# Fisher's Exact Test

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## Definition: Fisher's Exact Test

Fisher’s exact test is a test for finding out the statistical significance, generally employed for small sample sizes. It is used mostly in analyzing the contingency tables. The major advantage of this test is that the amount of deviation from null hypothesis can be obtained without any approximation. When we classify objects in two different ways, Fisher’s test uses that data to find out dependency or contingency of one classification on the other.

E.g.: Analyzing a group of college students classified as male and female and also as those who use their own vehicle to come to college and those who don’t. The data may be:

 Boys Girls Total Not own vehicle 1        (a) 2        9 (b) 10 Own vehicle 11    c) 12    3 (d) 14 Total 12 12 24 (a +b +c +d=n)

According to Fisher’s formula, to find out the association between these classifications, we can use the probability of getting such a set of values using the hyper geometric distribution:

p   =           (a+b)! * (c+d)! * (a+c)! * (b+d)!        / a! * b! * c! * d! * n!

! stands for factorial sign.

Hence in this example, p = (10! * 14! * 12! * 12! ) / (1! * 9! * 11! * 3! * 24! ) = 0.001346076

Hence, this concludes the definition of Fisher's Exact Test along with its overview.

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