Anderson-Darling Test

Anderson-Darling test is a goodness-of-fit test of whether a sample comes from a normal distribution, giving more weight to discrepancies in the tails than the Kolmogorov-Smirnov test does.

앤더슨-달링 검정은 표본이 정규분포에서 나왔는지를 판단하는 적합도 검정으로, 콜모고로프-스미르노프 검정보다 분포 꼬리 부분의 차이에 더 큰 가중치를 둔다.

How do I test normality in a way that is sensitive to heavy or light tails?

분포의 꼬리 부분까지 민감하게 정규성을 검정하려면 어떻게 하나요?

The Anderson-Darling test compares the empirical cumulative distribution of a continuous variable with a fitted normal distribution, and a significant A² statistic indicates a departure from normality. It weights the tails more heavily than the Kolmogorov-Smirnov test, so it is often preferred when outliers or tail behaviour matter.

When to use Anderson-Darling Test

• Checking normality of a continuous variable or of model residuals
• Tail behaviour matters, for example in risk, reliability or measurement-error data
• Moderate samples where a formal normality test is requested alongside a Q-Q plot

When to use something else

• Small samples where the most powerful general normality test is wanted: use the Shapiro-Wilk test
• Discrete or heavily tied data: use the chi-square goodness-of-fit test

Assumptions and requirements

• Independent observations
• Continuous variable without many tied values
• Mean and standard deviation estimated from the sample, with the p-value adjusted for this estimation

What the analysis reports

• A² statistic
• p-value with the small-sample adjustment for estimated parameters
• Critical value at the 5% level
• Histogram and normal Q-Q plot

How to report it

An Anderson-Darling test indicated that [variable] did not deviate significantly from normality, A² = [value], p = [value].

Related methods

• Shapiro-Wilk Test
• Kolmogorov-Smirnov Test
• Jarque-Bera Test

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