Table 2.
Estimated size (%) of the WMW test and three FP tests: FP*, which uses the original variance estimator from Fligner and Policello (1981), and (2) and (3), which use the variance estimators based on formula (2) and (3), respectively. Nominal level 5%. X,Y ~ Logistic(0, 1).
| m | n = m | n = 2m | n = 4m | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| WMW | FP* | (2) | (3) | WMW | FP* | (2) | (3) | WMW | FP* | (2) | (3) | |
| normal approx. | ||||||||||||
| 5 | 3.21 | 8.01 | 8.01 | 8.01 | 4.06 | 8.51 | 8.24 | 8.57 | 4.07 | 9.95 | 9.29 | 9.78 |
| 10 | 4.46 | 6.45 | 6.45 | 6.71 | 4.39 | 6.77 | 6.62 | 6.97 | 4.88 | 7.46 | 7.09 | 7.29 |
| 20 | 5.29 | 6.10 | 6.10 | 6.30 | 5.03 | 6.13 | 6.05 | 6.18 | 5.14 | 6.52 | 6.25 | 6.40 |
| 30 | 4.70 | 5.28 | 5.28 | 5.47 | 5.11 | 5.74 | 5.70 | 5.78 | 5.19 | 5.96 | 5.82 | 5.90 |
| 50 | 5.19 | 5.46 | 5.46 | 5.63 | 5.30 | 5.66 | 5.64 | 5.72 | 5.27 | 5.81 | 5.66 | 5.76 |
|
| ||||||||||||
| permutation | ||||||||||||
| 5 | 3.21 | 4.10 | 4.10 | 4.10 | 4.06 | 5.02 | 5.02 | 4.95 | 4.07 | 4.83 | 4.81 | 4.82 |
| 10 | 4.46 | 4.99 | 4.99 | 5.00 | 4.86 | 5.16 | 5.22 | 5.18 | 5.13 | 5.21 | 5.16 | 5.14 |
| 20 | 5.29 | 5.44 | 5.44 | 5.45 | 5.03 | 5.35 | 5.38 | 5.37 | 5.14 | 5.31 | 5.29 | 5.28 |
| 30 | 4.84 | 4.91 | 4.91 | 4.90 | 5.11 | 5.20 | 5.19 | 5.20 | 5.19 | 5.35 | 5.37 | 5.36 |
| 50 | 5.19 | 5.24 | 5.24 | 5.25 | 5.32 | 5.37 | 5.38 | 5.39 | 5.27 | 5.30 | 5.30 | 5.30 |