One-Proportion z-test

One-proportion z-test is a large-sample test of whether the proportion of a binary outcome in one sample differs from a hypothesised population proportion, using the normal approximation to the binomial distribution.

일표본 비율 z검정은 이항분포의 정규근사를 이용하여 한 표본에서 이분형 결과의 비율이 가정한 모집단 비율과 다른지를 검정하는 대표본 검정이다.

How do I test whether the share of yes responses in my sample differs from a target percentage?

표본에서 '예'라고 답한 비율이 목표 비율과 다른지 어떻게 검정하나요?

The one-proportion z-test compares an observed sample proportion with a hypothesised value, such as 50% or a published benchmark, using a normal approximation to the binomial distribution. It is appropriate when the expected numbers of successes and failures are both reasonably large; otherwise the exact binomial test is safer.

When to use One-Proportion z-test

• One binary variable and a hypothesised proportion to compare it with
• Large samples where expected successes and failures are both at least about 10
• Reporting a sample proportion with a confidence interval

When to use something else

• Small samples or proportions near 0 or 1: use the exact binomial test
• Comparing proportions between two independent groups: use the chi-square test or a two-proportion z-test

Assumptions and requirements

• Binary outcome, with the higher of the two values counted as the success
• Independent observations
• Sample large enough for the normal approximation (np and n(1 − p) of about 10 or more)

What the analysis reports

• z statistic (standard error based on the hypothesised proportion p0) and two-sided p-value
• Sample proportion and number of successes
• Hypothesised proportion p0 (0.5 unless set)
• 95% Wilson confidence interval for the proportion

How to report it

A one-proportion z-test indicated that the proportion of [outcome] ([value], 95% CI [[value], [value]]) differed significantly from [p0], z = [value], p = [value].

Related methods

• Exact Binomial Test
• Chi Square Test
• One-Sample t-test

Run One-Proportion z-test on Quorant