I was doing a little mental calisthenics today and got myself confused
about how this test is calculated. My (perhaps naive) understanding is
that all potential sets of results from, say, a 2x2 table are
calculated and then the exact probability of the actual observed
result occurring simply by chance is determined. This is why there is
no associated test statistic, just p.

My question is: If the test is distributionless, wouldn't the
probability of all unique results be equal? Or...put another way...Is
Fisher's exact one of those sneaky nonparametrics that really does
rely upon an underlying distribution?

Thanks.
.
.
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