Table 2:
Evaluation of one-tail empirical type I error rates of six methods for testing medians with nominal level α = 0.05 for each tail.
| Test Statistics | ||||||||
|---|---|---|---|---|---|---|---|---|
| n | SD | Ratio SDs | t | Wiicoxon | Score | Wald | R | R* |
| 3 | 2 | 1 | 0.0382* | 0 | 0.0265 | 0.0379 | 0.0959 | 0.0404 |
| 3 | 2 | 1 | 0.0424† | 0 | 0.0222 | 0.0207 | 0.0951 | 0.0422 |
| 3 | 2 | 2 | 0.0418 | 0 | 0.0310 | 0.0394 | 0.1020 | 0.0472 |
| 3 | 2 | 2 | 0.0469 | 0 | 0.0275 | 0.0262 | 0.0983 | 0.0457 |
| 3 | 2 | 3 | 0.0423 | 0 | 0.0312 | 0.0376 | 0.1087 | 0.0489 |
| 3 | 2 | 3 | 0.0535 | 0 | 0.0272 | 0.0261 | 0.1066 | 0.0493 |
| 3 | 3 | 1 | 0.0373 | 0 | 0.0271 | 0.0445 | 0.0957 | 0.0424 |
| 3 | 3 | 1 | 0.0402 | 0 | 0.0230 | 0.0221 | 0.0878 | 0.0378 |
| 3 | 3 | 2 | 0.0388 | 0 | 0.0312 | 0.0408 | 0.1023 | 0.0475 |
| 3 | 3 | 2 | 0.0486 | 0 | 0.0263 | 0.0247 | 0.0958 | 0.0458 |
| 3 | 3 | 3 | 0.0393 | 0 | 0.0332 | 0.0394 | 0.1074 | 0.0499 |
| 3 | 3 | 3 | 0.0534 | 0 | 0.0244 | 0.0242 | 0.1004 | 0.0467 |
| 3 | 4 | 1 | 0.0396 | 0 | 0.0297 | 0.0523 | 0.0989 | 0.0439 |
| 3 | 4 | 1 | 0.0394 | 0 | 0.0191 | 0.0177 | 0.0901 | 0.0390 |
| 3 | 4 | 2 | 0.0413 | 0 | 0.0351 | 0.0501 | 0.1053 | 0.0495 |
| 3 | 4 | 2 | 0.0458 | 0 | 0.0233 | 0.0221 | 0.0908 | 0.0414 |
| 3 | 4 | 3 | 0.0410 | 0 | 0.0360 | 0.0445 | 0.1084 | 0.0545 |
| 3 | 4 | 3 | 0.0540 | 0 | 0.0266 | 0.0259 | 0.0988 | 0.0458 |
| 15 | 2 | 1 | 0.0631 | 0.0271 | 0.0548 | 0.0559 | 0.0595 | 0.0522 |
| 15 | 2 | 1 | 0.0391 | 0.0187 | 0.0520 | 0.0505 | 0.0553 | 0.0495 |
| 15 | 2 | 2 | 0.0785 | 0.0303 | 0.0535 | 0.0538 | 0.0591 | 0.0511 |
| 15 | 2 | 2 | 0.0267 | 0.0186 | 0.0459 | 0.0455 | 0.0524 | 0.0443 |
| 15 | 2 | 3 | 0.0981 | 0.0352 | 0.0548 | 0.0548 | 0.0631 | 0.0537 |
| 15 | 2 | 3 | 0.0235 | 0.0268 | 0.0496 | 0.0494 | 0.0548 | 0.0486 |
| 15 | 3 | 1 | 0.0707 | 0.0273 | 0.0571 | 0.0590 | 0.0607 | 0.0532 |
| 15 | 3 | 1 | 0.0345 | 0.0163 | 0.0508 | 0.0486 | 0.0561 | 0.0486 |
| 15 | 3 | 2 | 0.0966 | 0.0357 | 0.0597 | 0.0606 | 0.0652 | 0.0566 |
| 15 | 3 | 2 | 0.0255 | 0.0211 | 0.0534 | 0.0526 | 0.0586 | 0.0517 |
| 15 | 3 | 3 | 0.1146 | 0.0373 | 0.0531 | 0.0533 | 0.0603 | 0.0508 |
| 15 | 3 | 3 | 0.0202 | 0.0236 | 0.0485 | 0.0485 | 0.0554 | 0.0485 |
| 15 | 4 | 1 | 0.0723 | 0.0260 | 0.0501 | 0.0532 | 0.0546 | 0.0469 |
| 15 | 4 | 1 | 0.0329 | 0.0182 | 0.0486 | 0.0470 | 0.0532 | 0.0478 |
| 15 | 4 | 2 | 0.1108 | 0.0353 | 0.0561 | 0.0571 | 0.0611 | 0.0524 |
| 15 | 4 | 2 | 0.0226 | 0.0190 | 0.0534 | 0.0518 | 0.0585 | 0.0522 |
| 15 | 4 | 3 | 0.1399 | 0.0373 | 0.0553 | 0.0556 | 0.0621 | 0.0521 |
| 15 | 4 | 3 | 0.0161 | 0.0216 | 0.0473 | 0.0469 | 0.0549 | 0.0465 |
SD: control (untreated) group standard deviation; Ratio SDs: ratio of standard deviations of treatment group vs. untreated group
*
, left trial empirical type I error
†
, right trial empirical type I error.