Traditional design | CEP design | ||||||||
---|---|---|---|---|---|---|---|---|---|
(m 1,m 2) | \(\tau _{1}^{2}=\tau _{2}^{2}\) | \(\hat {N}\) | Performance | CEP | N ∗ | Performance | E(π 2−π 1|π 2>π 1) | P(π 2>π 1) | Marginal benefit |
(0.1,0.9) | 0.001 | 10 | 0.797 | 0.518 | 12 | 0.742 | 0.783 | 1 | 0.1120 |
0.01 | 10 | 0.622 | 0.242 | 16 | 0.627 | 0.674 | 1 | 0.0642 | |
0.02 | 10 | 0.508 | 0.164 | 26 | 0.673 | 0.585 | 0.993 | 0.0318 | |
0.03 | 10 | 0.433 | 0.123 | 40 | 0.687 | 0.519 | 0.965 | 0.0188 | |
0.04 | 10 | 0.381 | 0.099 | 60 | 0.698 | 0.469 | 0.915 | 0.0120 | |
0.05 | 10 | 0.342 | 0.082 | 86 | 0.705 | 0.429 | 0.846 | 0.0082 | |
0.06 | 10 | 0.311 | 0.070 | 120 | 0.710 | 0.397 | 0.761 | 0.0058 | |
0.07 | 10 | 0.285 | 0.060 | 160 | 0.713 | 0.369 | 0.662 | 0.0044 | |
0.08 | 10 | 0.262 | 0.052 | 214 | 0.716 | 0.342 | 0.545 | 0.0033 | |
(0.1,0.8) or (0.2,0.9) | 0.001 | 14 | 0.804 | 0.559 | 14 | 0.559 | 0.688 | 1 | 0 |
0.01 | 14 | 0.656 | 0.314 | 22 | 0.623 | 0.602 | 1 | 0.0386 | |
0.02 | 14 | 0.553 | 0.237 | 34 | 0.674 | 0.529 | 0.989 | 0.0218 | |
0.03 | 14 | 0.486 | 0.195 | 52 | 0.692 | 0.476 | 0.953 | 0.0131 | |
0.04 | 14 | 0.439 | 0.168 | 76 | 0.702 | 0.438 | 0.896 | 0.0086 | |
0.05 | 14 | 0.405 | 0.149 | 102 | 0.706 | 0.408 | 0.823 | 0.0063 | |
0.06 | 14 | 0.377 | 0.134 | 134 | 0.711 | 0.383 | 0.740 | 0.0048 | |
0.07 | 14 | 0.353 | 0.121 | 172 | 0.713 | 0.361 | 0.646 | 0.0037 | |
0.08 | 14 | 0.331 | 0.110 | 218 | 0.716 | 0.340 | 0.540 | 0.0030 | |
(0.1,0.7) or (0.3,0.9) | 0.001 | 20 | 0.814 | 0.616 | 20 | 0.616 | 0.590 | 1 | 0 |
0.01 | 20 | 0.670 | 0.364 | 30 | 0.636 | 0.518 | 0.999 | 0.0272 | |
0.02 | 20 | 0.578 | 0.295 | 48 | 0.677 | 0.463 | 0.979 | 0.0136 | |
0.03 | 20 | 0.523 | 0.260 | 72 | 0.697 | 0.426 | 0.931 | 0.0084 | |
0.04 | 20 | 0.488 | 0.238 | 98 | 0.705 | 0.401 | 0.866 | 0.0060 | |
0.05 | 20 | 0.462 | 0.223 | 126 | 0.708 | 0.382 | 0.792 | 0.0046 | |
0.06 | 20 | 0.442 | 0.211 | 154 | 0.712 | 0.367 | 0.712 | 0.0037 | |
0.07 | 20 | 0.424 | 0.200 | 186 | 0.714 | 0.353 | 0.627 | 0.0031 | |
0.08 | 20 | 0.407 | 0.189 | 222 | 0.716 | 0.338 | 0.534 | 0.0026 | |
(0.2,0.8) | 0.001 | 20 | 0.800 | 0.537 | 22 | 0.644 | 0.593 | 1 | 0.0537 |
0.01 | 20 | 0.676 | 0.372 | 30 | 0.643 | 0.530 | 0.999 | 0.0271 | |
0.02 | 20 | 0.588 | 0.308 | 48 | 0.680 | 0.474 | 0.982 | 0.0133 | |
0.03 | 20 | 0.532 | 0.272 | 70 | 0.695 | 0.435 | 0.936 | 0.0085 | |
0.04 | 20 | 0.495 | 0.247 | 94 | 0.703 | 0.408 | 0.872 | 0.0062 | |
0.05 | 20 | 0.467 | 0.229 | 122 | 0.709 | 0.387 | 0.798 | 0.0047 | |
0.06 | 20 | 0.445 | 0.215 | 152 | 0.711 | 0.370 | 0.717 | 0.0038 | |
0.07 | 20 | 0.425 | 0.202 | 184 | 0.714 | 0.354 | 0.630 | 0.0031 | |
0.08 | 20 | 0.407 | 0.189 | 222 | 0.716 | 0.339 | 0.534 | 0.0026 | |
(0.1,0.6) or (0.4,0.9) | 0.001 | 28 | 0.804 | 0.572 | 28 | 0.572 | 0.491 | 1 | 0 |
0.01 | 28 | 0.655 | 0.368 | 48 | 0.660 | 0.430 | 0.996 | 0.0146 | |
0.02 | 28 | 0.578 | 0.319 | 76 | 0.689 | 0.393 | 0.958 | 0.0077 | |
0.03 | 28 | 0.540 | 0.299 | 106 | 0.701 | 0.374 | 0.895 | 0.0052 | |
0.04 | 28 | 0.518 | 0.290 | 132 | 0.706 | 0.362 | 0.824 | 0.0040 | |
0.05 | 28 | 0.504 | 0.285 | 158 | 0.710 | 0.355 | 0.752 | 0.0033 | |
0.06 | 28 | 0.494 | 0.281 | 180 | 0.713 | 0.349 | 0.680 | 0.0028 | |
0.07 | 28 | 0.486 | 0.278 | 202 | 0.714 | 0.343 | 0.606 | 0.0025 | |
0.08 | 28 | 0.476 | 0.272 | 226 | 0.715 | 0.336 | 0.528 | 0.0022 | |
(0.2,0.7) or (0.3,0.8) | 0.001 | 30 | 0.803 | 0.558 | 30 | 0.558 | 0.494 | 1 | 0 |
0.01 | 30 | 0.682 | 0.412 | 46 | 0.653 | 0.446 | 0.998 | 0.0151 | |
0.02 | 30 | 0.609 | 0.365 | 72 | 0.686 | 0.410 | 0.966 | 0.0076 | |
0.03 | 30 | 0.570 | 0.342 | 100 | 0.700 | 0.388 | 0.907 | 0.0051 | |
0.04 | 30 | 0.546 | 0.328 | 126 | 0.706 | 0.374 | 0.837 | 0.0039 | |
0.05 | 30 | 0.529 | 0.317 | 150 | 0.710 | 0.363 | 0.763 | 0.0033 | |
0.06 | 30 | 0.515 | 0.309 | 174 | 0.713 | 0.354 | 0.688 | 0.0028 | |
0.07 | 30 | 0.503 | 0.300 | 198 | 0.714 | 0.346 | 0.611 | 0.0025 | |
0.08 | 30 | 0.491 | 0.291 | 226 | 0.716 | 0.337 | 0.529 | 0.0022 | |
(0.1,0.5) or (0.5,0.9) | 0.001 | 40 | 0.781 | 0.488 | 42 | 0.566 | 0.392 | 1 | 0.0393 |
0.01 | 40 | 0.627 | 0.358 | 80 | 0.675 | 0.343 | 0.985 | 0.0079 | |
0.02 | 40 | 0.573 | 0.335 | 124 | 0.697 | 0.326 | 0.918 | 0.0043 | |
0.03 | 40 | 0.553 | 0.334 | 160 | 0.706 | 0.322 | 0.841 | 0.0031 | |
0.04 | 40 | 0.546 | 0.339 | 182 | 0.709 | 0.324 | 0.769 | 0.0026 | |
0.05 | 40 | 0.545 | 0.346 | 200 | 0.712 | 0.327 | 0.703 | 0.0023 | |
0.06 | 40 | 0.545 | 0.353 | 210 | 0.713 | 0.331 | 0.642 | 0.0021 | |
0.07 | 40 | 0.546 | 0.359 | 220 | 0.715 | 0.334 | 0.584 | 0.0020 | |
0.08 | 40 | 0.545 | 0.362 | 230 | 0.716 | 0.334 | 0.522 | 0.0019 | |
(0.2,0.6) or (0.4,0.8) | 0.001 | 46 | 0.791 | 0.518 | 48 | 0.587 | 0.395 | 1 | 0.0345 |
0.01 | 46 | 0.668 | 0.422 | 80 | 0.668 | 0.360 | 0.991 | 0.0072 | |
0.02 | 46 | 0.617 | 0.401 | 118 | 0.694 | 0.343 | 0.933 | 0.0041 | |
0.03 | 46 | 0.597 | 0.397 | 150 | 0.704 | 0.339 | 0.860 | 0.0030 | |
0.04 | 46 | 0.588 | 0.397 | 172 | 0.709 | 0.338 | 0.787 | 0.0025 | |
0.05 | 46 | 0.584 | 0.399 | 190 | 0.712 | 0.338 | 0.719 | 0.0022 | |
0.06 | 46 | 0.580 | 0.400 | 202 | 0.713 | 0.337 | 0.654 | 0.0020 | |
0.07 | 46 | 0.577 | 0.400 | 216 | 0.714 | 0.337 | 0.589 | 0.0018 | |
0.08 | 46 | 0.572 | 0.398 | 230 | 0.715 | 0.335 | 0.523 | 0.0017 | |
(0.3,0.7) | 0.001 | 48 | 0.793 | 0.524 | 50 | 0.558 | 0.396 | 1 | 0.0167 |
0.01 | 48 | 0.678 | 0.438 | 80 | 0.665 | 0.365 | 0.992 | 0.0071 | |
0.02 | 48 | 0.629 | 0.419 | 118 | 0.695 | 0.349 | 0.938 | 0.0039 | |
0.03 | 48 | 0.610 | 0.415 | 146 | 0.704 | 0.344 | 0.866 | 0.0029 | |
0.04 | 48 | 0.601 | 0.415 | 168 | 0.709 | 0.342 | 0.794 | 0.0024 | |
0.05 | 48 | 0.595 | 0.415 | 186 | 0.711 | 0.341 | 0.724 | 0.0021 | |
0.06 | 48 | 0.591 | 0.415 | 200 | 0.714 | 0.340 | 0.658 | 0.0020 | |
0.07 | 48 | 0.586 | 0.413 | 214 | 0.715 | 0.338 | 0.591 | 0.0018 | |
0.08 | 48 | 0.580 | 0.409 | 230 | 0.715 | 0.335 | 0.523 | 0.0017 | |
(0.1,0.4) or (0.6,0.9) | 0.001 | 64 | 0.763 | 0.461 | 72 | 0.588 | 0.292 | 1 | 0.0159 |
0.01 | 64 | 0.612 | 0.377 | 156 | 0.689 | 0.262 | 0.951 | 0.0034 | |
0.02 | 64 | 0.588 | 0.381 | 216 | 0.705 | 0.265 | 0.850 | 0.0021 | |
0.03 | 64 | 0.588 | 0.397 | 242 | 0.709 | 0.276 | 0.768 | 0.0018 | |
0.04 | 64 | 0.594 | 0.414 | 250 | 0.712 | 0.289 | 0.703 | 0.0016 | |
0.05 | 64 | 0.603 | 0.432 | 250 | 0.714 | 0.302 | 0.649 | 0.0015 | |
0.06 | 64 | 0.613 | 0.449 | 246 | 0.715 | 0.314 | 0.603 | 0.0015 | |
0.07 | 64 | 0.622 | 0.464 | 238 | 0.715 | 0.325 | 0.560 | 0.0014 | |
0.08 | 64 | 0.628 | 0.474 | 234 | 0.715 | 0.332 | 0.516 | 0.0014 | |
(0.2,0.5) or (0.5,0.8) | 0.001 | 78 | 0.776 | 0.491 | 84 | 0.584 | 0.296 | 1 | 0.0154 |
0.01 | 78 | 0.654 | 0.441 | 158 | 0.686 | 0.277 | 0.964 | 0.0031 | |
0.02 | 78 | 0.635 | 0.450 | 210 | 0.703 | 0.282 | 0.872 | 0.0019 | |
0.03 | 78 | 0.635 | 0.465 | 232 | 0.709 | 0.292 | 0.791 | 0.0016 | |
0.04 | 78 | 0.640 | 0.480 | 238 | 0.711 | 0.302 | 0.724 | 0.0014 | |
0.05 | 78 | 0.647 | 0.493 | 240 | 0.713 | 0.312 | 0.666 | 0.0014 | |
0.06 | 78 | 0.653 | 0.504 | 238 | 0.714 | 0.321 | 0.615 | 0.0013 | |
0.07 | 78 | 0.658 | 0.514 | 234 | 0.715 | 0.328 | 0.566 | 0.0013 | |
0.08 | 78 | 0.661 | 0.520 | 234 | 0.716 | 0.332 | 0.517 | 0.0013 | |
(0.3,0.6) or (0.4,0.7) | 0.001 | 84 | 0.775 | 0.483 | 92 | 0.584 | 0.297 | 1 | 0.0126 |
0.01 | 84 | 0.666 | 0.457 | 162 | 0.683 | 0.283 | 0.968 | 0.0029 | |
0.02 | 84 | 0.649 | 0.471 | 210 | 0.702 | 0.289 | 0.881 | 0.0018 | |
0.03 | 84 | 0.652 | 0.489 | 228 | 0.708 | 0.300 | 0.802 | 0.0015 | |
0.04 | 84 | 0.658 | 0.504 | 234 | 0.712 | 0.309 | 0.735 | 0.0014 | |
0.05 | 84 | 0.663 | 0.516 | 234 | 0.713 | 0.318 | 0.676 | 0.0013 | |
0.06 | 84 | 0.668 | 0.525 | 232 | 0.714 | 0.324 | 0.621 | 0.0013 | |
0.07 | 84 | 0.671 | 0.532 | 232 | 0.715 | 0.329 | 0.569 | 0.0012 | |
0.08 | 84 | 0.672 | 0.536 | 234 | 0.716 | 0.333 | 0.517 | 0.0012 | |
(0.1,0.3) or (0.7,0.9) | 0.001 | 124 | 0.736 | 0.453 | 152 | 0.614 | 0.194 | 1 | 0.0057 |
0.01 | 124 | 0.625 | 0.434 | 346 | 0.703 | 0.193 | 0.866 | 0.0012 | |
0.02 | 124 | 0.636 | 0.470 | 374 | 0.710 | 0.216 | 0.750 | 0.0010 | |
0.03 | 124 | 0.654 | 0.501 | 358 | 0.712 | 0.239 | 0.680 | 0.0009 | |
0.04 | 124 | 0.671 | 0.528 | 334 | 0.714 | 0.261 | 0.631 | 0.0009 | |
0.05 | 124 | 0.687 | 0.553 | 306 | 0.714 | 0.281 | 0.594 | 0.0009 | |
0.06 | 124 | 0.701 | 0.575 | 280 | 0.715 | 0.300 | 0.565 | 0.0009 | |
0.07 | 124 | 0.714 | 0.594 | 258 | 0.715 | 0.317 | 0.538 | 0.0009 | |
0.08 | 124 | 0.725 | 0.610 | 240 | 0.716 | 0.330 | 0.510 | 0.0009 | |
(0.2,0.4) or (0.6,0.8) | 0.001 | 164 | 0.754 | 0.487 | 190 | 0.605 | 0.197 | 1 | 0.0045 |
0.01 | 164 | 0.667 | 0.496 | 372 | 0.702 | 0.205 | 0.887 | 0.0010 | |
0.02 | 164 | 0.683 | 0.537 | 380 | 0.709 | 0.229 | 0.774 | 0.0008 | |
0.03 | 164 | 0.701 | 0.568 | 356 | 0.712 | 0.251 | 0.702 | 0.0007 | |
0.04 | 164 | 0.716 | 0.593 | 326 | 0.714 | 0.271 | 0.650 | 0.0007 | |
0.05 | 164 | 0.730 | 0.614 | 300 | 0.714 | 0.289 | 0.609 | 0.0007 | |
0.06 | 164 | 0.742 | 0.632 | 276 | 0.715 | 0.305 | 0.574 | 0.0007 | |
0.07 | 164 | 0.752 | 0.647 | 254 | 0.715 | 0.319 | 0.543 | 0.0008 | |
0.08 | 164 | 0.760 | 0.659 | 240 | 0.716 | 0.330 | 0.511 | 0.0008 | |
(0.3,0.5) or (0.5,0.7) | 0.001 | 186 | 0.755 | 0.487 | 214 | 0.605 | 0.198 | 1 | 0.0042 |
0.01 | 186 | 0.679 | 0.513 | 394 | 0.700 | 0.210 | 0.896 | 0.0009 | |
0.02 | 186 | 0.699 | 0.560 | 390 | 0.709 | 0.236 | 0.787 | 0.0007 | |
0.03 | 186 | 0.719 | 0.594 | 356 | 0.712 | 0.259 | 0.715 | 0.0007 | |
0.04 | 186 | 0.735 | 0.620 | 324 | 0.713 | 0.278 | 0.662 | 0.0007 | |
0.05 | 186 | 0.748 | 0.640 | 294 | 0.714 | 0.294 | 0.619 | 0.0007 | |
0.06 | 186 | 0.759 | 0.656 | 272 | 0.715 | 0.308 | 0.581 | 0.0007 | |
0.07 | 186 | 0.768 | 0.669 | 252 | 0.715 | 0.321 | 0.546 | 0.0007 | |
0.08 | 186 | 0.774 | 0.679 | 238 | 0.716 | 0.331 | 0.511 | 0.0007 | |
(0.4,0.6) | 0.001 | 194 | 0.757 | 0.491 | 222 | 0.603 | 0.198 | 1 | 0.0040 |
0.01 | 194 | 0.683 | 0.518 | 402 | 0.700 | 0.211 | 0.898 | 0.0009 | |
0.02 | 194 | 0.704 | 0.567 | 396 | 0.709 | 0.238 | 0.791 | 0.0007 | |
0.03 | 194 | 0.724 | 0.602 | 358 | 0.712 | 0.261 | 0.720 | 0.0007 | |
0.04 | 194 | 0.741 | 0.628 | 322 | 0.713 | 0.280 | 0.666 | 0.0007 | |
0.05 | 194 | 0.754 | 0.648 | 294 | 0.714 | 0.296 | 0.622 | 0.0007 | |
0.06 | 194 | 0.765 | 0.664 | 270 | 0.715 | 0.310 | 0.583 | 0.0007 | |
0.07 | 194 | 0.773 | 0.677 | 252 | 0.715 | 0.321 | 0.547 | 0.0007 | |
0.08 | 194 | 0.779 | 0.686 | 238 | 0.716 | 0.331 | 0.511 | 0.0007 | |
(0.1,0.2) or (0.8,0.9) | 0.001 | 398 | 0.683 | 0.470 | 676 | 0.675 | 0.098 | 0.981 | 0.0007 |
0.01 | 398 | 0.712 | 0.584 | 794 | 0.712 | 0.141 | 0.708 | 0.0003 | |
0.02 | 398 | 0.750 | 0.642 | 618 | 0.714 | 0.179 | 0.626 | 0.0003 | |
0.03 | 398 | 0.775 | 0.679 | 504 | 0.715 | 0.211 | 0.586 | 0.0003 | |
0.04 | 398 | 0.794 | 0.706 | 424 | 0.715 | 0.239 | 0.562 | 0.0003 | |
0.05 | 398 | 0.809 | 0.728 | 364 | 0.715 | 0.265 | 0.544 | 0.0004 | |
0.06 | 398 | 0.822 | 0.747 | 316 | 0.716 | 0.288 | 0.530 | 0.0004 | |
0.07 | 398 | 0.833 | 0.763 | 276 | 0.716 | 0.310 | 0.518 | 0.0004 | |
0.08 | 398 | 0.843 | 0.777 | 244 | 0.716 | 0.328 | 0.505 | 0.0004 | |
(0.2,0.3) or (0.7,0.8) | 0.001 | 588 | 0.701 | 0.495 | 924 | 0.672 | 0.100 | 0.985 | 0.0005 |
0.01 | 588 | 0.746 | 0.633 | 922 | 0.711 | 0.149 | 0.727 | 0.0002 | |
0.02 | 588 | 0.787 | 0.695 | 666 | 0.714 | 0.188 | 0.644 | 0.0002 | |
0.03 | 588 | 0.812 | 0.731 | 524 | 0.715 | 0.218 | 0.601 | 0.0003 | |
0.04 | 588 | 0.829 | 0.756 | 432 | 0.715 | 0.245 | 0.573 | 0.0003 | |
0.05 | 588 | 0.842 | 0.775 | 366 | 0.716 | 0.269 | 0.552 | 0.0003 | |
0.06 | 588 | 0.853 | 0.791 | 316 | 0.716 | 0.291 | 0.535 | 0.0003 | |
0.07 | 588 | 0.863 | 0.805 | 276 | 0.716 | 0.311 | 0.520 | 0.0003 | |
0.08 | 588 | 0.871 | 0.816 | 244 | 0.716 | 0.328 | 0.506 | 0.0003 | |
(0.3,0.4) or (0.6,0.7) | 0.001 | 712 | 0.704 | 0.500 | 1100 | 0.671 | 0.101 | 0.986 | 0.0004 |
0.01 | 712 | 0.756 | 0.647 | 1034 | 0.711 | 0.153 | 0.736 | 0.0002 | |
0.02 | 712 | 0.800 | 0.713 | 714 | 0.714 | 0.193 | 0.654 | 0.0005 | |
0.03 | 712 | 0.825 | 0.751 | 544 | 0.714 | 0.224 | 0.611 | 0.0002 | |
0.04 | 712 | 0.843 | 0.776 | 440 | 0.715 | 0.250 | 0.581 | 0.0002 | |
0.05 | 712 | 0.856 | 0.795 | 368 | 0.715 | 0.273 | 0.559 | 0.0002 | |
0.06 | 712 | 0.867 | 0.810 | 314 | 0.716 | 0.294 | 0.540 | 0.0002 | |
0.07 | 712 | 0.875 | 0.823 | 274 | 0.716 | 0.312 | 0.523 | 0.0002 | |
0.08 | 712 | 0.882 | 0.833 | 244 | 0.716 | 0.329 | 0.506 | 0.0003 | |
(0.4,0.5) or (0.5,0.6) | 0.001 | 776 | 0.706 | 0.502 | 1190 | 0.670 | 0.101 | 0.986 | 0.0004 |
0.01 | 776 | 0.760 | 0.652 | 1096 | 0.711 | 0.154 | 0.740 | 0.0002 | |
0.02 | 776 | 0.804 | 0.720 | 744 | 0.713 | 0.195 | 0.659 | 0.0002 | |
0.03 | 776 | 0.831 | 0.758 | 558 | 0.714 | 0.226 | 0.615 | 0.0002 | |
0.04 | 776 | 0.849 | 0.784 | 446 | 0.715 | 0.253 | 0.586 | 0.0002 | |
0.05 | 776 | 0.862 | 0.803 | 368 | 0.715 | 0.275 | 0.562 | 0.0002 | |
0.06 | 776 | 0.872 | 0.818 | 314 | 0.716 | 0.295 | 0.542 | 0.0002 | |
0.07 | 776 | 0.881 | 0.830 | 274 | 0.716 | 0.313 | 0.524 | 0.0002 | |
0.08 | 776 | 0.887 | 0.840 | 244 | 0.716 | 0.329 | 0.506 | 0.0002 |