Anderson-Darling Normality Test
Also known as: Anderson-Darling Normallik Testi, A-squared test, AD test, Anderson-Darling goodness-of-fit test
The Anderson-Darling test is an empirical distribution function (EDF) goodness-of-fit test, introduced by Anderson and Darling in 1952, that checks whether a continuous sample comes from a specified distribution such as the normal, exponential, or Weibull. By weighting deviations more heavily in the tails, it detects departures in the distribution's extremes more powerfully than the Kolmogorov-Smirnov test.
Key highlights
- More powerful than the Kolmogorov-Smirnov test at detecting departures in the distribution's tails, because deviations there receive extra weight.
- Flexible: applies not only to normality but also to exponential, Weibull, and other distribution checks.
- Simple to run and easy to interpret as a single goodness-of-fit statistic with a p-value.
Intuition
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How it works
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When to use it
Use the Anderson-Darling test when you have a single continuous variable and need to check whether it follows a normal (or other named) distribution, for example as an assumption check before a t-test, ANOVA, or regression. It needs at least about 8 observations to be meaningful and is most informative from roughly n ≥ 10 upward; below n = 5 a normality test is essentially uninformative. Reach for it instead of Kolmogorov-Smirnov when you care about tail behaviour, and consider Shapiro-Wilk for very small samples where it tends to have higher power.
Strengths & limitations
- More powerful than the Kolmogorov-Smirnov test at detecting departures in the distribution's tails, because deviations there receive extra weight.
- Flexible: applies not only to normality but also to exponential, Weibull, and other distribution checks.
- Simple to run and easy to interpret as a single goodness-of-fit statistic with a p-value.
- Statistical power is low in very small samples (n < 10), where Shapiro-Wilk is usually preferred.
- With fewer than 5 observations a normality test is essentially meaningless.
- Like all omnibus normality tests it becomes hypersensitive in very large samples, flagging trivial, practically harmless departures as significant.
Common pitfalls
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Applications
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Frequently asked
How is Anderson-Darling different from Kolmogorov-Smirnov?
Both compare the empirical distribution to a candidate distribution, but Kolmogorov-Smirnov uses the single largest gap and treats the centre and tails equally, while Anderson-Darling integrates the squared gap with a weight that grows toward the tails. This makes Anderson-Darling more powerful at catching tail departures such as heavy tails or extreme outliers.
What sample size do I need?
The test needs at least about 8 observations and becomes more trustworthy from roughly n ≥ 10. With n below 5 a normality test is essentially uninformative; in such small samples Shapiro-Wilk or a permutation-based approach is preferable.
What does a significant result mean?
A small p-value (large A²) is evidence that the data do not follow the assumed distribution. For a normality test that means the data depart from normal, often in the tails. In very large samples even trivial departures turn significant, so pair the test with a Q-Q plot to judge whether the deviation matters.
Can it test distributions other than the normal?
Yes. The same A² statistic applies to other distributions, including the exponential and Weibull, as long as you use the critical values appropriate for that distribution rather than the normal cut-offs.
Sources
- 1.Anderson, T. W., & Darling, D. A. (1952). Asymptotic Theory of Certain 'Goodness of Fit' Criteria Based on Stochastic Processes. The Annals of Mathematical Statistics, 23(2), 193-212.
- 2.Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association, 69(347), 730-737.
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ScholarGate. (2026, June 1). Anderson-Darling Test. ScholarGate. https://scholargate.app/statistics/anderson-darling-test