Multivariate analysis of variance

The image above depicts a visual comparison between multivariate analysis of variance (MANOVA) and univariate analysis of variance (ANOVA). In MANOVA, researchers are examining the group differences of a singular independent variable across multiple outcome variables, whereas in an ANOVA, researchers are examining the group differences of sometimes multiple independent variables on a singular outcome variable. In the provided example, the levels of the IV might include high school, college, and graduate school. The results of a MANOVA can tell us whether an individual who completed graduate school showed higher life AND job satisfaction than an individual who completed only high school or college. Results of an ANOVA can only tell us this information for life satisfaction. Analyzing group differences across multiple outcome variables often provides more accurate information as a pure relationship between only X and only Y rarely exists in nature.

In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables,[1] and is often followed by significance tests involving individual dependent variables separately.[2]

Without relation to the image, the dependent variables may be k life satisfactions scores measured at sequential time points 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.

  1. ^ Warne, R. T. (2014). "A primer on multivariate analysis of variance (MANOVA) for behavioral scientists". Practical Assessment, Research & Evaluation. 19 (17): 1–10.
  2. ^ Stevens, J. P. (2002). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erblaum.