# FISHERTEST (Scripts) 1.0

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## FISHERTEST (Scripts) Publisher's description

### FISHERTEST - Fisher Exact test for 2-x-2 contingency tables

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.

permtest, cochranqtest (File Exchange)

This file does not require the Statistics Toolbox.

#### System Requirements:

MATLAB 6.5 (R13)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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