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Table 3 Estimated powers and type I error rates of ordered tests under significance level 0.05

From: Using the Bernoulli trial approaches for detecting ordered alternatives

Location parameter KTMB KTP JT MJT TM DP Location parameter KTMB KTP JT MJT TM DP
n1=4, n2=4, n3=4        n1=10, n2=10, n3=5       
Log-F (2,4.5)        Log-F (2,4.5)       
(0, 0, 0) 0.0492 0.0496 0.0489 0.0496 0.0494   (0, 0, 0) 0.0494 0.0481 0.0488 0.0494 0.0509  
(0, 0.25, 0.5) 0.1176 0.1243 0.1096 0.1243 0.1255 -6.29% (0, 0.25, 0.5) 0.1491 0.1542 0.1566 0.1554 0.1491 0%
(0.5, 0, 0.25) 0.0295 0.0344 0.0295 0.0344 0.0346 0.00% (0.25, 0.5, 0) 0.0209 0.022 0.0346 0.0316 0.0217 3.83%
(0.25, 0.75, 0) 0.021 0.029 0.0212 0.029 0.0236 0.95% (0.5, 0.75, 0) 0.0086 0.0094 0.0167 0.0143 0.0096 9.30%
Log-F (4.5, 4.5)        Log- F (4.5, 4.5       
(0, 0, 0) 0.0511 0.0521 0.0518 0.0521 0.0531   (0, 0, 0) 0.0492 0.0478 0.0501 0.0488 0.0512  
(0, 0.25, 0.5) 0.1533 0.1612 0.1447 0.1612 0.1604 -4.43% (0, 0.25, 0.5) 0.2079 0.2118 0.2181 0.217 0.2021 2.87%
(0.5, 0, 0.25) 0.0189 0.0259 0.0212 0.0259 0.0237 12.17% (0.25, 0.5, 0) 0.0207 0.0217 0.034 0.0303 0.0215 3.86%
(0.25, 0.75, 0) 0.0207 0.0246 0.0213 0.0246 0.0239 2.90% (0.5, 0.75, 0) 0.0058 0.0058 0.012 0.0093 0.006 0.00%
Log-F (10, 4.5)        Log-F (10, 4.5)       
(0, 0, 0) 0.0509 0.0523 0.0519 0.0523 0.0527   (0, 0, 0) 0.0488 0.0494 0.0517 0.0505 0.051  
(0, 0.25, 0.5) 0.1802 0.1961 0.1742 0.1961 0.1843 -2.22% (0, 0.25, 0.5) 0.2522 0.2634 0.27 0.268 0.2446 3.11%
(0.5, 0, 0.25) 0.016 0.021 0.0166 0.021 0.0192 3.75% (0.25, 0.5, 0) 0.0217 0.0195 0.0353 0.0302 0.024 -10.14%
(0.25, 0.75, 0) 0.0161 0.0196 0.0161 0.0196 0.0198 0.00% (0.5, 0.75, 0) 0.0064 0.0058 0.0119 0.0093 0.0076 -9.38%
n1=4, n2=4,        n1=8, n2=8,       
n3=4, n4=4        n3=8, n4=4       
Log-F (2,4.5)        Log-F (2,4.5)       
(0, 0, 0, 0) 0.0512 0.0519 0.0515 0.0519 0.0514   (0, 0, 0, 0) 0.0505 0.0484 0.0518 0.0507 0.0479  
(0, 0.25, 0.5, 0.75) 0.165 0.1806 0.188 0.1806 0.1615 2.17% (0, 0.25, 0.5, 0.75) 0.2042 0.2313 0.2408 0.2372 0.1915 6.67%
(0.75, 0, 0.25, 0.5) 0.0388 0.0388 0.0417 0.0388 0.0471 0.00% (0.5, 0.5, 0.5, 0) 0.0121 0.0152 0.0197 0.018 0.013 7.44%
(0.25, 0.75, 1.25, 0) 0.0225 0.0315 0.0313 0.0315 0.0276 22.67% (0.25, 0.5, 0.75, 0) 0.0258 0.0332 0.0641 0.0575 0.0283 9.69%
Log-F (4.5, 4.5)        Log-F (4.5,4.5)       
(0, 0, 0, 0) 0.0507 0.0503 0.0509 0.0503 0.0508   (0, 0, 0, 0) 0.0505 0.0487 0.0508 0.0477 0.048  
(0, 0.25, 0.5, 0.75) 0.2242 0.2513 0.2606 0.2513 0.2143 4.62% (0, 0.25, 0.5, 0.75) 0.2987 0.3358 0.3572 0.3562 0.2795 6.87%
(0.75, 0, 0.25, 0.5) 0.0297 0.0282 0.0304 0.0282 0.0385 -5.05% (0.5, 0.5, 0.5, 0) 0.0092 0.0086 0.0122 0.0111 0.0111 -6.52%
(0.25, 0.75, 1.25, 0) 0.0237 0.0291 0.0298 0.0291 0.0277 16.88% (0.25, 0.5, 0.75, 0) 0.025 0.0285 0.0714 0.0592 0.0302 14.00%
Log-F (10, 4.5)        Log-F (10, 4.5)       
(0, 0, 0, 0) 0.0527 0.0513 0.0509 0.0513 0.0527   (0, 0, 0, 0) 0.0504 0.0492 0.0493 0.0514 0.0508  
(0, 0.25, 0.5, 0.75) 0.2882 0.3179 0.3316 0.3179 0.259 11.27% (0, 0.25, 0.5, 0.75) 0.3697 0.4268 0.4489 0.4492 0.3458 6.91%
(0.75, 0, 0.25, 0.5) 0.0168 0.0211 0.0204 0.0211 0.0216 21.43% (0.5, 0.5, 0.5, 0) 0.0049 0.0055 0.01 0.0079 0.0079 12.24%
(0.25, 0.75, 1.25, 0) 0.025 0.0259 0.029 0.0259 0.0317 3.60% (0.25, 0.5, 0.75, 0) 0.0273 0.027 0.076 0.0568 0.0328 -1.10%