Visualizing Type II Error in Normality Tests

José A. Sánchez-Espigares, Pere Grima and Lluís Marco-Almagro

The American Statistician, 2018, vol. 72, issue 2, 158-162

Abstract: A skewed exponential power distribution, with parameters defining kurtosis and skewness, is introduced as a way to visualize Type II error in normality tests. By varying these parameters a mosaic of distributions is built, ranging from double exponential to uniform or from positive to negative exponential; the normal distribution is a particular case located in the center of the mosaic. Using a sequential color scheme, a different color is assigned to each distribution in the mosaic depending on the probability of committing a Type II error. This graph gives a visual representation of the power of the performed test. This way of representing results facilitates the comparison of the power of various tests and the influence of sample size. A script to perform this graphical representation, programmed in the R statistical software, is available online as supplementary material.

Date: 2018
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DOI: 10.1080/00031305.2016.1278035

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