2-way ANOVA

Question

I have run a 2-way ANOVA in SAS JMP by Fit Model and so on. As I understand it, the Prob>T given in the effect tests of the parameter estimates is identical to the p-value of the parameter test.

However, when I then go on and do LS means student's t-test to compare the different levels of my parameters in a pair wise way, I sometimes find that parameters which are not significant (higher than p=0.05) in the "main model" test give rise to significant effects in the students t-test and vice versa...(levels not connected by same letter)..? Moreover, there are no "pair wise" p-values just as for the 1-way ANOVA.
Shouldn't there be a way of getting these p-values just as for the 1-way ANOVA..

Is this because the students t-test uses a different algorithm, or am I mixing things up.

Cheers

unknown · Answer

> I have run a 2-way ANOVA in SAS JMP by Fit Model and
> so on. As I understand it, the Prob>T given in the
> effect tests of the parameter estimates is identical
> to the p-value of the parameter test.

This is correct if your independent variable has 2 levels. It is not correct if the independent variable has more than 2 levels.

> However, when I then go on and do LS means student's
> t-test to compare the different levels of my
> parameters in a pair wise way, I sometimes find that
> parameters which are not significant (higher than
> p=0.05) in the "main model" test give rise to
> significant effects in the students t-test and vice
> versa...(levels not connected by same letter)..?
> Moreover, there are no "pair wise" p-values just as
> for the 1-way ANOVA.
> Shouldn't there be a way of getting these p-values
> just as for the 1-way ANOVA..
> 
> Is this because the students t-test uses a different
> algorithm, or am I mixing things up.

Yes, t-tests use a different algorithm (and different measure of error, and different degrees of freedom) than the model test. Furthermore, the model test and the pairwise t-tests are not transitive ... that is, if you know the model test result, you cannot use this to determine the pairwise t-test result.

The technically correct method is to examine the tests in the ANOVA table, if one of those is statistically significant, only then could you look at predetermined t-tests. Of course, some people don't do it that way, and the world doesn't end.