To proceed, enter the values of X_{0}Y_{1}, X_{1}Y_{1}, etc., into the designated cells. When all four cell values have been entered, click the «Calculate» button. To perform a new analysis with a new set of data, click the «Reset» button.
The logic and computational details of the Chi
Square and Fisher tests are described in Chapter 8 and Subchapter 8a, respectively, of Concepts and Applications. A briefer account of the Fisher test will be found toward the bottom of this page.
Data Entry_{T}
Fisher Exact Probability Test:_{T}
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©Richard Lowry 2001
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Fisher Exact Probability Test: Logic and Procedure
Consider a 2x2 contingency table of the sort described above, with the cell frequencies represented by a, b, c, d, and the marginal totals represented by a+b, c+d, a+c, b+d, and n.
 0
 1
 Totals

1
 a
 b
 a+b

0
 c
 d
 c+d

Totals
 a+c
 b+d
 n

If there were no systematic association between the variables A and B within the population from which the cell frequencies are randomly drawn, the probability of any particular possible array of cell frequencies, a, b, c, d, given fixed values for the marginal totals a+b, c+d, etc., would be given by the hypergeometric rule
which for computational purposes reduces to
Also, the degree of disproportion within any array of cell frequencies—in effect, the degree of ostensible association between variables A and B within the sample—can be measured by the absolute difference
For any particular observed array of cell frequencies, the programming embedded in this page calculates the probability of that particular array plus the probabilities of all other possible arrays whose degree of disproportion is equal to or greater than that of the observed array. Thus, for the observed array
the onetailed probability would be the sum of the separate probabilities for the arrays


 probability

2
 7



8
 2

 0.01754

1
 8



9
 1

 0.00097

0
 9



10
 0

 0.00001


sum = 0.01852
 (onetailed probability)

And the twotailed probability would be that sum plus the sum of the separate probabilities for the arrays of equal or greater disproportion at the other extreme:


 probability

8
 1



2
 8

 0.00438

9
 0



1
 9

 0.00011


sum = 0.00449

twotailed probability = 0.01852 + 0.00449 = 0.02301
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©Richard Lowry 1998
All rights reserved.