(J,K) and Skew Power P(type 1 error) SAM sam-roc FC Med. FC Rank Prod. SAM sam-roc FC Med. FC Rank Prod. (4,4) 0.0613 0.3986 0.4395 0.4445 0.4677 0.0022 0.0448 0.0427 0.0409 0.0809 L M 0.0338 0.379 0.4538 0.4742 0.4528 0.0014 0.0433 0.044 0.0478 0.0791 H 0.018 0.3599 0.4638 0.479 0.4318 0.001 0.0413 0.0438 0.0474 0.0768 (8,8) 0.3594 0.6436 0.7109 0.7235 0.6725 0.0116 0.0473 0.0472 0.047 0.0807 L M 0.2415 0.584 0.6854 0.7072 0.6415 0.008 0.0452 0.0481 0.048 0.079 H 0.1224 0.5245 0.6468 0.6818 0.5965 0.0041 0.0417 0.0476 0.048 0.0772 (8,15) 0.4194 0.7142 0.8144 0.8182 0.7677 0.0132 0.0492 0.0496 0.0492 0.0745 L M 0.3806 0.65 0.7767 0.7907 0.728 0.0118 0.0477 0.05 0.0494 0.0728 H 0.3229 0.5843 0.7154 0.7521 0.6649 0.0098 0.0444 0.0497 0.049 0.0703 (8,20) 0.4305 0.7243 0.8409 0.8579 0.8091 0.0134 0.0499 0.0472 0.0481 0.0716 L M 0.4137 0.6596 0.8005 0.8225 0.7616 0.0125 0.0483 0.0475 0.0482 0.0691 H 0.3864 0.5935 0.7327 0.782 0.6932 0.0114 0.0462 0.0473 0.0485 0.0667 (8,25) 0.4369 0.7208 0.8638 0.873 0.8383 0.0135 0.0498 0.0496 0.0489 0.0687 L M 0.4341 0.6653 0.8248 0.8408 0.7874 0.0131 0.0489 0.0496 0.049 0.0663 H 0.4236 0.5999 0.7543 0.7961 0.7116 0.0126 0.0471 0.0498 0.0491 0.0637 (12,8) 0.5427 0.7418 0.7979 0.8108 0.7452 0.0174 0.0481 0.049 0.0493 0.0813 L M 0.397 0.6644 0.7409 0.7845 0.708 0.0126 0.0456 0.041 0.0485 0.0795 H 0.2371 0.5836 0.6944 0.7531 0.6531 0.0074 0.0427 0.0475 0.0484 0.0774 (10,15) 0.5984 0.7959 0.8588 0.8601 0.8132 0.0187 0.0488 0.049 0.048 0.0773 L M 0.4731 0.7204 0.8154 0.8284 0.7703 0.0144 0.0473 0.0489 0.0469 0.0754 H 0.3608 0.632 0.7427 0.7928 0.7028 0.0106 0.0443 0.0488 0.047 0.0732 (10,20) 0.5895 0.8107 0.8905 0.8973 0.8559 0.0181 0.0496 0.0499 0.0468 0.0744 L M 0.488 0.744 0.8498 0.8713 0.8099 0.0146 0.0482 0.0497 0.0491 0.0722 H 0.4168 0.6474 0.7674 0.829 0.7354 0.0121 0.0454 0.0498 0.0487 0.0699 (10,26) 0.5567 0.8149 0.9068 0.9149 0.886 0.0168 0.0499 0.0486 0.0486 0.0722 L M 0.4855 0.7487 0.8648 0.8861 0.8378 0.0145 0.0491 0.0484 0.0485 0.0699 H 0.4476 0.6574 0.7806 0.8432 0.756 0.0132 0.047 0.0488 0.0489 0.0673 (15,15) 0.8165 0.8931 0.9176 0.9106 0.8735 0.0261 0.0489 0.0485 0.0482 0.0821 L M 0.6801 0.8087 0.8747 0.8889 0.8318 0.021 0.047 0.0485 0.0483 0.0805 H 0.4591 0.6829 0.7765 0.8544 0.7588 0.0136 0.0434 0.0483 0.048 0.0789 (15,20) 0.8581 0.916 0.9461 0.9471 0.9169 0.0267 0.0485 0.0496 0.0496 0.0794 L M 0.7353 0.8465 0.9063 0.9261 0.8758 0.0226 0.0482 0.0497 0.0496 0.0778 H 0.5245 0.7177 0.8052 0.8913 0.7973 0.0153 0.0449 0.0495 0.0496 0.0762 (15,25) 0.8775 0.9242 0.9596 0.9585 0.9433 0.0272 0.0492 0.0481 0.0485 0.0777 L M 0.7625 0.8622 0.9219 0.939 0.9039 0.023 0.0481 0.0482 0.0485 0.0755 H 0.5577 0.7374 0.8211 0.9036 0.8243 0.0162 0.0462 0.0485 0.0487 0.0738 (20,20) 0.9223 0.9537 0.9692 0.9735 0.9423 0.0289 0.0485 0.0495 0.0473 0.0829 L M 0.8192 0.8876 0.9327 0.9592 0.9073 0.025 0.0475 0.0495 0.0473 0.0815 H 0.5906 0.7447 0.8247 0.935 0.8312 0.0172 0.0445 0.0497 0.0471 0.08 (20,25) 0.9416 0.9634 0.9796 0.9827 0.9656 0.0295 0.0483 0.05 0.0493 0.0812 L M 0.8542 0.9098 0.9491 0.9715 0.9346 0.026 0.0478 0.0499 0.0495 0.0797 H 0.6364 0.7702 0.8422 0.9488 0.8602 0.0184 0.0457 0.0497 0.0495 0.078 (25,25) 0.9657 0.9784 0.9882 0.989 0.977 0.0303 0.0486 0.05 0.0488 0.0844 L M 0.8903 0.9319 0.9624 0.981 0.9507 0.0268 0.0476 0.05 0.0488 0.0829 H 0.6616 0.7857 0.855 0.9644 0.8841 0.0187 0.0453 0.0499 0.0487 0.0815

Table 1: Power and P(type 1 error) for simulations under lognormal distribution.