(\(\tau _{1}^{2}=0.08\)) | Traditional design | CEP design | |||||||
---|---|---|---|---|---|---|---|---|---|
(m 1,m 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 | 0.127 | 0.389 | 70 | 0.703 | 0.459 | 0.913 | 0.0096 |
0.01 | 10 | 0.097 | 0.356 | 88 | 0.707 | 0.435 | 0.861 | 0.0078 | |
0.02 | 10 | 0.083 | 0.335 | 102 | 0.709 | 0.417 | 0.815 | 0.0068 | |
0.03 | 10 | 0.075 | 0.319 | 118 | 0.711 | 0.402 | 0.774 | 0.0059 | |
0.04 | 10 | 0.069 | 0.306 | 132 | 0.712 | 0.389 | 0.734 | 0.0053 | |
0.05 | 10 | 0.064 | 0.294 | 148 | 0.713 | 0.378 | 0.693 | 0.0047 | |
0.06 | 10 | 0.060 | 0.283 | 166 | 0.713 | 0.366 | 0.650 | 0.0042 | |
0.07 | 10 | 0.056 | 0.273 | 186 | 0.714 | 0.355 | 0.602 | 0.0037 | |
(0.1,0.8) | 0.001 | 14 | 0.147 | 0.399 | 114 | 0.710 | 0.407 | 0.825 | 0.0056 |
0.01 | 14 | 0.134 | 0.387 | 124 | 0.710 | 0.396 | 0.794 | 0.0052 | |
0.02 | 14 | 0.128 | 0.377 | 134 | 0.711 | 0.386 | 0.760 | 0.0049 | |
0.03 | 14 | 0.124 | 0.368 | 146 | 0.712 | 0.378 | 0.728 | 0.0045 | |
0.04 | 14 | 0.121 | 0.360 | 158 | 0.713 | 0.370 | 0.695 | 0.0041 | |
0.05 | 14 | 0.118 | 0.353 | 170 | 0.713 | 0.362 | 0.661 | 0.0038 | |
0.06 | 14 | 0.116 | 0.346 | 184 | 0.714 | 0.355 | 0.625 | 0.0035 | |
0.07 | 14 | 0.113 | 0.339 | 198 | 0.715 | 0.348 | 0.586 | 0.0033 | |
(0.1,0.7) | 0.001 | 20 | 0.174 | 0.415 | 172 | 0.713 | 0.355 | 0.731 | 0.0035 |
0.01 | 20 | 0.172 | 0.414 | 176 | 0.713 | 0.353 | 0.712 | 0.0035 | |
0.02 | 20 | 0.174 | 0.413 | 182 | 0.713 | 0.350 | 0.691 | 0.0033 | |
0.03 | 20 | 0.177 | 0.412 | 188 | 0.714 | 0.348 | 0.669 | 0.0032 | |
0.04 | 20 | 0.180 | 0.411 | 192 | 0.714 | 0.346 | 0.646 | 0.0031 | |
0.05 | 20 | 0.183 | 0.410 | 200 | 0.715 | 0.344 | 0.622 | 0.0030 | |
0.06 | 20 | 0.185 | 0.409 | 206 | 0.714 | 0.342 | 0.596 | 0.0028 | |
0.07 | 20 | 0.187 | 0.408 | 214 | 0.715 | 0.340 | 0.567 | 0.0027 | |
(0.2,0.8) | 0.001 | 20 | 0.264 | 0.488 | 118 | 0.710 | 0.403 | 0.821 | 0.0046 |
0.01 | 20 | 0.247 | 0.475 | 128 | 0.711 | 0.393 | 0.789 | 0.0043 | |
0.02 | 20 | 0.233 | 0.462 | 138 | 0.712 | 0.384 | 0.755 | 0.0041 | |
0.03 | 20 | 0.223 | 0.451 | 150 | 0.712 | 0.375 | 0.723 | 0.0038 | |
0.04 | 20 | 0.215 | 0.442 | 162 | 0.713 | 0.367 | 0.690 | 0.0035 | |
0.05 | 20 | 0.208 | 0.433 | 174 | 0.713 | 0.360 | 0.656 | 0.0033 | |
0.06 | 20 | 0.201 | 0.424 | 188 | 0.714 | 0.353 | 0.620 | 0.0031 | |
0.07 | 20 | 0.195 | 0.416 | 202 | 0.715 | 0.346 | 0.580 | 0.0029 | |
(0.1,0.6) | 0.001 | 28 | 0.193 | 0.426 | 252 | 0.715 | 0.303 | 0.632 | 0.0023 |
0.01 | 28 | 0.199 | 0.431 | 250 | 0.715 | 0.307 | 0.623 | 0.0023 | |
0.02 | 28 | 0.209 | 0.437 | 246 | 0.715 | 0.311 | 0.613 | 0.0023 | |
0.03 | 28 | 0.220 | 0.443 | 244 | 0.715 | 0.316 | 0.601 | 0.0023 | |
0.04 | 28 | 0.231 | 0.449 | 240 | 0.715 | 0.320 | 0.589 | 0.0023 | |
0.05 | 28 | 0.241 | 0.456 | 238 | 0.715 | 0.324 | 0.576 | 0.0023 | |
0.06 | 28 | 0.252 | 0.463 | 234 | 0.715 | 0.328 | 0.562 | 0.0022 | |
0.07 | 28 | 0.262 | 0.469 | 230 | 0.715 | 0.332 | 0.546 | 0.0022 | |
(0.2,0.7) | 0.001 | 30 | 0.302 | 0.510 | 178 | 0.713 | 0.352 | 0.725 | 0.0028 |
0.01 | 30 | 0.298 | 0.507 | 182 | 0.713 | 0.350 | 0.706 | 0.0027 | |
0.02 | 30 | 0.295 | 0.504 | 186 | 0.714 | 0.348 | 0.685 | 0.0027 | |
0.03 | 30 | 0.293 | 0.502 | 192 | 0.714 | 0.346 | 0.663 | 0.0026 | |
0.04 | 30 | 0.292 | 0.499 | 198 | 0.714 | 0.344 | 0.640 | 0.0025 | |
0.05 | 30 | 0.291 | 0.497 | 204 | 0.714 | 0.342 | 0.616 | 0.0024 | |
0.06 | 30 | 0.291 | 0.495 | 210 | 0.715 | 0.340 | 0.590 | 0.0024 | |
0.07 | 30 | 0.291 | 0.493 | 218 | 0.715 | 0.338 | 0.561 | 0.0023 | |
(0.1,0.5) | 0.001 | 40 | 0.213 | 0.437 | 364 | 0.716 | 0.253 | 0.531 | 0.0016 |
0.01 | 40 | 0.226 | 0.448 | 350 | 0.716 | 0.262 | 0.530 | 0.0016 | |
0.02 | 40 | 0.244 | 0.461 | 334 | 0.716 | 0.272 | 0.529 | 0.0016 | |
0.03 | 40 | 0.264 | 0.474 | 318 | 0.716 | 0.282 | 0.528 | 0.0016 | |
0.04 | 40 | 0.283 | 0.488 | 300 | 0.715 | 0.293 | 0.527 | 0.0017 | |
0.05 | 40 | 0.303 | 0.502 | 284 | 0.716 | 0.303 | 0.526 | 0.0017 | |
0.06 | 40 | 0.323 | 0.516 | 266 | 0.716 | 0.313 | 0.525 | 0.0017 | |
0.07 | 40 | 0.342 | 0.530 | 248 | 0.716 | 0.324 | 0.523 | 0.0018 | |
(0.2,0.6) | 0.001 | 46 | 0.343 | 0.536 | 258 | 0.715 | 0.301 | 0.625 | 0.0018 |
0.01 | 46 | 0.347 | 0.539 | 256 | 0.715 | 0.305 | 0.617 | 0.0018 | |
0.02 | 46 | 0.352 | 0.543 | 252 | 0.715 | 0.309 | 0.606 | 0.0018 | |
0.03 | 46 | 0.359 | 0.547 | 250 | 0.715 | 0.314 | 0.595 | 0.0017 | |
0.04 | 46 | 0.366 | 0.552 | 246 | 0.715 | 0.318 | 0.583 | 0.0017 | |
0.05 | 46 | 0.373 | 0.556 | 242 | 0.715 | 0.322 | 0.570 | 0.0017 | |
0.06 | 46 | 0.382 | 0.562 | 238 | 0.715 | 0.326 | 0.556 | 0.0017 | |
0.07 | 46 | 0.390 | 0.567 | 234 | 0.716 | 0.330 | 0.540 | 0.0017 | |
(0.3,0.7) | 0.001 | 48 | 0.435 | 0.605 | 182 | 0.713 | 0.349 | 0.718 | 0.0021 |
0.01 | 48 | 0.431 | 0.602 | 186 | 0.713 | 0.347 | 0.700 | 0.0020 | |
0.02 | 48 | 0.427 | 0.599 | 192 | 0.714 | 0.345 | 0.679 | 0.0020 | |
0.03 | 48 | 0.423 | 0.596 | 196 | 0.714 | 0.343 | 0.657 | 0.0020 | |
0.04 | 48 | 0.419 | 0.592 | 202 | 0.714 | 0.342 | 0.634 | 0.0019 | |
0.05 | 48 | 0.416 | 0.589 | 208 | 0.715 | 0.340 | 0.610 | 0.0019 | |
0.06 | 48 | 0.414 | 0.586 | 214 | 0.715 | 0.338 | 0.584 | 0.0018 | |
0.07 | 48 | 0.411 | 0.583 | 222 | 0.715 | 0.336 | 0.555 | 0.0017 | |
(0.1,0.4) | 0.001 | 64 | 0.258 | 0.468 | 532 | 0.716 | 0.202 | 0.428 | 0.0010 |
0.01 | 64 | 0.281 | 0.486 | 494 | 0.716 | 0.217 | 0.435 | 0.0010 | |
0.02 | 64 | 0.308 | 0.506 | 452 | 0.716 | 0.234 | 0.444 | 0.0011 | |
0.03 | 64 | 0.336 | 0.526 | 412 | 0.716 | 0.250 | 0.454 | 0.0011 | |
0.04 | 64 | 0.363 | 0.546 | 374 | 0.716 | 0.267 | 0.464 | 0.0011 | |
0.05 | 64 | 0.391 | 0.566 | 338 | 0.716 | 0.283 | 0.475 | 0.0012 | |
0.06 | 64 | 0.418 | 0.586 | 302 | 0.716 | 0.299 | 0.487 | 0.0013 | |
0.07 | 64 | 0.446 | 0.607 | 268 | 0.716 | 0.316 | 0.501 | 0.0013 | |
(0.2,0.5) | 0.001 | 78 | 0.404 | 0.577 | 374 | 0.716 | 0.251 | 0.524 | 0.0011 |
0.01 | 78 | 0.414 | 0.585 | 358 | 0.716 | 0.260 | 0.523 | 0.0011 | |
0.02 | 78 | 0.427 | 0.594 | 342 | 0.716 | 0.270 | 0.522 | 0.0011 | |
0.03 | 78 | 0.441 | 0.604 | 326 | 0.716 | 0.281 | 0.521 | 0.0011 | |
0.04 | 78 | 0.455 | 0.615 | 308 | 0.716 | 0.291 | 0.521 | 0.0011 | |
0.05 | 78 | 0.470 | 0.625 | 290 | 0.716 | 0.301 | 0.520 | 0.0012 | |
0.06 | 78 | 0.486 | 0.637 | 272 | 0.716 | 0.312 | 0.519 | 0.0012 | |
0.07 | 78 | 0.503 | 0.649 | 254 | 0.716 | 0.322 | 0.518 | 0.0012 | |
(0.3,0.6) | 0.001 | 84 | 0.497 | 0.647 | 266 | 0.715 | 0.299 | 0.618 | 0.0012 |
0.01 | 84 | 0.501 | 0.649 | 264 | 0.715 | 0.303 | 0.609 | 0.0012 | |
0.02 | 84 | 0.505 | 0.652 | 260 | 0.715 | 0.307 | 0.599 | 0.0012 | |
0.03 | 84 | 0.509 | 0.655 | 256 | 0.715 | 0.311 | 0.588 | 0.0012 | |
0.04 | 84 | 0.514 | 0.658 | 252 | 0.715 | 0.316 | 0.576 | 0.0012 | |
0.05 | 84 | 0.519 | 0.661 | 248 | 0.715 | 0.320 | 0.564 | 0.0012 | |
0.06 | 84 | 0.524 | 0.665 | 244 | 0.715 | 0.324 | 0.550 | 0.0012 | |
0.07 | 84 | 0.530 | 0.668 | 240 | 0.716 | 0.328 | 0.534 | 0.0012 | |
(0.1,0.3) | 0.001 | 124 | 0.339 | 0.526 | 808 | 0.717 | 0.153 | 0.323 | 0.0006 |
0.01 | 124 | 0.376 | 0.554 | 708 | 0.717 | 0.176 | 0.341 | 0.0006 | |
0.02 | 124 | 0.414 | 0.582 | 612 | 0.717 | 0.200 | 0.361 | 0.0006 | |
0.03 | 124 | 0.450 | 0.608 | 530 | 0.717 | 0.223 | 0.382 | 0.0007 | |
0.04 | 124 | 0.483 | 0.632 | 458 | 0.717 | 0.245 | 0.404 | 0.0007 | |
0.05 | 124 | 0.515 | 0.656 | 394 | 0.717 | 0.266 | 0.428 | 0.0007 | |
0.06 | 124 | 0.546 | 0.679 | 338 | 0.717 | 0.287 | 0.452 | 0.0008 | |
0.07 | 124 | 0.578 | 0.702 | 286 | 0.716 | 0.308 | 0.480 | 0.0009 | |
(0.2,0.4) | 0.001 | 164 | 0.502 | 0.647 | 546 | 0.717 | 0.201 | 0.420 | 0.0006 |
0.01 | 164 | 0.519 | 0.659 | 506 | 0.716 | 0.216 | 0.428 | 0.0006 | |
0.02 | 164 | 0.537 | 0.672 | 464 | 0.717 | 0.233 | 0.437 | 0.0006 | |
0.03 | 164 | 0.557 | 0.686 | 422 | 0.717 | 0.249 | 0.447 | 0.0006 | |
0.04 | 164 | 0.576 | 0.700 | 382 | 0.716 | 0.265 | 0.457 | 0.0006 | |
0.05 | 164 | 0.596 | 0.715 | 344 | 0.716 | 0.282 | 0.469 | 0.0007 | |
0.06 | 164 | 0.617 | 0.730 | 308 | 0.716 | 0.298 | 0.482 | 0.0007 | |
0.07 | 164 | 0.638 | 0.745 | 272 | 0.716 | 0.314 | 0.495 | 0.0007 | |
(0.3,0.5) | 0.001 | 186 | 0.597 | 0.716 | 384 | 0.716 | 0.249 | 0.516 | 0.0006 |
0.01 | 186 | 0.605 | 0.721 | 368 | 0.716 | 0.258 | 0.515 | 0.0006 | |
0.02 | 186 | 0.614 | 0.728 | 352 | 0.716 | 0.269 | 0.515 | 0.0006 | |
0.03 | 186 | 0.623 | 0.735 | 334 | 0.716 | 0.279 | 0.514 | 0.0006 | |
0.04 | 186 | 0.633 | 0.742 | 314 | 0.716 | 0.289 | 0.514 | 0.0006 | |
0.05 | 186 | 0.644 | 0.749 | 296 | 0.716 | 0.299 | 0.513 | 0.0007 | |
0.06 | 186 | 0.655 | 0.757 | 278 | 0.716 | 0.310 | 0.513 | 0.0007 | |
0.07 | 186 | 0.667 | 0.766 | 258 | 0.716 | 0.320 | 0.512 | 0.0007 | |
(0.4,0.6) | 0.001 | 194 | 0.662 | 0.763 | 274 | 0.715 | 0.296 | 0.610 | 0.0007 |
0.01 | 194 | 0.664 | 0.764 | 270 | 0.715 | 0.301 | 0.602 | 0.0007 | |
0.02 | 194 | 0.667 | 0.766 | 266 | 0.715 | 0.305 | 0.592 | 0.0007 | |
0.03 | 194 | 0.669 | 0.768 | 262 | 0.715 | 0.309 | 0.581 | 0.0007 | |
0.04 | 194 | 0.672 | 0.770 | 258 | 0.715 | 0.314 | 0.569 | 0.0007 | |
0.05 | 194 | 0.675 | 0.772 | 254 | 0.715 | 0.318 | 0.557 | 0.0007 | |
0.06 | 194 | 0.679 | 0.774 | 250 | 0.716 | 0.322 | 0.543 | 0.0007 | |
0.07 | 194 | 0.682 | 0.777 | 244 | 0.716 | 0.326 | 0.528 | 0.0007 | |
(0.1,0.2) | 0.001 | 398 | 0.506 | 0.648 | 1346 | 0.717 | 0.104 | 0.218 | 0.0002 |
0.01 | 398 | 0.563 | 0.691 | 978 | 0.714 | 0.139 | 0.247 | 0.0003 | |
0.02 | 398 | 0.606 | 0.720 | 814 | 0.717 | 0.172 | 0.286 | 0.0003 | |
0.03 | 398 | 0.642 | 0.746 | 660 | 0.717 | 0.201 | 0.319 | 0.0003 | |
0.04 | 398 | 0.673 | 0.768 | 542 | 0.717 | 0.227 | 0.352 | 0.0003 | |
0.05 | 398 | 0.700 | 0.788 | 450 | 0.717 | 0.253 | 0.386 | 0.0003 | |
0.06 | 398 | 0.726 | 0.807 | 372 | 0.717 | 0.277 | 0.422 | 0.0004 | |
0.07 | 398 | 0.751 | 0.825 | 304 | 0.716 | 0.302 | 0.460 | 0.0004 | |
(0.2,0.3) | 0.001 | 588 | 0.667 | 0.765 | 828 | 0.717 | 0.152 | 0.316 | 0.0002 |
0.01 | 588 | 0.691 | 0.783 | 694 | 0.714 | 0.175 | 0.330 | 0.0002 | |
0.02 | 588 | 0.709 | 0.794 | 624 | 0.717 | 0.199 | 0.355 | 0.0002 | |
0.03 | 588 | 0.728 | 0.808 | 540 | 0.717 | 0.222 | 0.376 | 0.0002 | |
0.04 | 588 | 0.747 | 0.821 | 466 | 0.717 | 0.243 | 0.398 | 0.0002 | |
0.05 | 588 | 0.764 | 0.834 | 402 | 0.717 | 0.265 | 0.422 | 0.0003 | |
0.06 | 588 | 0.781 | 0.846 | 344 | 0.717 | 0.286 | 0.447 | 0.0003 | |
0.07 | 588 | 0.799 | 0.858 | 292 | 0.716 | 0.307 | 0.474 | 0.0003 | |
(0.3,0.4) | 0.001 | 712 | 0.748 | 0.822 | 560 | 0.717 | 0.200 | 0.413 | 0.0002 |
0.01 | 712 | 0.761 | 0.832 | 502 | 0.715 | 0.215 | 0.416 | 0.0002 | |
0.02 | 712 | 0.767 | 0.836 | 474 | 0.717 | 0.231 | 0.430 | 0.0002 | |
0.03 | 712 | 0.778 | 0.843 | 432 | 0.716 | 0.248 | 0.440 | 0.0002 | |
0.04 | 712 | 0.788 | 0.851 | 390 | 0.716 | 0.264 | 0.451 | 0.0002 | |
0.05 | 712 | 0.799 | 0.859 | 352 | 0.716 | 0.280 | 0.462 | 0.0002 | |
0.06 | 712 | 0.810 | 0.866 | 314 | 0.716 | 0.296 | 0.475 | 0.0002 | |
0.07 | 712 | 0.821 | 0.874 | 278 | 0.716 | 0.312 | 0.490 | 0.0002 | |
(0.4,0.5) | 0.001 | 776 | 0.797 | 0.857 | 394 | 0.716 | 0.247 | 0.508 | 0.0002 |
0.01 | 776 | 0.803 | 0.863 | 368 | 0.714 | 0.257 | 0.503 | 0.0002 | |
0.02 | 776 | 0.806 | 0.863 | 360 | 0.716 | 0.267 | 0.507 | 0.0002 | |
0.03 | 776 | 0.811 | 0.867 | 342 | 0.716 | 0.277 | 0.507 | 0.0002 | |
0.04 | 776 | 0.816 | 0.871 | 322 | 0.716 | 0.287 | 0.507 | 0.0002 | |
0.05 | 776 | 0.822 | 0.875 | 302 | 0.716 | 0.298 | 0.506 | 0.0002 | |
0.06 | 776 | 0.827 | 0.879 | 284 | 0.716 | 0.308 | 0.506 | 0.0002 | |
0.07 | 776 | 0.834 | 0.883 | 264 | 0.716 | 0.318 | 0.506 | 0.0002 |