Two-way analysis of variance: Difference between revisions

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{{short description|Statistical test examining influence of two categorical variables on one continuous variable}}

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==

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Finally, the sums of squared deviations required for the [[analysis of variance]] can be calculated.<ref>{{cite book|last=Mecklin|first=Christopher|title=STA 265 Notes (Methods of Statistics and Data Science)|date=20 October 2020|access-date=6 December 2024|chapter-url=https://bookdown.org/cmecklin/sta265notes/anova-with-interaction.html|chapter=Chapter 7: ANOVA with Interaction|via=bookdown.org}}</ref>

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| Composite (correction factor<ref>{{cite book|chapter-url=https://iastate.pressbooks.pub/quantitativeplantbreeding/chapter/the-analysis-of-variance-anova/|title=Quantitative Methods for Plant Breeding|chapter=Chapter 8: The Analysis of Variance (ANOVA)|last1=Moore|first1=Ken|last2=Mowers|first2=Ron|last3=Harbur|first3=M.L.|last4=Merrick|first4=Laura|last5=Mahama|first5=Anthony Assibi|publisher=Iowa State University Digital Press|editor-last1=Suza|editor-first1=W.P.|editor-last2=Lamkey|editor-first2=K.R.|year=2023|access-date=6 December 2024}}</ref>)

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| Squared deviations (<math>\sigma^2</math>)

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| Mean square variance

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| 14.668

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==See also==

* [[Analysis of variance]]

* [[F -test]] (''Includes a one-way ANOVA example'')

* [[Mixed model]]

* [[Multivariate analysis of variance|Multivariate analysis of variance (MANOVA)]]