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Testing the Normality of Several Independent Samples Using the Anderson‐Darling Statistic

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  • A. N. Pettitt

Abstract

In a recent paper, the Anderson‐Darling goodness‐of‐fit statistic was shown to be a powerful omnibus test of normality when the mean and variance are unknown. In this paper, tables for calculating small sample percentage points of the statistic are given. The percentage points are derived from smoothing empirical percentage points using the asymptotic percentage points. These percentage points are then used to make a joint assessment of normality based on several independent samples using Fisher's method. Empirical power comparisons are then made with the method based on the Shapiro‐Wilk statistic. There is seen to be little difference between the methods based on the two different statistics.

Suggested Citation

  • A. N. Pettitt, 1977. "Testing the Normality of Several Independent Samples Using the Anderson‐Darling Statistic," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(2), pages 156-161, June.
    • Handle: RePEc:bla:jorssc:v:26:y:1977:i:2:p:156-161
    DOI: 10.2307/2347023
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    Cited by:

    1. Arzu Ozkaya & Zuhal Akyurek, 2019. "Evaluating the use of bias-corrected radar rainfall data in three flood events in Samsun, Turkey," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 98(2), pages 643-674, September.
    2. Heuts, R.M.J. & Rens, P.J., 1977. "A Monte Carlo study to obtain the percentage points of some goodness of fit tests in testing normality, when observations satisfy a certain low order ARMA-scheme," Other publications TiSEM 90cad915-010b-4c3f-9697-9, Tilburg University, School of Economics and Management.
    3. Fernández de Marcos Giménez de los Galanes, Alberto & García Portugués, Eduardo, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    5. Max Chacón & José Luis Jara & Ronney B Panerai, 2014. "A New Model-Free Index of Dynamic Cerebral Blood Flow Autoregulation," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-11, October.

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