A proportion test is a statistical test used to determine whether the proportion of successes in a sample differs significantly from a known value or whether two or more groups have different proportions. When sample sizes are large, normal approximation methods like the one-sample or two-sample proportion z-tests are typically used. When sample sizes are small or the success/failure counts are very low, exact methods like the binomial exact test (for one proportion) or Fisher’s exact test (for two proportions) are preferred because they do not rely on normality assumptions. For comparisons involving more than two groups, a chi-square test for independence is commonly used to assess whether proportions differ across categories.
For example, researchers might want to test whether a flu vaccine reduces infection rates. Suppose in a clinical trial, 10% of vaccinated individuals and 20% of unvaccinated individuals became infected with the flu. A two-sample proportion test could be used to compare the infection rates between the two groups. If the sample sizes were large enough, a two-proportion z-test would be appropriate. If the sample sizes were small, Fisher’s exact test would provide a more accurate p-value.
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