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Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

100%

Hanusz Z., Tarasińska J.

Biometrical Letters

2015

tom 52

nr 2

85-93

Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.

On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality

81%

Hanusz Z., Tarasińska J., Osypiuk Z.

Biometrical Letters

2012

tom 49

nr 2

159-175

The kurtosis-based tests of Mardia and Srivastava for assessing multivariate normality (MVN) are considered. The asymptotic standard normal distribution of their test statistics, under normality, is often misused for too small samples. The purpose of this paper is to suggest mean-and-variance corrected versions of the Mardia and Srivastava test statistics. Simulation studies evaluating both the true sizes and the powers of original and corrected tests against selected alternatives are presented and compared to the size and the power of the Henze-Zirkler test. The proposed corrected statistics have empirical sizes closer to a nominal significance level than the original ones. It is also shown that the corrected versions of the tests can be more powerful than the original ones.

Ograniczanie wyników

2 Biometrical Letters

2 Hanusz Z.

2 Tarasińska J.

1 Osypiuk Z.

1 2015

1 2012

Wyniki wyszukiwania

Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality