k-Sample Anderson-Darling Test
The k-sample Anderson-Darling test checks whether several independent samples come from the same distribution by comparing each sample's empirical distribution function with the pooled one, giving extra weight to the tails.
k 표본 Anderson-Darling 검정은 각 표본의 경험분포함수를 합친 분포와 비교하되 꼬리에 더 큰 가중을 주어, 여러 독립 표본이 같은 분포에서 나왔는지 판정하는 검정입니다.
Do the response-time distributions of my three groups differ in shape or tails, not just in their medians?
세 집단의 반응시간 분포가 중앙값뿐 아니라 모양이나 꼬리에서도 다른지 어떻게 검정하나요?
The Scholz-Stephens statistic sums weighted squared differences between each sample's empirical distribution function and the pooled distribution, with weights that emphasize the tails, and is standardized by its mean and variance under the null hypothesis. A large standardized value means at least one sample comes from a different distribution, whether the difference is in location, spread or tails.
When to use k-Sample Anderson-Darling Test
- You want to test whether two or more samples share the same distribution, not only the same median.
- Differences in the tails matter, for example for extreme values or reliability data.
- You want to check whether data from several batches or sites can be pooled.
When to use something else
- You only want to compare locations; use the Kruskal-Wallis test.
- The samples are paired or blocked; use the Friedman or Quade test.
Assumptions and requirements
- Samples are independent of each other and observations are independent within samples.
- The outcome is continuous; with ties the midrank version is used.
- Each sample has at least two observations.
What the analysis reports
- A2 statistic and standardized T statistic
- Interpolated p value (bounded to 0.001-0.25) and critical values
- Optional permutation p value
- Group sizes, means, medians and standard deviations
How to report it
A k-sample Anderson-Darling test showed that the distributions of [outcome] differed across the [k] groups, A2 = [value], T = [value], p = [value].
Related methods
Run k-Sample Anderson-Darling Test on Quorant
- Data you need
- a table (CSV or Excel) with an outcome variable and a grouping variable
- Price
- 250 credits for one analysis up to 10,000 rows (complexity level 2); larger or wider data costs more. Optional methodologist review: 1200 credits.
- Checking
- Checked by property tests in every deployment
- Before you pay
- A free pre-analysis diagnosis checks your data and gives an exact quote; nothing is deducted until you approve it.