Visualizing Type II Error in Normality Tests

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.

KEYWORDS:

• Normality test
• SEPD distributions
• Teaching statistics
• Type II error
• Visualizing information

Supplementary Materials

An R script named “Visualizing Type II Error.R” is provided online as supplementary material. The script allows graphical representations as those shown in this article. Instructions on how to use the script are contained in the script code.