MultivariatTests

MultivariatTests is a class of statistical methods and, in some contexts, software tools designed to test hypotheses across multiple outcome variables simultaneously. The approach is used when outcomes are correlated or when a joint assessment provides greater interpretive value than separate univariate tests. MultivariatTests encompasses techniques such as multivariate analysis of variance (MANOVA), Hotelling's T-squared test, and multivariate regression, as well as broader multivariate testing frameworks used in experimental design and A/B/n experiments.

In practice, MultivariatTests aims to determine whether experimental groups differ on a set of related metrics, taking into account intervariable correlations to improve power and to control the experimentwise error rate. Typical workflows include specifying a design (e.g., factor groups), checking assumptions (multivariate normality, equality of covariance matrices), performing the multivariate test, and, if significant, interpreting which linear combinations of outcomes drive effects (often via post hoc analyses or follow-up univariate tests).

Common methods include MANOVA for group differences on multiple outcomes, Hotelling's T^2 for two-group comparisons, and multivariate regression variants. Nonparametric alternatives exist when normality assumptions fail.

MultivariatTests is applicable in psychology, medicine, marketing, and finance, where multiple performance metrics or safety outcomes are observed jointly. Limitations include the need for adequate sample size, interpretability challenges, and sensitivity to model assumptions. Software implementations exist in R, Python, SAS, and SPSS, enabling researchers to conduct these tests and report multivariate effect sizes.