First, it is important to think about what are proportions and what variables are being evaluated with these tests. Proportions include the incidence of something and these tests evaluate categorical variables. These are variables that you cannot put a bell curve through. This is different from tests of means which compares the means of 2 independent and normally distributed groups.
Examples of Categorical variables:
- Nominal (Male/Female) = labels as opposed to numbers, central tendency = mode, does not follow normal bell curve distribution.
- Ordinal (Severity 1, 2, 3)
There are 3 tests used in statistics that are tests of proportions including Z-test, Chi-square, and Fisher-exact. The Z-test is used when comparing the difference in population proportions between 2 groups. The Chi-square test is used when comparing the difference in population proportions between 2 or more groups or when comparing a group with a value. The Fisher-exact test is used when comparing the difference in population proportions of 2 very small groups. Small groups include total number in each group less than 30 or absolute number of occurrences in each group less than 5 when overall incidence is less than 20%.