Fisher Exact test

The Fisher Exact test is a test of significance that is used in the place of chi square test in 2 by 2 tables, especially in cases of small samples.

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The Fisher Exact test tests the probability of getting a table that is as strong due to the chance of sampling. In the case of the Fisher Exact test, the word ‘strong’ is defined as the proportion of the cases that are diagonal with the most cases.

The Fisher Exact test is generally used in one tailed tests. However, the Fisher Exact test can also be used as a two tailed test as well. The Fisher Exact test is sometimes called a Fisher Irwin test. The Fisher Exact test is called by this name because the Fisher Exact test was developed at the same time by Fisher, Irwin and Yates in 1930.

In SPSS, the Fisher Exact test is computed in addition to the chi square test for a 2X2 table when the table consists of a cell where the expected number of frequencies is fewer than 5.

There are certain terminologies that help in understanding the theory of Fisher Exact test.

The Fisher Exact test uses the following formula:

p= ( ( a + b ) ! ( c + d ) ! ( a + c ) ! ( b + d ) ! ) / a ! b ! c ! d ! N !

In this formula of the Fisher Exact test, the ‘a,’ ‘b,’ ‘c’ and ‘d’ are the individual frequencies of the 2X2 contingency table, and ‘N’ is the total frequency.

The Fisher Exact test uses this formula to obtain the probability of the combination of the frequencies that are actually obtained. The Fisher Exact test also involves the finding of the probability of every possible combination which indicates more evidence of association.

There are certain assumptions on which the Fisher Exact test is based.

In the Fisher Exact test, it is assumed that the sample that has been drawn from the population is done by the process of random sampling. This assumption of the Fisher Exact test is also assumed in general in all the significance tests.

In the Fisher Exact test, a directional hypothesis is assumed. The directional hypothesis assumed in the Fisher Exact test is nothing but the hypothesis based on the one tailed test. In other words, the directional hypothesis assumed in the Fisher Exact test is that type of hypothesis which predicts either a positive association or a negative association, but not both.
In the Fisher Exact test, it is assumed that the value of the first person or the unit of items that are being sampled do not get affected by the value of the second person or the other unit of item being sampled. This assumption of the Fisher Exact test would be violated if the data is pooled or united.

In the Fisher Exact test, mutual exclusivity within the observations is assumed. In other words, in the Fisher Exact test, the given case should fall in only one cell in the table.
In the Fisher Exact test, the dichotomous level of measurement of the variables is assumed.