Visualizing Type II Error in Normality Tests |
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Authors: | José A. Sánchez-Espigares Pere Grima Lluís Marco-Almagro |
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Affiliation: | Department of Statistics and Operational Research, Universitat Politècnica de Catalunya - Barcelona Tech, Barcelona, Spain |
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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. |
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Keywords: | Normality test SEPD distributions Teaching statistics Type II error Visualizing information |
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