chi-square (χ²) test and Chi-square distribution

#statistics #datascience #chisquare A chi-square (χ²) test is a statistical method used to evaluate relationships between categorical variables by comparing observed data frequencies against the expected frequencies predicted under a null hypothesis. By calculating the squared differences between observed and expected outcomes across categories and dividing them by the expected values, the test generates a statistic that indicates whether deviations occur purely by chance. It primarily exists as a Goodness-of-Fit test to see if a single variable matches a known distribution, or as a Test of Independence to determine if a significant association exists between two distinct variables. Ultimately, a resulting p-value below 0.05 allows researchers to reject the null hypothesis, confirming a statistically significant pattern or relationship in the data.