[R] help comparing two median with R

Peter Dalgaard p.dalgaard at biostat.ku.dk
Tue Apr 17 21:00:01 CEST 2007

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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