Research Article
Comparison of Test Statistics of Nonnormal and Unbalanced Samples for Multivariate Analysis of Variance in terms of Type-I Error Rates
Table 1
Type-1 error rates of simulation results for Gamma distribution.
| Number of variables | | | Test statistic | | R | | H | W | R | | H | W |
| Homogeneous variance | Gamma distribution (4-4-4; 0.5) | (10-10-10) | 0.0473 | 0.0491 | 0.0437 | 0.0490 | 0.0501 | 0.0507 | 0.0469 | 0.0513 | (20-20-20) | 0.0514 | 0.0497 | 0.0527 | 0.0449 | 0.0513 | 0.0541 | 0.0452 | 0.0495 | (50-50-50) | 0.0492 | 0.0506 | 0.0541 | 0.0493 | 0.0510 | 0.0491 | 0.0511 | 0.0475 | (10-10-20) | 0.0491 | 0.0539 | 0.0518 | 0.0509 | 0.0482 | 0.0470 | 0.0506 | 0.0460 | (10-10-50) | 0.0501 | 0.0493 | 0.0493 | 0.0448 | 0.0487 | 0.0529 | 0.0462 | 0.0490 | (10-20-20) | 0.0473 | 0.0517 | 0.0489 | 0.0485 | 0.0498 | 0.0513 | 0.0513 | 0.0478 | (10-20-50) | 0.0555 | 0.0508 | 0.0502 | 0.0472 | 0.0494 | 0.0484 | 0.0487 | 0.0514 | (10-50-50) | 0.0486 | 0.0502 | 0.0514 | 0.0546 | 0.0553 | 0.0500 | 0.0496 | 0.0519 | (20-20-50) | 0.0475 | 0.0502 | 0.0489 | 0.0472 | 0.0473 | 0.0491 | 0.0483 | 0.0517 | (20-50-50) | 0.0492 | 0.0491 | 0.0501 | 0.0515 | 0.0471 | 0.0503 | 0.0489 | 0.0475 |
| Heterogeneous variance | Gamma distribution (4-9-36; 0.5) | (10-10-10) | 0.0480 | 0.0458 | 0.0491 | 0.0474 | 0.0517 | 0.0505 | 0.0502 | 0.0483 | (20-20-20) | 0.0488 | 0.0486 | 0.0474 | 0.0501 | 0.0514 | 0.0478 | 0.0509 | 0.0513 | (50-50-50) | 0.0458 | 0.0518 | 0.0469 | 0.0533 | 0.0499 | 0.0493 | 0.0500 | 0.0481 | (10-10-20) | 0.0459 | 0.0503 | 0.0518 | 0.0497 | 0.0490 | 0.0447 | 0.0498 | 0.0477 | (10-10-50) | 0.0462 | 0.0492 | 0.0496 | 0.0474 | 0.0518 | 0.0487 | 0.0489 | 0.0512 | (10-20-20) | 0.0487 | 0.0506 | 0.0477 | 0.0535 | 0.0497 | 0.0485 | 0.0507 | 0.0497 | (10-20-50) | 0.0483 | 0.0516 | 0.0499 | 0.0504 | 0.0513 | 0.0457 | 0.0564 | 0.0531 | (10-50-50) | 0.0508 | 0.0514 | 0.0485 | 0.0528 | 0.0509 | 0.0515 | 0.0519 | 0.0449 | (20-20-50) | 0.0477 | 0.0483 | 0.0484 | 0.0481 | 0.0479 | 0.0506 | 0.0544 | 0.0492 | (20-50-50) | 0.0488 | 0.0525 | 0.0481 | 0.0480 | 0.0500 | 0.0482 | 0.0495 | 0.0504 |
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