Chi-square association testing

Learning objectives

• Build a contingency table for two categorical variables.
• Check expected counts and interpret residuals.
• Distinguish association from causation.

Chi-square association

H0 is independence between the two categorical variables. Compare observed and expected counts; large discrepancies produce a large chi-square statistic.

Use counts (not percentages), independent observations, mutually exclusive categories and adequate expected counts.

Garment-factory example

Test whether defect-type distribution differs by production line, using counts (not percentages) per cell.

Method

1. Cross-tabulate raw counts.
2. Compute expected counts.
3. Run the test in a free tool.
4. Inspect standardised residuals to see which cells drive association.

Common mistakes

• Entering percentages instead of counts.
• Treating association as causation.