Two Samples Hotelling’s T2 Test

Hotelling's T2 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