Invalid Permutation Tests

Table 3

Simulated power of tests.

𝜃	Null	Conventional	Adjusted	Orthogonal
0	0.053	0.053	0.067	0.061
0.1	0.112	0.1	0.132	0.123
0.2	0.212	0.186	0.221	0.212
0.3	0.337	0.283	0.34	0.316
0.4	0.487	0.426	0.487	0.47
0.5	0.643	0.574	0.645	0.619
0.6	0.759	0.726	0.768	0.756
0.7	0.857	0.835	0.876	0.862
0.8	0.924	0.913	0.94	0.929
0.9	0.963	0.965	0.978	0.974
1	0.984	0.986	0.991	0.991
1.1	0.996	0.995	0.996	0.996
1.2	0.997	0.998	0.999	0.999
1.3	0.999	0.999	1	0.999

Powers of the tests based on the estimators in Table 1.