The Ranked-Set Sampling Fisher’s Exact Test

Thomas M. Menino Convention & Exhibition Center 

We study the analog of Fisher's exact test in the case where the data come from two independent samples drawn using ranked-set sampling (RSS) rather than simple random sampling. The exactness property is preserved not just under perfect rankings, but also under imperfect rankings as long as the same ranking scheme is used for both samples. We compare the new test to the simple random sampling Fisher's exact test and to existing RSS competitors in terms of power, and we also study what happens under imperfect rankings when the ranking schemes differ between the two samples. Fisher's exact test is famous for being conservative. We show that in the RSS case, the conservativeness of the test can be significantly reduced by using a data-based tie-breaking procedure that does not require randomization.

Exact tests

Judgment rankings

Test of homogeneity 

Section on Nonparametric Statistics