Multivariate analysis of variance: Difference between revisions

Revision as of 06:36, 28 May 2025

Revision as of 06:36, 18 June 2025

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In [[statistics]], '''multivariate analysis of variance''' ('''MANOVA''') is a procedure for comparing [[multivariate random variable|multivariate]] sample means. As a multivariate procedure, it is used when there are two or more [[dependent variables]],<ref name="Warne2014">{{cite journal |last=Warne |first=R. T. |year=2014 |title=A primer on multivariate analysis of variance (MANOVA) for behavioral scientists |journal=Practical Assessment, Research & Evaluation |volume=19 |issue=17 |pages=1–10 |url=https://scholarworks.umass.edu/pare/vol19/iss1/17/ }}</ref> and is often followed by significance tests involving individual dependent variables separately.<ref>Stevens, J. P. (2002). ''Applied multivariate statistics for the social sciences.'' Mahwah, NJ: Lawrence Erblaum.</ref>

Without relation to the image, the dependent variables may be k life satisfactions scores measured at sequential [[time pointspoint]]<nowiki/>s and p job satisfaction scores measured at sequential time points. In this case there are k+p dependent variables whose [[linear combination]] follows a multivariate [[normal distribution]], multivariate variance-covariance matrix homogeneity, and linear relationship, no multicollinearity, and each without outliers.

== Model ==