Plots and tests for symmetry

Abstract

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with the power of the Shapiro–Wilk statistic.