=The analysis of multiple classifications with unequal numbers in the different classes |url=http://www.jstor.org/stable/=2278459 |journal=Journal of the American Statistical Association |publisher=American Statistical Association |volume=29 |issue=185 |pages=51–66 |accessdate=19 June 2014 |doi=10.1080/01621459.1934.10502686}}</ref> Since then, an extensive literature has been produced. The topic was reviewed in 1993 by [[Yasunori Fujikoshi]].<ref>{{cite journal |last=Fujikoshi |first=Yasunori |date=1993 |title=Two-way ANOVA models with unbalanced data |url=http://www.sciencedirect.com/science/article/pii/0012365X9390410U |journal=Discrete Mathematics |publisher=Elsevier |volume=116 |issue=1 |pages=315–334 |doi=10.1016/0012-365X(93)90410-U |accessdate=19 June 2014}}</ref> In 2005, [[Andrew Gelman]] proposed a different approach of ANOVA, viewed as a [[multilevel model]].<ref>{{cite journal |last=Gelman |first=Andrew |date=February 2005 |title=Analysis of variance? why it is more important than ever |journal=The Annals of Statistics |volume=33 |issue=1 |pages=1–53 |doi=10.1214/009053604000001048 |url=http://projecteuclid.org/euclid.aos/1112967698 |accessdate=19 June 2014}}</ref>

==Data set==