Comparisons of various types of normality tests

By Bee Wah Yap, Chiaw-Hock Sim. 2011

820 citations recorded by the source corpus.

Normality tests can be classified into tests based on chi-squared, moments, empirical distribution, spacings, regression and correlation and other special tests. This paper studies and compares the power of eight selected normality tests: the Shapiro–Wilk test, the Kolmogorov–Smirnov test, the Lilliefors test, the Cramer–von Mises test, the Anderson–Darling test, the D'Agostino–Pearson test, the Jarque–Bera test and chi-squared test. Power comparisons of these eight tests were obtained via the Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric short-tailed, symmetric long-tailed and asymmetric distributions. Our simulation results show that for symmetric short-tailed distributions, D'Agostino and Shapiro–Wilk tests have better power. For symmetric long-tailed distributions, the power of Jarque–Bera and D'Agostino tests is quite comparable with the Shapiro–Wilk test. As for asymmetric distributions, the Shapiro–Wilk test is the most powerful test followed by the Anderson–Darling test.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6c30253f48adf517865719f8d63d41e5e6d4f557

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Citations in the corpus

Computation of Probability Associated with Anderson–Darling Statistic (2018, methodology): “The comparisons between different goodness-of-fit tests is frequently conducted by comparing their power [37,38], using or not confidence intervals [39], distribution of p-values [40], or ROC (receiver operating characteristic) analysis [32].”
Shapiro–Francia test compared to other normality test using expected p-value (2015, background): “The SW test has been shown by others to have the best power over a wide range of symmetric distributions, however, in those studies, the SF test was not investigated.[1,2] This study also contradicts a study that observed the JB test to have the highest power compared to the SW, SF for the logistic ”
Decline in Mobility: Public Transport in Poland in the time of the COVID-19 Pandemic (2020, methodology): “The Shapiro-Wilk test is the most powerful normality test that can be also applied for small sample size and for all levels of skewness and kurtosis of distributions (Yap and Sim 2011).”