Tag: Fisher’s exact test on 2×2 matrix

Fisher’s Exact Test On 2×2 Matrix Download [Updated]

 

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There are five possible combinations between two grades, and we would like to see if there is any significant difference

Fisher’s exact test on 2×2 matrix

Introduction and examples

Contingency table

A contingency table summarizes the relations of multiple variables to a given categorical outcome of interest. In population census data, for example, the variables might be “sex”, “age”, “birthplace”, and “occupation”. The outcome, “employment status”, is binary: either the person is employed or not. The entries in a contingency table are counts of people in the population who have all possible combinations of the categories in each variable. The table should have four cells, for each combination of the values of each variable. Table 1 displays a sampling from a contingency table, in this case a 5% significance test for the significance of the difference in the proportion of employed men in the sample and the population.

Table 1

Covariate and Expected Counts in Contingency Table

x

R

Expected

Sample

30

0

0

0

4

0

0

100

30

10

0

0

6

0

0

100

20

10

0

0

4

0

0

100

20

0

0

0

4

0

0

100

10

10

0

0

0

0

0

100

Table 1: The leftmost column shows the covariate/expectation. The second column shows the counts in the sample. The third column shows the counts in the population. The fourth column is the result of hypothesis test, Fisher’s exact test (p=0.05).

Note that the probabilities are the ratios of the counts in the cells to the counts in the top-right cell. For the purpose of Fisher’s exact test, this is a total of 64 cases, and … Read the rest