ABSTRACT
In general, it is advisable to use a combination of univariate and multivariate approaches when there are multiple responses of interest. This chapter considers several ways to summarize information about variation and covariation among multiple responses explained by deviations from the null hypothesis, relative to unexplained error variation and covariation. Once the important responses have been identified, multiple comparisons can be addressed either on individual responses or on linear combinations suggested by analysis. The chapter examines connection between causal models and analysis of covariance through step-down analysis. Discriminant analysis is a method to formalize the process of attributing differences in group means to a few linear combinations of responses. Designed experiments involving two or more responses could be interpreted as simply having correlated responses. The chapter progresses the overall null hypothesis of no group differences and corresponding pivot statistics for multiple responses.
