Fast implementation of Fisher exact test (hypergeometric test) in Matlab. This function requires no toolbox to be installed (tested on Matlab v2016b).
One can use fisher exact test to calculate degree of association between two groups. The following is a contingency table for association between being a man (or woman) and wearing hat.
| Men | Women | Row Total | |
|---|---|---|---|
| Have hat | a | b | a+b |
| No hat | c | d | c+d |
| Column Total | a + c | b + d | N |
P-value of such a table can be calculated by:
My tests showed that this implementation is at least 20 times faster than current implementation in Matlab (ver 2016b).
This code is heavily inspired by an implementation by Jia Meng: MatWorks FileExchange
This example calculates "left tail" (i.e. mutual exclusivity) p-value as well as "right tail" (i.e. cooperation) p-value:
[pval_left_tail, pval_right_tail] = FastFisherExactTest(a, b, c, d)
In my tests, I could identify 1e-10 difference between my implementation and Matlab. I think it is due to round-off errors. A script is provided in "testcode.m" to compare results with Matlab.