One- and two-proportion tests

Learning objectives

• Compare a proportion with a target or between groups.
• Check expected count assumptions.
• Distinguish defects from defective units.

Structure

• One-proportion H0: p = target.
• Two-proportion H0: p1 − p2 = 0.
• Independent binary observations at the unit level.
• Adequate expected counts; otherwise use exact methods.

Garment-factory example

Test final defective rate against a 2% target, or compare needle-damage occurrence between two fabric constructions.

Method

1. Define success/failure at unit level.
2. Count units, not observations from the same bundle repeatedly.
3. Calculate rate and CI in a free spreadsheet.
4. Assess operational effect against the CTQ.

Common mistakes

• Feeding defects-per-garment counts to a proportion test.
• Repeated units from the same bundle treated as independent.