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I have two independent samples 1 and 2, and want to test a null hypothesis that the median of sample 2 is lower or equal to the median of sample 1. Is there a non-parametric test for that?

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    $\begingroup$ What are you willing to assume? The only test that assumes nothing other than continuity of measurements, the Mood median test, is not very efficient. Note that in general medians don’t work well when there are tied values around the middle of the distribution. $\endgroup$ Commented Oct 10, 2023 at 15:06
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    $\begingroup$ A Fisher permutation/randomization test based around medians would work. $\endgroup$ Commented Oct 10, 2023 at 16:06
  • $\begingroup$ @FrankHarrell the sample values are weighted averages of integers from a small range 0, ..., N. I have two cases: one in which the number of averaged integers is fixed, another in which it's random. $\endgroup$
    – quant_dev
    Commented Oct 11, 2023 at 9:26
  • $\begingroup$ @GrahamBornholt But the null hypothesis of the permutation test is that the distributions are the same? I just want to compare the medians. $\endgroup$
    – quant_dev
    Commented Oct 11, 2023 at 9:27
  • $\begingroup$ @FrankHarrell Hence, my values are not continuous, just rational, but I'm OK with assuming they are continuous. $\endgroup$
    – quant_dev
    Commented Oct 11, 2023 at 9:36

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