4.3.3—Independence test

For a contingency table, H₀ states that the two categorical variables are independent. Expected count in a cell is row total × column total ÷ grand total, then use the chi-squared statistic.

Use counts rather than percentages, check expected-count conditions, and describe any rejection as evidence of association—not proof of causation.

If a row total is 40, a column total is 30 and the grand total is 100, the independent expected count is 12. Compare the observed cell with 12.

Independence is not mutual exclusivity, and a significant association can be produced by confounding or sampling bias.