论文信息 - A Suggestion for Using Powerful and Informative Tests of Normality

A Suggestion for Using Powerful and Informative Tests of Normality

Abstract For testing that an underlying population is normally distributed the skewness and kurtosis statistics, √b 1 and b 2, and the D'Agostino–Pearson K 2 statistic that combines these two statistics have been shown to be powerful and informative tests. Their use, however, has not been as prevalent as their usefulness. We review these tests and show how readily available and popular statistical software can be used to implement them. Their relationship to deviations from linearity in normal probability plotting is also presented.

R. D'Agostino | A. Belanger

[1] K. Pearson. Contributions to the Mathematical Theory of Evolution , 1894 .

[2] K. Pearson. Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material , 1895 .

[3] F. David,et al. Statistical Estimates and Transformed Beta-Variables. , 1960 .

[4] S. Shapiro,et al. An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[5] R. D'Agostino. Transformation to normality of the null distribution of g1 , 1970 .

[6] R. D'Agostino. An omnibus test of normality for moderate and large size samples , 1971 .

[7] D. A. Lury,et al. Statistical Methods for Research Workers , 1930, Nature.

[8] E. S. Pearson,et al. Tests for departure from normality. Empirical results for the distributions of b2 and √b1 , 1973 .

[9] F. J. Anscombe,et al. Distribution of the Kurtosis Statistic b2 for Normal Samples. , 1983 .

[10] Ralph B. D'Agostino,et al. Goodness-of-Fit-Techniques , 2020 .

[11] K. Balanda,et al. Kurtosis: A Critical Review , 1988 .