Table 3.

Simulation B: Empirical rejection frequencies (in $\mathrm{\%}$).

		LR	Rank test	Sign test	NN	ID-rank test
	Hollander	Bell and Haller	Snijders	Modarres	Modarres	Modarres
Contamination proportion 0 (i.e.  $H_0^{\ast }$ holds)
Permutation tests of bivariate symmetry (for individual pairs of variables)
1-2	0.053	0.055	0.046	0.057	0.054	0.058
1-3	0.046	0.052	0.051	0.049	0.049	0.050
2-3	0.055	0.044	0.053	0.053	0.052	0.051
Multivariate procedures
Fisher	0.060	0.052	0.051	0.053	0.050	0.057
Lipták	0.053	0.055	0.054	0.060	0.044	0.052
Tippett	0.051	0.048	0.053	0.052	0.052	0.052
B-Y	0.010	0.011	0.008	0.007	0.010	0.011
Bonferroni	0.015	0.019	0.013	0.014	0.016	0.020
Contamination proportion 0.1
Permutation tests of bivariate symmetry (for individual pairs of variables)
1-2	0.270	0.312	0.229	0.226	0.263	0.303
1-3	0.319	0.361	0.268	0.262	0.315	0.364
2-3	0.195	0.234	0.150	0.137	0.169	0.223
Multivariate procedures
Fisher	0.366	0.431	0.365	0.312	0.362	0.411
Lipták	0.327	0.359	0.313	0.290	0.314	0.376
Tippett	0.419	0.472	0.385	0.375	0.389	0.454
B-Y	0.049	0.051	0.046	0.033	0.047	0.052
Bonferroni	0.044	0.046	0.041	0.038	0.045	0.049
Contamination proportion 0.2
Permutation tests of bivariate symmetry (for individual pairs of variables)
1-2	0.708	0.765	0.692	0.678	0.723	0.797
1-3	0.771	0.815	0.734	0.730	0.779	0.832
2-3	0.270	0.310	0.245	0.263	0.276	0.332
Multivariate procedures
Fisher	0.764	0.818	0.713	0.712	0.769	0.826
Lipták	0.713	0.770	0.697	0.671	0.743	0.769
Tippett	0.814	0.855	0.756	0.730	0.813	0.867
B-Y	0.946	0.972	0.928	0.796	0.904	0.897
Bonferroni	0.962	0.980	0.941	0.848	0.925	0.941