Key Concepts

• The null hypothesis is that the distribution of the two populations is the same. The alternative hypothesis is that the distribution of the two populations is not the same.
• The expected count for each cell is found by taking the row total times the column total and dividing it by the grand total.
• The expected counts need to be 5 or more to conduct a chi-square test and are NOT rounded to the nearest whole number.
• The degrees of freedom for a chi-square test of homogeneity for two populations is [latex]k – 1[/latex], where [latex]k[/latex] is the number of response values.
• The chi-square test statistic is the sum of [latex]\frac{(\mathrm{Observed} \ - \ \mathrm{Expected})^2}{\mathrm{Expected}}[/latex] for each category.

Glossary

Chi-square test of homogeneity: a type of hypotheses test to determine if data is two separate populations follow the same categorical distribution