Table 6.
ANOVA Models, Using Nonnormal Data.
| Effect | df | Successful replications | Bias | Standardized bias | Efficiency |
|---|---|---|---|---|---|
| I | 2 | 124.49*** | 168.59*** | 270.76*** | 240.69*** |
| γ | 2 | 0.00 | 1215.43*** | 2449.80*** | 2974.83*** |
| CD | 5 | 1219.83*** | 686.33*** | 1266.31*** | 6770.51*** |
| Method | 4 | 183.97*** | 528.00*** | 525.92*** | 190.16*** |
| n | 3 | 79.03*** | 4.31* | 4.24* | 2657.27*** |
| Nonnormality (NN) | 1 | 2100.28*** | 299.53*** | 342.32*** | 8044.76*** |
| Method *CD | 20 | 121.49*** | 110.43*** | 122.62*** | 15.08*** |
| Method *γ | 8 | 0.00 | 262.68*** | 264.49*** | 3.55** |
| Method *I | 8 | 28.19*** | 22.15*** | 25.99*** | 3.15* |
| Method *n | 12 | 1.83+ | 0.55 | 0.20 | 0.49 |
| Method * NN | 4 | 153.36*** | 5.82** | 7.09*** | 3.15* |
| CD*γ | 10 | 0.00 | 340.41*** | 615.95*** | 644.05*** |
| CD*I | 10 | 36.24*** | 33.25*** | 45.76*** | 32.18*** |
| CD*n | 15 | 36.33*** | 2.64** | 1.77 | 62.45*** |
| CD* NN | 5 | 1087.06*** | 111.44*** | 92.32*** | 1874.78*** |
| γ*I | 4 | 0.00 | 77.43*** | 126.66*** | 4.54* |
| γ*n | 6 | 0.00 | 1.88 | 1.33 | 2.57+ |
| γ* NN | 2 | 0.00 | 152.23*** | 165.91*** | 1060.31*** |
| I*n | 6 | 3.39* | 1.07 | 0.42 | 4.04** |
| I* NN | 2 | 61.01*** | 22.12*** | 14.55*** | 8.72** |
| n* NN | 3 | 54.25*** | 7.35*** | 2.89+ | 2.53 |
| Effect | df | MSE | Standard error bias | Type I error rate | Power |
| I | 2 | 96.50*** | 4.57+ | 3.83+ | 321.30*** |
| γ | 2 | 824.44*** | 2473.21*** | / | 3549.41*** |
| CD | 5 | 935.59*** | 2733.13*** | 378.18*** | 1307.85*** |
| Method | 4 | 48.17*** | 95.91*** | 35.50*** | 0.72 |
| n | 3 | 70.00*** | 4.67* | 31.634*** | 810.00*** |
| Nonnormality (NN) | 1 | 657.45*** | 6300.45*** | 1804.36*** | 365.06*** |
| Method *CD | 20 | 20.40*** | 35.43*** | 31.72*** | 1.49 |
| Method *γ | 8 | 64.50*** | 70.14*** | / | 0.99 |
| Method *I | 8 | 3.88** | 2.19+ | 1.27 | 0.57 |
| Method *n | 12 | 0.48 | 0.68 | 1.21 | 0.05 |
| Method * NN | 4 | 5.28** | 22.85*** | 33.79*** | 2.11 |
| CD*γ | 10 | 408.33*** | 524.64*** | / | 926.40*** |
| CD* I | 10 | 38.39*** | 0.74 | 15.70*** | 111.62*** |
| CD*n | 15 | 16.93*** | 1.48 | 17.76*** | 114.89*** |
| CD* NN | 5 | 308.80*** | 1449.50*** | 340.35*** | 126.93 |
| γ*I | 4 | 55.55*** | 23.48*** | / | 198.07*** |
| γ*n | 6 | 4.79 | 9.81*** | / | 662.82*** |
| γ* NN | 2 | 265.38*** | 1037.45*** | / | 158.74*** |
| I*n | 6 | 1.13 | 0.64 | 1.36 | 22.92*** |
| I* NN | 2 | 3.88** | 8.01** | 0.31 | 26.26*** |
| n* NN | 3 | 11.56*** | 0.71 | 74.15*** | 13.08 |
| Residuals | 4,187 | 1,339 | 2,763 |
Note. ANOVA = analysis of variance; MSE = mean square error; CD = coefficient of determination.
+
p = .01-.05. *p = .001-.01. **p = .000-.001. ***p < .000.