chapter  3
Hotelling’s T2: Tests on One or Two Mean Vectors Single-Sample t and I 2
Pages 55

This chapter describes a rather direct generalization of Student’s t test to situations involving more than one outcome variable. The general approach, as in all of the multivariate techniques we study in this text except factor analysis, is to compute a combined score for each subject that is simply a linear combination of his or her scores on the various outcome measures. The weighting factors employed in obtaining this combined score are those that make the univariate t test conducted on the combined score as large as possible. Just as Student’s t test can be used either to test a single sample mean against some hypothetical value or to test the difference between two independent sample means and a hypothesized difference (usually zero) between the means of the populations from which they were drawn, so too is there a single-sample and a two-sample version of Hotelling’s T2 (the statistical procedure discussed in this chapter) corresponding to testing a mean outcome vector or the difference between two vectors of mean scores on dependent measures against corresponding population mean vectors. If the dependent measures are sampled from a multivariate normal distribution, the sampling distribution of Hotelling’s T2 (which is simply the square of the maximum possible univariate t computed on any linear combination of the various outcome measures) has the same shape as the F distribution. Now for the details.