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Biometrika 1977 64(2):231-246; doi:10.1093/biomet/64.2.231
© 1977 by Biometrika Trust
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Tests for departure from normality: Comparison of powers

E. S. PEARSON, R. B. D‘‘'AGOSTINO and K. O. BOWMAN

Department of Statistics and Computer Science, University College London
Department of Mathematics, Boston University Massachusetts
Computer Science Division, Union Carbide Corporation Oak Ridge, Tennessee

In the present paper we present results of a large scale simulation study of the power of various tests of normality. We follow the procedure adopted by Shapiro, Wilk & Chen of applying a considerable variety of tests to samples drawn from a wide range of nonnormal populations. We, however, consider some additional tests, emphasize the difference between ‘omnibus’ and ‘directional’ tests and show the difficulty of applying testa based on ordered observations, such as the Shapiro-Wilk test, when in practice the sample data may contain ‘ties’ resulting from grouping or rounding.

Key Words: Comparison of power • Computer simulation • Departure from normality • Directional test • Goodness of fit • Multiple ties • Omnibus test


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