Shapiro-Wilk Test

The Shapiro-Wilk test is a hypothesis test of whether a sample of a continuous variable comes from a normally distributed population, based on how well the ordered values match expected normal order statistics.

샤피로-윌크 검정은 연속형 변수의 표본이 정규분포를 따르는 모집단에서 나왔는지를, 정렬된 관측값이 정규 순서통계량의 기댓값과 얼마나 일치하는지로 판단하는 가설검정이다.

How do I test whether my data are normally distributed?

내 데이터가 정규분포를 따르는지 어떻게 검정하나요?

The Shapiro-Wilk test checks whether a continuous variable departs from a normal distribution, with a significant result indicating non-normality. It fits small to moderate samples and is usually read alongside a Q-Q plot, because in large samples it flags trivial departures.

When to use Shapiro-Wilk Test

• Checking normality of a continuous outcome before a t test or ANOVA
• Checking normality of regression or ANOVA residuals
• Small to moderate samples where a formal normality test is requested

When to use something else

• Very large samples where trivial deviations become significant; rely on Q-Q plots and skewness/kurtosis instead
• Testing fit to a non-normal distribution; use the Kolmogorov-Smirnov or Anderson-Darling test

Assumptions and requirements

• Independent observations
• Continuous variable
• Null hypothesis is that the population is normal

What the analysis reports

• W statistic
• p-value
• Q-Q plot
• Skewness and kurtosis as supporting descriptives

How to report it

A Shapiro-Wilk test indicated that [variable] did not deviate significantly from normality, W = [value], p = [value].

Related methods

• Kolmogorov-Smirnov Test
• Anderson-Darling Test
• Q-Q Plot

Run Shapiro-Wilk Test on Quorant