Two Proportion Z Test

When to use Two Proportion Z Test?

• Response variable is categorical with two outcomes

• The explanatory variable is categorical with two two independent groups

• Compare proportions from two different populations

Conditions (Assumption)

1. Categorical variable

2. Independent random sample

3. Success-Failure Condition

   1. The numbers of successes or failures must be larger than 10 for one tailed

   2. The numbers of successes or failures must be larger than 5 for two tailed

4. Independence Condition: population size larger than or greater to 20 x sample size

Two Proportion Z Confidence Interval Formula

Step 1: Hypotheses

Null: Ho: p1-p2=0

Alt: Ho: Right tailed (p1 - p2 > 0)

Left tailed (p1 - p2 <0)

Two Tailed: (p1-p2 ≠ 0)

Step 2: Test Statistic

Use pooled proportion

Step 3: P Value & Decision Rule

P value ≤ alpha: reject null

P value ≥ alpha: Do not reject null