Thomas Lumley wrote: > There actually is an exact test for the median that does not assume a > location shift: dichotomize your data at the pooled median to get a 2x2 > table of above/below median by group, and do Fisher's exact test on the > table. Fascinating. But can one be sure that the fisher test actually has the correct distribution in this setup? I feel somewhat unconvinced. It is fairly clear that the test is not independent of the joint sample median for instance (think two normals, one with a very small variance). > This is almost never useful (because it doesn't come with an > interval estimate), but is interesting because it (and the generalizations > to other quantiles) is the only exactly distribution-free location test > that does not have the 'non-transitivity' problem of the Mann-Whitney U > test. I believe this median test is attributed to Mood, but I have not > seen the primary source. >
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