Goodness-of-Fit Testing

The Anderson–Darling Test

From a weighted integral to the two familiar discrete formulas

Maruthy Pannala, PhD • Published July 21, 2026 • 20 min read • Difficulty: Intermediate

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About This Article

A step-by-step derivation of the Anderson–Darling goodness-of-fit statistic, starting from the defining weighted integral and ending at the two discrete formulas used in software and textbooks. Along the way it shows exactly where the odd-number weights, the tail-sensitivity, and the mysterious −n term actually come from — and proves the two commonly cited discrete forms are algebraically identical, not different statistics.

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Sources & Further Reading

What this article was researched from.

•T.W. Anderson and D.A. Darling, "Asymptotic Theory of Certain 'Goodness of Fit' Criteria Based on Stochastic Processes," Annals of Mathematical Statistics, 23(2), 1952, pp. 193–212 — the original paper introducing the test

How to Cite This Article

Plain text: Pannala, M. (2026). "The Anderson–Darling Test: From a Weighted Integral to the Two Familiar Discrete Formulas." StatisticsCorner™. https://www.statisticscorner.com/articles/anderson-darling-test

APA: Pannala, M. (2026). The Anderson–Darling test: From a weighted integral to the two familiar discrete formulas. StatisticsCorner™. https://www.statisticscorner.com/articles/anderson-darling-test

@misc{pannala2026andersondarling,
  author       = {Pannala, Maruthy},
  title        = {The Anderson-Darling Test: From a Weighted Integral to the Two Familiar Discrete Formulas},
  year         = {2026},
  howpublished = {StatisticsCorner™},
  url          = {https://www.statisticscorner.com/articles/anderson-darling-test}
}