FISHERTEST 1.0

FISHERTEST - Fisher Exact test for 2-x-2 contingency tables H = FISHERTEST(M) performs the non-parametric Fisher exact probability test on a 2-by-2 contingency table described by M, and returns the result in H. It calculates the exact probability of observing the given and more extreme distributions on two variables. H==0 indicates that the null hypothesis (H0: "the score on one variable is independent from the score on the other variable") cannot be rejected at the 5% significance level. H==1 indicates that the null hypothesis can be rejected at the 5% level. For practical convenience, the variables can be considered as "0/1 questions" and each observation is casted in one of the cells of the 2-by-2 contingency table [1/1, 1/0 ; 0/1, 0/0]. If M is a 2-by-2 array, it specifies this 2-by-2 contingency table directly. It holds the observations for each of the four possible combinations. If M is a N-by-2 logical or binary array, the 2-by-2 contingency table is created from it. Each row of M is a single observation that is casted in the appropriate cell of M. [H,P,STATS] = FISHERTEST(..) also returns the exact probability P of observing the null-hypothesis and some statistics in the structure STATS, which has the following fields: .M - the 2-by-2 contingency table .P - a list of probabilities for the original and all more extreme observations .phi - the phi coefficient of association between the two attributes .Chi2 - the Chi Square value for the 2-by-2 contingency table H =FISHERTEST(M, APLHA) performs the test at the significance level (100*ALPHA)%. ALPHA must be a scalar between 0 and 1. Example: % We have measured the responses of 15 subjects on two 0-1 % "questions" and obtained the following results: % Q1: 1 0 % Q2: 1 5 1 % 0 2 7 % (so 5 subjects answered yes on both questions, etc.) M = [ 5 1 ; 2 7] % Our null-hypothesis is that the answers on the two questions are % independent. We apply the Fisher exact test, since the data is % measured on an ordinal scale, and we have far to few observations to % apply a Chi2 test. The result of ... [H,P] = fishertest(M) % (-> H = 1, P = 0.0350) % shows that the probability of observing this distribution M or the % more extreme distributions (i.e., only one in this case: [6 0 ; 1 8]) is 0.035. Since this is less than 0.05, we can reject our null-hypothesis indicated by H being 1. The Fisher Exact test is most suitable for small numbers of observations, that have been measured on a nominal or ordinal scale. Note that the values 0 and 1 have only arbitray meanings, and do reflect a nominal category, such as yes/no, short/long, above/below average, etc. In matlab words, So, M, M.', flipud(M), etc. all give the same results. See also signtest, ranksum, kruskalwallis, ttest, ttest2 (stats Toolbox) permtest, cochranqtest (File Exchange) This file does not require the Statistics Toolbox.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Answered,  Answers,  Apply,  Distribution,  Obtained,  Ordinal,  Questions,  Results
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