Chi-square tests for homogeneity and independence

Learning objectives

Choose between a chi-square test for homogeneity, which compares the distribution of one categorical variable across several populations or treatment groups, and a chi-square test for independence, which looks for an association between two categorical variables in one population, from the way the data were collected

State the null and alternative hypotheses of a chi-square test for homogeneity or for independence in context

Calculate expected counts as row total × column total ÷ table total, and check the conditions: random samples or random assignment, the 10% condition, and every expected count at least 5

Calculate the chi-square statistic Σ (observed − expected)² ÷ expected, state the degrees of freedom (rows − 1)(columns − 1), and find the p-value as the area to the right of the statistic

Write a conclusion in context by comparing the p-value with the significance level, and use the cells that contribute most to the statistic to describe how the data depart from the null hypothesis