Abstract
The problem of testing for normality is fundamental in both theoretical and empirical statistical research. This paper compares the performances of eighteen normality tests available in literature. Since a theoretical comparison is not possible, MonteCarlo simulation were done from various symmetric and asymmetric distributions for different sample sizes ranging from 10 to 1000. The performance of the test statistics are compared based on empirical Type I error rate and power of the test. The simulations results show that the Kurtosis Test is the most powerful for symmetric data and Shapiro Wilk test is the most powerful for asymmetric data.
Highlights
Many of the statistical procedures including correlation, regression, t tests, and analysis of variance are based on the assumption that the data follows a normal distribution or a Gaussian distribution
We have considered eighteen different tests of normality comprising the most popular along with some of the recently proposed tests
The type I error rate is the rate of rejection of the hypothesis of normality for data from the normal distribution while the power of the test is the rate of rejection of normality hypothesis for data generated from a non-normal distribution
Summary
Many of the statistical procedures including correlation, regression, t tests, and analysis of variance are based on the assumption that the data follows a normal distribution or a Gaussian distribution. Under which the statistical procedures are developed, do not hold the conclusion made using these procedures may not be accurate. Checking the validity of the normality assumption in a statistical procedure can be done in two ways: empirical procedure using graphical analysis and the goodnessof-fit tests methods. The goodness-of-fit tests which are formal statistical procedures for assessing the underlying distribution of a data set are our focus here. These tests usually provide more reliable results than graphical analysis. In this article we review most commonly used methods for normality test and compare them using power and observed significance value
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