Hotelling t2 test followed by multiple t-tests (Bonferroni corrected?)

[Dusan Petrovic]

Dear Statalisters,

For this post, I would have two statistics questions, rather than STATA questions, I hope you don't mind.

Question 1:

I have a dataset that has one independent variable (Group = 2 levels : Group A vs. Group B) and 10 quantitative response variables (i.e. 10 physiological parameters).

I'm using a Hotelling T2 test, that will tell whether at least one of the 10 response variables is different between Group A and Group B, but it won't tell me which one(s) of the 10 response variables are different.

I am assuming that if I want to find out which one(s) of 10 response variables are different, I would need to perform 10 t-tests (Group A vs. Group B), for each of the 10 response variables, and that I would need to divide the alpha threshold by 10, thus alpha = 0.05/10 = 0.005.

Is this correct?

Thank you very much for your reply.


Question 2
I have the same dataset, but 3 (A,B,C) Groups instead of 2 (A,B).

Here, I should do a MANOVA test. But what test, and what correction should I do to find which one(s) ot the 10 variables are different between the 3 groups? TUkey, as for ANOVA ?, also what kind of correction should I apply to the Tukey test, divide alpha by 10?

Thank you very very much

Dusan

[Dusan Petrovic]

For those interested I found the solution(s).

Question 1

(a) Indeed, perform Hotelling test that will tell whether at least one of the 10 response variable is different between the two groups, but not which one.
(b) Indeed, to find which of the 10 response variables, 10 t-tests can be performed with alpha threshold divided by 10.

Question 2
a) Perform a MANOVA, that will tell whether at least one of the 10 response variable is different between the groups, but not which one.
b) Perform 10 ANOVA tests, corrected for Bonferroni, this will allow to identify which variables are different
c) For variables identified in b), perform TukeyHSD, or pairwise t-tests corrected for bonferroni (alpha threshold divided by 3 if 3 groups (or the number of comparisons)). That will help identify which group has a mean different from the others