Chapter 8 - Inferential Statistics V: Multiple and Multivariate Hypothesis Testing

Abstract

This chapter covers parametric techniques for dealing with multiple hypothesis tests and/or multivariate data. First, Bonferroni's correction is introduced as a way of controlling the probability of at least one type I error (the familywise error rate) when testing multiple hypotheses. ANOVA (analysis of variance) is described, which enables the hypothesis of a common mean to be tested about multiple groups of univariate data. ANOVA formulations are provided for groups with equal and unequal sizes. Hypothesis tests for use with multivariate data are also introduced: Hotelling's T2 test is a generalization of the Student's t-test to multivariate data; MANOVA (multivariate analysis of variance) is a generalization of ANOVA to multivariate data. A summary is provided of how to decide which test is appropriate for different scenarios. An overview of MATLAB capabilities with regard to multiple and multivariate hypothesis testing is provided.