 Fisher's Exact Test

The equation below is the basic equation for the chi square two by two test. Use the Chi square Webulator to enter your data and compute the Chi square observed score.

 Variable 1 Condition 1 Condition 2 Row Sums Variable 2Condition 1 Variable 2Condition 2 Sum ofColumn 1 Sum ofColumn 2 GrandTotal

 Formula for column 1 Expected Responses Column 1 Formula for column 2 Expected Responses Column 2 (row1 sum × col1 sum)grand total (row1 sum × col2 sum)grand total (row2 sum × col1 sum)grand total (row2 sum × col2 sum)grand total

 Chi Square Computations Column 1 Column 2 (observed- expected)2expected (observed- expected)2expected Chi square formula Chi-Square=

The computed score is referred to as the chi-square observed. After computing the chi-square for the observed scores we next determine the chi-square critical score which represents the chi-square for the expected population.
The chi-square critical score for a two by two frequency table is determined by computing the “degrees of freedom” for our response set.

The computation of the degrees of freedom is:

degrees of freedom = (number of rows - 1) x (number of columns -1)

degrees of freedom = (2-1) x (2-1)

degrees of freedom = (1) x (1)

degrees of freedom = 1

and the "chi-square critical value” for degrees of freedom of "1”at p<0.05 = 3.84

If the "chi-square observed value” is the "chi-square critical value of 3.84”, we would reject the null hypothesis and state that the two distributions ARE NOT EQUAL. However, if the "chi-square observed value ” is the "chi-square critical value of 3.84”, we would ACCEPT the null hypothesis and state that the two distributions ARE EQUAL.

However we could also compute the exact probability using the Fisher's Exact test. The elements of the numerator are:

 (a+b)!= (c+d)!= (a+c)!= (b+d)!=

and the elements of the denominator are:
 (N)!= (a)!= (b)!= (c)!= (d)!=

After we compute the factorial terms we can compute the numerator and denominator terms and then compute the Fisher's Exact Probability value.

 Numerator value = Denominator value =
 Fisher's Exact p = Click here to return to the Webulator Menu Page