(\(\tau _{1}^{2}=0.001\)) | 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) | 0.01 | 10 | 0.344 | 0.706 | 14 | 0.640 | 0.728 | 1 | 0.0740 |
0.02 | 10 | 0.280 | 0.639 | 16 | 0.615 | 0.682 | 1 | 0.0559 | |
0.03 | 10 | 0.239 | 0.586 | 20 | 0.655 | 0.640 | 0.999 | 0.0416 | |
0.04 | 10 | 0.208 | 0.539 | 24 | 0.659 | 0.601 | 0.997 | 0.0322 | |
0.05 | 10 | 0.184 | 0.497 | 30 | 0.671 | 0.564 | 0.991 | 0.0244 | |
0.06 | 10 | 0.163 | 0.459 | 38 | 0.687 | 0.528 | 0.979 | 0.0187 | |
0.07 | 10 | 0.144 | 0.424 | 50 | 0.693 | 0.494 | 0.955 | 0.0137 | |
0.08 | 10 | 0.127 | 0.389 | 70 | 0.703 | 0.459 | 0.913 | 0.0096 | |
(0.1,0.8) | 0.01 | 14 | 0.439 | 0.748 | 16 | 0.586 | 0.656 | 1 | 0.0735 |
0.02 | 14 | 0.389 | 0.697 | 20 | 0.623 | 0.624 | 1 | 0.0390 | |
0.03 | 14 | 0.353 | 0.652 | 24 | 0.651 | 0.592 | 0.999 | 0.0298 | |
0.04 | 14 | 0.324 | 0.611 | 28 | 0.667 | 0.561 | 0.997 | 0.0245 | |
0.05 | 14 | 0.299 | 0.574 | 34 | 0.674 | 0.533 | 0.990 | 0.0187 | |
0.06 | 14 | 0.278 | 0.540 | 44 | 0.687 | 0.505 | 0.975 | 0.0136 | |
0.07 | 14 | 0.259 | 0.509 | 56 | 0.695 | 0.480 | 0.950 | 0.0104 | |
0.08 | 14 | 0.241 | 0.480 | 72 | 0.703 | 0.455 | 0.910 | 0.0080 | |
(0.1,0.7) | 0.01 | 20 | 0.507 | 0.773 | 22 | 0.603 | 0.572 | 1 | 0.0481 |
0.02 | 20 | 0.466 | 0.732 | 26 | 0.623 | 0.552 | 1 | 0.0262 | |
0.03 | 20 | 0.438 | 0.695 | 30 | 0.643 | 0.532 | 0.999 | 0.0205 | |
0.04 | 20 | 0.416 | 0.662 | 36 | 0.667 | 0.513 | 0.995 | 0.0157 | |
0.05 | 20 | 0.397 | 0.633 | 42 | 0.680 | 0.494 | 0.986 | 0.0129 | |
0.06 | 20 | 0.382 | 0.607 | 52 | 0.691 | 0.478 | 0.969 | 0.0097 | |
0.07 | 20 | 0.369 | 0.585 | 62 | 0.696 | 0.464 | 0.943 | 0.0078 | |
0.08 | 20 | 0.358 | 0.566 | 76 | 0.705 | 0.450 | 0.906 | 0.0062 | |
(0.2,0.8) | 0.01 | 20 | 0.430 | 0.734 | 24 | 0.601 | 0.561 | 1 | 0.0428 |
0.02 | 20 | 0.382 | 0.676 | 30 | 0.641 | 0.528 | 0.999 | 0.0259 | |
0.03 | 20 | 0.349 | 0.628 | 38 | 0.666 | 0.499 | 0.995 | 0.0176 | |
0.04 | 20 | 0.324 | 0.589 | 48 | 0.681 | 0.473 | 0.982 | 0.0127 | |
0.05 | 20 | 0.305 | 0.557 | 62 | 0.693 | 0.452 | 0.960 | 0.0092 | |
0.06 | 20 | 0.289 | 0.530 | 76 | 0.699 | 0.434 | 0.927 | 0.0073 | |
0.07 | 20 | 0.276 | 0.508 | 96 | 0.706 | 0.418 | 0.881 | 0.0057 | |
0.08 | 20 | 0.264 | 0.488 | 118 | 0.710 | 0.403 | 0.821 | 0.0046 | |
(0.1,0.6) | 0.01 | 28 | 0.511 | 0.770 | 32 | 0.604 | 0.483 | 1 | 0.0231 |
0.02 | 28 | 0.490 | 0.737 | 36 | 0.631 | 0.474 | 1 | 0.0175 | |
0.03 | 28 | 0.477 | 0.708 | 40 | 0.651 | 0.465 | 0.998 | 0.0145 | |
0.04 | 28 | 0.467 | 0.685 | 46 | 0.667 | 0.457 | 0.991 | 0.0111 | |
0.05 | 28 | 0.461 | 0.667 | 54 | 0.685 | 0.452 | 0.978 | 0.0086 | |
0.06 | 28 | 0.458 | 0.653 | 62 | 0.691 | 0.448 | 0.959 | 0.0069 | |
0.07 | 28 | 0.457 | 0.643 | 70 | 0.698 | 0.446 | 0.934 | 0.0057 | |
0.08 | 28 | 0.458 | 0.636 | 78 | 0.704 | 0.446 | 0.903 | 0.0049 | |
(0.2,0.7) | 0.01 | 30 | 0.479 | 0.750 | 36 | 0.608 | 0.477 | 1 | 0.0214 |
0.02 | 30 | 0.447 | 0.702 | 44 | 0.649 | 0.458 | 0.999 | 0.0144 | |
0.03 | 30 | 0.426 | 0.664 | 54 | 0.671 | 0.441 | 0.991 | 0.0102 | |
0.04 | 30 | 0.411 | 0.636 | 66 | 0.686 | 0.427 | 0.974 | 0.0076 | |
0.05 | 30 | 0.401 | 0.615 | 78 | 0.695 | 0.417 | 0.947 | 0.0061 | |
0.06 | 30 | 0.395 | 0.599 | 92 | 0.702 | 0.410 | 0.912 | 0.0050 | |
0.07 | 30 | 0.391 | 0.587 | 106 | 0.706 | 0.404 | 0.868 | 0.0042 | |
0.08 | 30 | 0.388 | 0.578 | 122 | 0.711 | 0.400 | 0.816 | 0.0035 | |
(0.1,0.5) | 0.01 | 40 | 0.490 | 0.751 | 48 | 0.614 | 0.392 | 1 | 0.0155 |
0.02 | 40 | 0.493 | 0.725 | 54 | 0.643 | 0.392 | 0.999 | 0.0107 | |
0.03 | 40 | 0.498 | 0.708 | 60 | 0.666 | 0.395 | 0.993 | 0.0084 | |
0.04 | 40 | 0.504 | 0.697 | 66 | 0.678 | 0.400 | 0.981 | 0.0067 | |
0.05 | 40 | 0.514 | 0.692 | 72 | 0.689 | 0.407 | 0.965 | 0.0055 | |
0.06 | 40 | 0.525 | 0.692 | 76 | 0.695 | 0.417 | 0.945 | 0.0047 | |
0.07 | 40 | 0.538 | 0.694 | 80 | 0.701 | 0.429 | 0.923 | 0.0041 | |
0.08 | 40 | 0.552 | 0.699 | 80 | 0.705 | 0.442 | 0.899 | 0.0038 | |
(0.2,0.6) | 0.01 | 46 | 0.487 | 0.742 | 56 | 0.624 | 0.388 | 1 | 0.0137 |
0.02 | 46 | 0.475 | 0.704 | 68 | 0.659 | 0.380 | 0.996 | 0.0083 | |
0.03 | 46 | 0.471 | 0.679 | 82 | 0.678 | 0.376 | 0.981 | 0.0057 | |
0.04 | 46 | 0.472 | 0.665 | 94 | 0.691 | 0.376 | 0.956 | 0.0046 | |
0.05 | 46 | 0.477 | 0.658 | 106 | 0.698 | 0.379 | 0.925 | 0.0037 | |
0.06 | 46 | 0.484 | 0.655 | 114 | 0.704 | 0.384 | 0.890 | 0.0032 | |
0.07 | 46 | 0.493 | 0.655 | 120 | 0.707 | 0.390 | 0.851 | 0.0029 | |
0.08 | 46 | 0.502 | 0.658 | 126 | 0.711 | 0.396 | 0.810 | 0.0026 | |
(0.3,0.7) | 0.01 | 48 | 0.465 | 0.724 | 62 | 0.630 | 0.379 | 1 | 0.0118 |
0.02 | 48 | 0.440 | 0.673 | 82 | 0.670 | 0.363 | 0.990 | 0.0068 | |
0.03 | 48 | 0.429 | 0.643 | 104 | 0.689 | 0.354 | 0.963 | 0.0046 | |
0.04 | 48 | 0.426 | 0.626 | 124 | 0.698 | 0.349 | 0.924 | 0.0036 | |
0.05 | 48 | 0.425 | 0.616 | 144 | 0.705 | 0.347 | 0.879 | 0.0029 | |
0.06 | 48 | 0.427 | 0.610 | 158 | 0.708 | 0.347 | 0.829 | 0.0026 | |
0.07 | 48 | 0.431 | 0.607 | 172 | 0.711 | 0.348 | 0.776 | 0.0023 | |
0.08 | 48 | 0.435 | 0.605 | 182 | 0.713 | 0.349 | 0.718 | 0.0021 | |
(0.1,0.4) | 0.01 | 64 | 0.497 | 0.735 | 82 | 0.635 | 0.300 | 0.999 | 0.0077 |
0.02 | 64 | 0.519 | 0.720 | 92 | 0.667 | 0.312 | 0.992 | 0.0053 | |
0.03 | 64 | 0.540 | 0.717 | 98 | 0.680 | 0.328 | 0.977 | 0.0041 | |
0.04 | 64 | 0.563 | 0.722 | 102 | 0.691 | 0.346 | 0.960 | 0.0034 | |
0.05 | 64 | 0.585 | 0.730 | 100 | 0.696 | 0.366 | 0.942 | 0.0031 | |
0.06 | 64 | 0.608 | 0.741 | 96 | 0.700 | 0.388 | 0.925 | 0.0029 | |
0.07 | 64 | 0.632 | 0.754 | 90 | 0.703 | 0.412 | 0.909 | 0.0027 | |
0.08 | 64 | 0.656 | 0.768 | 84 | 0.706 | 0.437 | 0.895 | 0.0025 | |
(0.2,0.5) | 0.01 | 78 | 0.496 | 0.726 | 104 | 0.644 | 0.297 | 0.998 | 0.0057 |
0.02 | 78 | 0.505 | 0.701 | 126 | 0.677 | 0.302 | 0.982 | 0.0036 | |
0.03 | 78 | 0.521 | 0.695 | 140 | 0.691 | 0.313 | 0.954 | 0.0027 | |
0.04 | 78 | 0.540 | 0.698 | 148 | 0.699 | 0.327 | 0.922 | 0.0023 | |
0.05 | 78 | 0.559 | 0.705 | 148 | 0.704 | 0.342 | 0.890 | 0.0021 | |
0.06 | 78 | 0.579 | 0.715 | 144 | 0.707 | 0.358 | 0.860 | 0.0019 | |
0.07 | 78 | 0.599 | 0.726 | 138 | 0.709 | 0.375 | 0.831 | 0.0018 | |
0.08 | 78 | 0.620 | 0.738 | 130 | 0.711 | 0.393 | 0.804 | 0.0018 | |
(0.3,0.6) | 0.01 | 84 | 0.474 | 0.708 | 120 | 0.652 | 0.291 | 0.997 | 0.0049 |
0.02 | 84 | 0.477 | 0.677 | 156 | 0.684 | 0.290 | 0.970 | 0.0029 | |
0.03 | 84 | 0.489 | 0.668 | 180 | 0.697 | 0.297 | 0.928 | 0.0022 | |
0.04 | 84 | 0.504 | 0.669 | 194 | 0.704 | 0.305 | 0.882 | 0.0018 | |
0.05 | 84 | 0.520 | 0.674 | 198 | 0.707 | 0.315 | 0.838 | 0.0016 | |
0.06 | 84 | 0.536 | 0.681 | 198 | 0.710 | 0.325 | 0.795 | 0.0015 | |
0.07 | 84 | 0.551 | 0.689 | 194 | 0.712 | 0.336 | 0.753 | 0.0015 | |
0.08 | 84 | 0.566 | 0.698 | 188 | 0.713 | 0.346 | 0.712 | 0.0014 | |
(0.1,0.3) | 0.01 | 124 | 0.525 | 0.718 | 182 | 0.671 | 0.214 | 0.987 | 0.0025 |
0.02 | 124 | 0.574 | 0.730 | 186 | 0.688 | 0.242 | 0.960 | 0.0018 | |
0.03 | 124 | 0.614 | 0.749 | 174 | 0.695 | 0.271 | 0.937 | 0.0016 | |
0.04 | 124 | 0.650 | 0.768 | 156 | 0.699 | 0.301 | 0.920 | 0.0016 | |
0.05 | 124 | 0.681 | 0.787 | 138 | 0.702 | 0.332 | 0.908 | 0.0015 | |
0.06 | 124 | 0.710 | 0.805 | 120 | 0.704 | 0.363 | 0.899 | 0.0015 | |
0.07 | 124 | 0.738 | 0.822 | 102 | 0.704 | 0.397 | 0.894 | 0.0015 | |
0.08 | 124 | 0.765 | 0.840 | 86 | 0.705 | 0.433 | 0.891 | 0.0016 | |
(0.2,0.4) | 0.01 | 164 | 0.524 | 0.711 | 254 | 0.678 | 0.210 | 0.979 | 0.0017 |
0.02 | 164 | 0.565 | 0.718 | 272 | 0.695 | 0.233 | 0.934 | 0.0012 | |
0.03 | 164 | 0.602 | 0.735 | 260 | 0.702 | 0.258 | 0.895 | 0.0010 | |
0.04 | 164 | 0.635 | 0.753 | 236 | 0.706 | 0.283 | 0.864 | 0.0010 | |
0.05 | 164 | 0.665 | 0.771 | 208 | 0.708 | 0.309 | 0.841 | 0.0010 | |
0.06 | 164 | 0.692 | 0.789 | 182 | 0.710 | 0.335 | 0.822 | 0.0010 | |
0.07 | 164 | 0.718 | 0.805 | 156 | 0.710 | 0.362 | 0.809 | 0.0010 | |
0.08 | 164 | 0.742 | 0.822 | 134 | 0.711 | 0.389 | 0.798 | 0.0010 | |
(0.3,0.5) | 0.01 | 186 | 0.509 | 0.697 | 314 | 0.683 | 0.205 | 0.971 | 0.0014 |
0.02 | 186 | 0.545 | 0.701 | 348 | 0.699 | 0.224 | 0.909 | 0.0010 | |
0.03 | 186 | 0.580 | 0.717 | 336 | 0.705 | 0.244 | 0.857 | 0.0008 | |
0.04 | 186 | 0.610 | 0.734 | 310 | 0.708 | 0.265 | 0.815 | 0.0008 | |
0.05 | 186 | 0.638 | 0.751 | 280 | 0.711 | 0.285 | 0.780 | 0.0008 | |
0.06 | 186 | 0.663 | 0.767 | 250 | 0.711 | 0.304 | 0.751 | 0.0008 | |
0.07 | 186 | 0.686 | 0.782 | 222 | 0.713 | 0.324 | 0.726 | 0.0008 | |
0.08 | 186 | 0.707 | 0.796 | 194 | 0.714 | 0.343 | 0.704 | 0.0008 | |
(0.4,0.6) | 0.01 | 194 | 0.495 | 0.684 | 354 | 0.686 | 0.200 | 0.962 | 0.0012 |
0.02 | 194 | 0.526 | 0.685 | 406 | 0.702 | 0.214 | 0.885 | 0.0008 | |
0.03 | 194 | 0.556 | 0.698 | 402 | 0.707 | 0.229 | 0.820 | 0.0007 | |
0.04 | 194 | 0.582 | 0.712 | 382 | 0.710 | 0.244 | 0.767 | 0.0007 | |
0.05 | 194 | 0.605 | 0.726 | 354 | 0.712 | 0.258 | 0.722 | 0.0007 | |
0.06 | 194 | 0.626 | 0.739 | 326 | 0.713 | 0.272 | 0.682 | 0.0007 | |
0.07 | 194 | 0.645 | 0.751 | 300 | 0.714 | 0.284 | 0.646 | 0.0007 | |
0.08 | 194 | 0.662 | 0.763 | 274 | 0.715 | 0.296 | 0.610 | 0.0007 | |
(0.1,0.2) | 0.01 | 398 | 0.626 | 0.752 | 562 | 0.701 | 0.145 | 0.897 | 0.0005 |
0.02 | 398 | 0.703 | 0.799 | 402 | 0.705 | 0.190 | 0.870 | 0.0005 | |
0.03 | 398 | 0.751 | 0.830 | 302 | 0.706 | 0.230 | 0.861 | 0.0005 | |
0.04 | 398 | 0.786 | 0.853 | 234 | 0.706 | 0.268 | 0.861 | 0.0005 | |
0.05 | 398 | 0.814 | 0.872 | 184 | 0.707 | 0.305 | 0.864 | 0.0005 | |
0.06 | 398 | 0.837 | 0.888 | 146 | 0.707 | 0.343 | 0.870 | 0.0005 | |
0.07 | 398 | 0.859 | 0.903 | 116 | 0.707 | 0.384 | 0.878 | 0.0005 | |
0.08 | 398 | 0.879 | 0.917 | 88 | 0.706 | 0.429 | 0.887 | 0.0006 | |
(0.2,0.3) | 0.01 | 588 | 0.623 | 0.747 | 874 | 0.704 | 0.140 | 0.864 | 0.0003 |
0.02 | 588 | 0.697 | 0.792 | 630 | 0.708 | 0.180 | 0.813 | 0.0003 | |
0.03 | 588 | 0.743 | 0.823 | 470 | 0.710 | 0.216 | 0.791 | 0.0003 | |
0.04 | 588 | 0.778 | 0.846 | 362 | 0.711 | 0.250 | 0.782 | 0.0003 | |
0.05 | 588 | 0.806 | 0.865 | 284 | 0.711 | 0.283 | 0.779 | 0.0003 | |
0.06 | 588 | 0.829 | 0.881 | 224 | 0.711 | 0.316 | 0.780 | 0.0003 | |
0.07 | 588 | 0.849 | 0.895 | 176 | 0.711 | 0.350 | 0.785 | 0.0003 | |
0.08 | 588 | 0.868 | 0.909 | 138 | 0.711 | 0.386 | 0.793 | 0.0004 | |
(0.3,0.4) | 0.01 | 712 | 0.614 | 0.739 | 1126 | 0.706 | 0.136 | 0.841 | 0.0002 |
0.02 | 712 | 0.684 | 0.783 | 830 | 0.710 | 0.171 | 0.774 | 0.0002 | |
0.03 | 712 | 0.730 | 0.813 | 628 | 0.711 | 0.202 | 0.740 | 0.0002 | |
0.04 | 712 | 0.764 | 0.836 | 488 | 0.712 | 0.231 | 0.720 | 0.0002 | |
0.05 | 712 | 0.791 | 0.854 | 388 | 0.713 | 0.259 | 0.708 | 0.0002 | |
0.06 | 712 | 0.814 | 0.870 | 310 | 0.713 | 0.286 | 0.701 | 0.0003 | |
0.07 | 712 | 0.834 | 0.884 | 250 | 0.713 | 0.313 | 0.697 | 0.0003 | |
0.08 | 712 | 0.852 | 0.896 | 200 | 0.714 | 0.341 | 0.697 | 0.0003 | |
(0.4,0.5) | 0.01 | 776 | 0.605 | 0.732 | 1298 | 0.707 | 0.132 | 0.823 | 0.0002 |
0.02 | 776 | 0.672 | 0.773 | 984 | 0.711 | 0.163 | 0.742 | 0.0002 | |
0.03 | 776 | 0.715 | 0.802 | 762 | 0.712 | 0.189 | 0.698 | 0.0002 | |
0.04 | 776 | 0.747 | 0.824 | 608 | 0.713 | 0.213 | 0.668 | 0.0002 | |
0.05 | 776 | 0.773 | 0.841 | 494 | 0.714 | 0.234 | 0.646 | 0.0002 | |
0.06 | 776 | 0.794 | 0.856 | 406 | 0.714 | 0.255 | 0.629 | 0.0002 | |
0.07 | 776 | 0.813 | 0.869 | 338 | 0.715 | 0.275 | 0.614 | 0.0002 | |
0.08 | 776 | 0.829 | 0.880 | 282 | 0.715 | 0.294 | 0.602 | 0.0002 |