Two Proportion z Test

The two proportion z test compares the success proportions of two independent groups using a pooled-proportion standard error and a normal approximation to the sampling distribution.

두 비율 z 검정은 합동 비율로 구한 표준오차와 정규근사를 이용해 두 독립 집단의 성공 비율을 비교한다.

Is the conversion rate in group A significantly different from that in group B?

A 집단과 B 집단의 전환율이 통계적으로 다른가요?

The two proportion z test divides the difference between sample proportions by its standard error under the null hypothesis of a common proportion. Its square equals the Pearson chi-square for the 2 × 2 table, and a Newcombe hybrid score interval describes the size of the difference.

When to use Two Proportion z Test

• A binary outcome is compared between two independent groups.
• Expected counts of successes and failures are at least five in each group.
• A confidence interval for the risk difference is needed.

When to use something else

• Expected counts are small; use Fisher's exact test.
• The two proportions come from the same participants; use McNemar's test.

Assumptions and requirements

• Observations are independent within and between groups.
• Each observation is a binary outcome.
• Sample sizes are large enough for the normal approximation.

What the analysis reports

• z statistic
• p value
• Group proportions
• Difference with Newcombe confidence interval
• Cohen's h

How to report it

A two-proportion z test indicated that the proportion in group 1 ([x1]/[n1], [p1]) differed from that in group 2 ([x2]/[n2], [p2]), z = [z], p = [p], difference = [diff], 95% CI [[lower], [upper]].

Related methods

• Fisher's Exact Test
• Chi Square Test
• One-Proportion z-test

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