Summary
Efficiency properties of the Cramér-von Mises, Anderson-Darling, Watson, and DeWet-Venter statistics for assessing normality are investigated. For these statistics, the approximate slopes are determined, and the equivalence of ratios of limiting approximate slopes to limiting Pitman efficiencies is established. From relative efficiency comparisons, the Cramér-von Mises and Watson statistics perform rather poorly; choice between the Anderson-Darling and DeWet-Venter statistics should be made on the basis of anticipated alternatives.
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Koziol, J.A. Relative efficiencies of goodness of fit procedures for assessing univariate normality. Ann Inst Stat Math 38, 485–493 (1986). https://doi.org/10.1007/BF02482535
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DOI: https://doi.org/10.1007/BF02482535