Key Concepts

• The null hypothesis is that there is no association between the two categorical variables. The alternative hypothesis is that there is an association between the two categorical variables.
• The degrees of freedom is $(r – 1)(c – 1)$, where $r$ is the number of rows in the contingency table and c is the number of columns in the contingency table.
• The expected count for each cell is found by taking the row total times the column total and dividing 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 chi-square test statistic is the sum of $\frac{(\mathrm{Observed} \ - \ \mathrm{Expected})^2}{\mathrm{Expected}}$ for each cell in the contingency table.

Glossary

Chi-square test of independence: a type of hypotheses test to determine if there is an association between two categorical variables

Contingency Table: a table that displays sample values for two different factors that may be dependent or contingent on one another; it facilitates determining conditional probabilities