New confidence bands in Q–Q Plots to detect non-normality

Abstract

We have developed a new method for including confidence bands in a Q–Q Plot to detect non-normality in a set of observations. We provide an algorithm to obtain the proposed confidence bands and also compare our method with others described in the literature such as Michel's acceptance region, Fox's bands, and the Shapiro–Wilk and Kolmogorov–Smirnov tests by means of a simulation study. A Normal Q–Q Plot is used to check whether a set of sample observations derives from a normal distribution. If the plotted points are more or less rectilinear then the hypothesis of normality cannot be rejected. These techniques are more intuitive and more easily interpretable than analytical ones, but their disadvantage lies in the fact that the conclusions arrived at may be influenced by the subjectivity of the observer. Confidence bands are used to avoid this drawback and ensure the objectivity of the conclusions regardless of the observer.

Keywords:

• normal Q–Q Plot
• confidence bands
• goodness of fit
• non-normality test

2010 AMS Subject Classifications::

• 62-09
• 62-07
• 62G10
• 62G30