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## MyBarnard

version 1.4 (5.63 KB) by

A very compact and fast routine for Barnard's exact test on 2x2 matrix

Updated

There are two fundamentally different exact tests for comparing the equality of two binomial probabilities – Fisher’s exact test (Fisher, 1925), and Barnard’s exact test (Barnard, 1945). Fisher’s exact test (Fisher, 1925) is the more popular of the two. In fact, Fisher was bitterly critical of Barnard’s proposal for esoteric reasons that we will not go into here. For 2 × 2 tables, Barnard’s test is more powerful than Fisher’s, as Barnard noted in his 1945 paper, much to Fisher’s chagrin (see C.R. Mehta and P. Senchaudhuri: Conditional versus unconditional exact tests for comparing two binomials. www.cytel.com/papers/twobinomials.pdf). Anyway, perhaps due to its computational difficulty the Barnard's is not widely used. This function is completely vectorized and without for...end loops, and so, the computation is very fast. In FEX there is only one other function that computes the Barnard's exact test by Antonio Trujillo-Ortiz.
Using this matrix x=[7 12; 8 3]; switching off the input error checks and display results sections in both functions; the performs are:
L=1000; times=zeros(1,L); for I=1:L, tic; mybarnard(x); times(I)=toc; end, median(times)
ans = 0.0028

L=1000; times=zeros(1,L); for I=1:L, tic; Barnardextest(7,12,8,3); times(I)=toc; end, median(times)
ans = 1.2478

So my function is about 450 times faster.

More details on:

You can visit my homepage http://home.tele2.it/cardillo
My profile on XING http://www.xing.com/go/invita/13675097

Giuseppe Cardillo

### Giuseppe Cardillo (view profile)

I dont know. I didnt read the original papers. Maybe now computation power is higher and more accurate and precise

Egon Geerardyn

### Egon Geerardyn (view profile)

Shouldn't the P(p) plot (the one shown on the left) be symmetric around p=0.5 as noted in the 1947 paper of Barnard and in the referenced paper?

 22 Mar 2010 1.4 I added: 1) the plots of Wald statistics; 2) a flag to choose if the plots must be shown 23 Dec 2009 1.3 Changes in description 10 Nov 2009 1.2 Change in description 6 Nov 2009 1.1 change in help section to correctly cite this function
##### MATLAB Release
MATLAB 7.6 (R2008a)