Visualizing Type II Error in Normality Tests

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 expon...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The American statistician 2018-04, Vol.72 (2), p.158-162
Hauptverfasser: Sánchez-Espigares, José A., Grima, Pere, Marco-Almagro, Lluís
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:0003-1305
1537-2731
DOI:10.1080/00031305.2016.1278035