MyFisher22

A very compact routine for Fisher's exact test on 2x2 matrix; power and sample sizes calculation

Fisher's exact test of 2x2 contingency tables permits calculation of precise probabilities in situation where, as a consequence of small cell frequencies, the much more rapid normal approximation and chi-square calculations are liable to be inaccurate.
The Fisher's exact test involves the computations of several factorials to obtain the probability of the observed and each of the more extreme tables. Factorials growth quickly, so it's necessary use logarithms of factorials. This computations is very easy in Matlab because x!=gamma(x+1) and log(x!)=gammaln(x+1).
I rewrote this function several times: now the fully vectorization, the preallocation, the using of a recursive relationship for the Fisher's exact test on 2x2 matrix and the using of logarithm greatly speed up the execution.
It is faster than the previously submitted Fisherextest. In fact, I performed this test comparing the core of both scripts (deleting the input error check, the code to display results and compute the power). X=[70 30; 29 80] (100 tables to evaluate)
times=zeros(1,1000); for I=1:1000, tic; myfisher22(X); times(I)=toc; end, median(times)
ans = 1.3000e-4
The same for Fisherextest: ans = 0.0024

So my function in about 18.5 fold faster

Actually, the function also computes the mid-P correction to make the test less conservative.
Moreover, the routine computes the Power and, if necessary, the sample sizes needed to achieve a power=0.80 using a modified asymptotic normal method with continuity correction as described by Hardeo Sahai and Anwer Khurshid in Statistics in Medicine, 1996, Vol. 15, Issue 1: 1-21.