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. Author manuscript; available in PMC: 2018 Apr 9.
Published in final edited form as: Aust N Z J Stat. 2017 Mar 1;59(1):119–135. doi: 10.1111/anzs.12183

Table 3.

Power of the tests with statistics P, M, W, and G (100 000 simulated values each) at nominal size α = 0.05, for d = 3, k = 3, (n1, n2, n3) = (20, 30, 40), two equal mean directions and one separated by δ = 5, 10, 15, 20, 25, 30, 35, 40 degrees, and ρ = 0.45, 0.60, 0.75, 0.85.

δ ρ = 0.45 ρ = 0.60


P M W G P M W G
5 0.06 0.07 0.09 0.06 0.06 0.06 0.07 0.07
10 0.07 0.09 0.12 0.08 0.10 0.10 0.11 0.11
15 0.10 0.12 0.16 0.11 0.17 0.17 0.18 0.18
20 0.15 0.18 0.22 0.16 0.27 0.28 0.30 0.29
25 0.22 0.25 0.30 0.23 0.42 0.42 0.45 0.44
30 0.30 0.34 0.39 0.32 0.58 0.58 0.61 0.60
35 0.40 0.44 0.50 0.42 0.72 0.73 0.75 0.74
40 0.50 0.54 0.61 0.52 0.85 0.85 0.87 0.86

δ ρ = 0.75 ρ = 0.85


P M W G P M W G

5 0.07 0.07 0.07 0.08 0.10 0.09 0.10 0.10
10 0.16 0.15 0.16 0.17 0.27 0.27 0.27 0.29
15 0.32 0.31 0.32 0.34 0.58 0.58 0.58 0.60
20 0.55 0.54 0.55 0.57 0.85 0.85 0.85 0.86
25 0.76 0.76 0.76 0.78 0.97 0.97 0.97 0.97
30 0.91 0.90 0.91 0.91 1.00 1.00 1.00 1.00
35 0.97 0.97 0.97 0.98 1.00 1.00 1.00 1.00
40 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00