What Fisher exact test is
The Fisher exact test is a statistical test used to examine the association between two categorical variables. It is used when the expected frequencies in each cell of a two-way table are too small to rely on the normal approximation to the binomial distribution. The Fisher exact test is an exact test of statistical significance, which means that the p-value it produces is without approximation.
Steps for Fisher exact test:
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Construct a two-way table with the observed frequencies.
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Calculate the expected frequencies for each cell in the table by multiplying the row and column totals and dividing by the table total.
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Calculate the test statistic, which is the sum of the differences between the observed and expected frequencies, squared, divided by the expected frequencies.
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Compute the p-value by counting the number of possible tables with the same or more extreme test statistic, and dividing by the total number of possible tables.
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Compare the p-value to the pre-specified significance level and draw conclusions about the association between the two variables.
Examples
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Fisher exact test can be used to determine the statistical significance of the difference between the proportions of two groups. For example, a researcher may use the test to compare the proportions of people who were successfully treated with a particular drug to the proportions of people who were not successfully treated with the same drug.
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Fisher exact test can be used to evaluate the association between two binary variables. For example, a researcher may use the test to determine the association between gender and the likelihood of developing a certain disease.
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Fisher exact test can be used to compare the observed proportions of two samples. For example, a researcher may use the test to compare the proportion of people who responded favorably to a survey question in two different groups.