**Two Samples ****Hotelling’s**** T ^{2} Test**

*Hotelling's** T ^{2}* is the multivariate extension of the common Student's t-test.

For
multivariate responses, the problems to use separate univariate
tests are:

(1)
Separate univariate tests will inflate
type I error (e.g. 10 responses, separate t test at α=0.05, then at least
1 type I error ≥ (1-0.95)^{10} ≈0.40);

(2)
Univariate tests
ignore correlations among responses;

(3)
Groups may not differ on any single response, but may differ on
several responses jointly.

Multivariate
test uses overall α=0.05, and takes into account of correlations among
responses, and can detect the joint difference.

Below is the **sample
input window**

Below is the **sample
output**:

Hotelling T-square test for:

INFO

SIMIL

ARITH

PICT

Group variable: GROUP

Group levels: 0, 1

N1 N2 T-square F df1 df2 P value

28 12 11.95053 2.751768 4 35 0.04331741