Graphical comparison of normality tests for unimodal distribution data

ABSTRACT

A methodology is proposed to compare the power of normality tests with a wide variety of alternative unimodal distributions. It is based on the representation of a distribution mosaic in which kurtosis varies vertically and skewness horizontally. The mosaic includes distributions such as exponential, Laplace or uniform, with normal occupying the centre. Simulation is used to determine the probability of a sample from each distribution in the mosaic being accepted as normal. We demonstrate our proposal by applying it to the analysis and comparison of some of the most well-known tests.

KEYWORDS:

• Goodness-of-fit
• test power
• graphical techniques
• comparing normality tests
• Anderson-Darling
• Shapiro-Wilk

Disclosure statement

No potential conflict of interest was reported by the authors.