Assessing the validity of a statistical distribution: some illustrative examples from dermatological research

Abstract

BACKGROUND: Assuming a statistical distribution is one of the key points before conducting a statistical analysis. Goodness-of-fit tests are used to assess the validity of an assumed statistical distribution. In dermatological research, the goodness-of-fit tests used are less powerful. AIM: We recommend the use of some specific goodness-of-fit tests for various distributions. A graphical technique called quantile-quantile plotting is introduced as an additional tool to assess the validity of an assumed distribution. We show why one should be careful in selecting a goodness-of-fit method by giving some relevant examples. METHODS: Goodness-of-fit tests for testing normal and non-normal distributions are introduced. Quantile-quantile plots were constructed, and we conducted a simulation study for testing normality. RESULTS: We found that the Shapiro-Wilk statistic is the most powerful test overall to test for normal distribution. Quantile-quantile plotting is a very effective graphical technique to identify a distribution for a dataset. CONCLUSION: The use of the Shapiro-Wilk test and quantile-quantile plotting is recommended for testing normality.