Chi-squared test

A statistical test that compares observed categorical counts with expected frequencies using a chi-squared statistic. Its result assesses whether discrepancies are larger than chance variation predicts.

Pearson's chi-squared statistic: A sum of squared differences between observed and expected counts, each divided by its expected count. This statistic turns count discrepancies into the test's numerical measure of evidence.
Chi-squared goodness-of-fit test: A test of whether observed counts across categories match specified proportions. It applies the statistic to one categorical variable and a stated distribution.
Null hypothesis: A statistical hypothesis specifying a reference condition, such as no association or a stated distribution. The expected frequencies are calculated from the condition the test evaluates.
Fisher's exact test: A test of association in contingency tables that calculates probabilities from fixed margins rather than relying on a large-sample approximation. It is often preferred to the asymptotic chi-squared test for sparse 2×2 tables.
Chi-squared distribution: A family of probability distributions formed by sums of squared independent standard normal variables. Under the null hypothesis, the statistic is compared with this distribution.
Pearson's chi-squared test of independence: A test of whether two categorical variables are statistically independent in a contingency table. It tests whether the joint counts depart from independence expectations.
Categorical variable: A variable whose values identify groups or categories rather than measured quantities. The test operates on counts classified into categories.
G-test: A likelihood-ratio test for categorical counts based on the logarithm of observed-to-expected frequency ratios. It tests similar hypotheses with a different statistic that approaches the chi-squared distribution.
Degrees of freedom: The number of independent values that can vary in a statistical calculation after constraints are applied. They select the chi-squared distribution used to calculate the p-value.
Chi-squared test of homogeneity: A test of whether categorical outcome proportions are the same across multiple populations. It compares category distributions across groups using a contingency table.

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