D'Agostino-Pearson Normality Test

The D'Agostino-Pearson test is an omnibus normality test that combines standardized sample skewness and kurtosis into a chi-square statistic with two degrees of freedom.

D'Agostino-Pearson 검정은 표본 왜도와 첨도를 각각 표준화한 z 값을 제곱해 더한 K² 통계량을 자유도 2 카이제곱분포와 비교하는 종합 정규성 검정이다.

How can I test normality and also see whether the problem is skewness or heavy tails?

정규성을 검정하면서 문제가 비대칭인지 두꺼운 꼬리인지도 알 수 있는 방법이 있나요?

The D'Agostino-Pearson test transforms sample skewness and kurtosis into approximately standard normal z scores and sums their squares into K², which is compared with a chi-square distribution on 2 df. The two component z scores show whether a departure comes from asymmetry, tail weight, or both.

When to use D'Agostino-Pearson Normality Test

• You want an omnibus normality test with diagnostic components.
• The sample has at least about 20 observations.
• Skewness or tail behavior matters for the planned analysis.

When to use something else

• The sample is very small (under 20); use the Shapiro-Wilk test instead.
• You need to test against a fully specified distribution; use the Kolmogorov-Smirnov or Anderson-Darling test instead.

Assumptions and requirements

• Observations are independent and identically distributed.
• The sample is large enough for the normal approximations to skewness and kurtosis.

What the analysis reports

• K² statistic and p-value
• Skewness z and p-value
• Kurtosis z and p-value
• Sample skewness and excess kurtosis

How to report it

The D'Agostino-Pearson omnibus test [did/did not] indicate a departure from normality, K²(2) = [value], p = [value] (skewness z = [value], kurtosis z = [value]).

Related methods

• Shapiro-Wilk Test
• Jarque-Bera Test
• Anderson-Darling Test

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