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I have run a single algorithm on a 50 problems with 3 different values for a parameter(tiebreak). The algorithm's job is to rank candidate values for a parameter(split) that will be fed into another algorithm. However, I would like to perform a rank correlation test to determine whether there is statistically significant evidence to suggest different rankings against the 3 different tiebreaks. What test would achieve this? I have considered tau's test but the problem is that I am using the same 50 problems accross the tests hence a higher chance of a type I error. Is there a way to adjust for this or even better still a nonparameteric test that is designed for multiple comparisons.

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