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?


It seems you're interested in something along the lines of:

$H_0: \mu_1=\mu_2=...=\mu_k$
$H_1: \mu_j>\mu_1,...,\mu_{j-1},\mu_{j+1},...,\mu_k\quad$ for some $j$

  1. There's no great difficulty in constructing a permutation test for this; for example, consider the statistic "largest sample mean minus the mean of the remaining samples", and then performing a one-tailed test.

  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.


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