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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