I have the following situations :
(1) Very large number of variables - say 100 variables and 200 samples (observations). Although level of each variable is just 2 or 3 or 4 max. I am doing linear ANOVA to test the hypothesis.
Say, for the first variable,
Ho: l1 = l2 = l3 = l4, here l1, l2,l3, and l4 are means at levels 1 to 4. The hypothesis is tested in similar way at all 100 variables independently (not a multiple regression rather talking one variable at time).
(2) a single variable with a high number of levels (lets say 100 levels)
Now the null hypothesis is single :
Ho: l1 = l2 = l3 = l4= ..... = l100