# Statistical test for a class versus multiple classes

We are given n classes of real values. The number of elements in each class is not too high and can be different between classes.

We want to test whether there exist a class with significantly higher (average) values from all other classes or not. The case is somehow similar to ANOVA, but slightly different.

What test do you propose?

$H_0: \mu_1=\mu_2=...=\mu_k$
$H_1: \mu_j>\mu_1,...,\mu_{j-1},\mu_{j+1},...,\mu_k\quad$ for some $j$
2. An alternative would be to frame it as a set of one-sided ANOVA contrasts (not orthogonal) of the form $c_i'\mu$ (e.g. $c_3'\,\propto\,(-1, -1, 9, -1, -1, -1, -1, -1, -1, -1)\,$) and test them all one-tailed, presumably with some adjustment for multiple testing.