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. 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, it can also be used as a two tailed test as well. It is sometimes called a Fisher Irwin test. It is given this name because it 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.
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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, 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. It 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.
It is assumed that the sample that has been drawn from the population is done by the process of random sampling. This assumption is also assumed in general in all the significance tests.
In the Fisher Exact test, a directional hypothesis is assumed. The directional hypothesis assumed is nothing but the hypothesis based on the one tailed test. In other words, the directional hypothesis assumed is that type of hypothesis which predicts either a positive association or a negative association, but not both.
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, the given case should fall in only one cell in the table.
The dichotomous level of measurement of the variables is assumed.