Addendum to “An asymptotically distribution-free test of symmetry ” [Journal of Statistical Planning and Inference 137

The authors note that the symbols which appear in the key to Fig. 6 are not the ones used within its panels, and that the scales used on the vertical axes of Figs. 5 and 6 are not the same. The corrected versions of Figs. 5 and 6 are given here. Since the classical test is not the best performing test of symmetry about an unknown value, it is worth comparing our test to the SK-based test by Cabilio and Masaro (1996) and the test of Boos (1982). The results of the simulation study of the test by Cabilio and Masaro are presented in Table 3 and Fig. 7. From the simulations we note that our test T is more powerful than the test SK for the close to Cauchy alternatives (except when n = 20 and a is large). Moreover, for the Cauchy distribution the actual Preprint submitted to Elsevier Science 29 August 2008 level of the SK-based test appears to increase with sample size, and the actual level is about twice the nominal level when n = 500. For the other alternatives considered in the simulation study, the test SK is the more powerful test of the two. The test suggested by Boos (1982) cannot be recommended for the Cauchy case, because the true level of the test is as high as 0.33 when the nominal level is 0.05 (and n = 20 or 50). Therefore, we decided not to include the test by Boos in the simulation study