Ability of goodness-of-fit tests to detect deviations from normality: the case of symmetric distributions with low values of excess kurtosis

The aim of this article is to verify the ability of goodness-of-fit tests (GoFTs) to detect deviations from normality. A very special case was considered: when the deviation from normality is obtained by means of symmetric distributions with low values of excess kurtosis. The first step in fulfilling the aim was to collect a set of normality-oriented tests that the source literature, especially the recent publications, recommends for use. The second step was to create a family of symmetric distributions with non-constant excess kurtosis, i.e. alternatives. Formulas for calculating the values of excess kurtosis are provided for each distribution. A relevant similarity measure was applied to compare the alternatives with the normal distribution. The third step involved carrying out a Monte Carlo simulation. The study used 20 GoFTs and 30 alternatives. The obtained results indicate that the considered GoFTs detect deviation from normality in distributions of positive excess kurtosis much better than those of negative excess kurtosis. The paper presents a set of recommended GoFTs most useful for the discussed purpose.