Table 3.
Power estimates for three-way interaction effects between two dichotomous predictors and a continuous predictor of various interrelations
| Two-tailed p < .05 | ||||||||||||
| N | r = .01, d = .02 | r = .05, d = .10 | r = .10, d = .20 | |||||||||
| r ab | 0 | .10 | .30 | .50 | 0 | .10 | .30 | .50 | 0 | .10 | .30 | .50 |
| 50 | 3% | 3% | 3% | 3% | 5% | 5% | 5% | 4% | 9% | 8% | 7 | 7 |
| 100 | 3% | 3% | 3% | 3% | 6% | 6% | 6% | 6% | 13% | 13% | 14% | 12% |
| 150 | 3% | 3% | 3% | 3% | 8% | 7% | 8% | 7% | 21% | 19% | 19% | 17% |
| 200 | 3% | 3% | 3% | 3% | 9% | 9% | 9% | 9% | 27% | 28% | 22% | 18% |
| 250 | 3% | 4% | 4% | 3% | 12% | 11% | 11% | 11% | 34% | 32% | 28% | 26% |
| 300 | 4% | 3% | 4% | 3% | 11% | 14% | 12% | 8% | 39% | 39% | 31% | 29% |
| 350 | 3% | 4% | 4% | 4% | 14% | 12% | 16% | 13% | 44% | 41% | 42% | 34% |
| 400 | 4% | 4% | 4% | 3% | 16% | 14% | 14% | 14% | 52% | 49% | 50% | 36% |
| 450 | 4% | 3% | 4% | 4% | 17% | 17% | 15% | 14% | 55% | 55% | 52% | 43% |
| 500 | 4% | 4% | 4% | 4% | 21% | 19% | 17% | 15% | 57% | 58% | 56% | 48% |
| 750 | 4% | 5% | 4% | 4% | 28% | 26% | 21% | 21% | 76% | 76% | 72% | 68% |
| 1,000 | 5% | 5% | 5% | 4% | 35% | 35% | 27% | 25% | 86% | 85% | 86% | 77% |
| 2,500 | 6% | 7% | 7% | 7% | 68% | 71% | 64% | 51% | 100% | 100% | 100% | 99% |
| 5,000 | 11% | 10% | 9% | 10% | 92% | 93% | 92% | 86% | 100% | 100% | 100% | 100% |
| 7,500 | 16% | 14% | 11% | 11% | 99% | 98% | 99% | 97% | 100% | 100% | 100% | 100% |
| 10,000 | 13% | 16% | 16% | 14% | 100% | 100% | 100% | 99% | 100% | 100% | 100% | 100% |
| 100,000 | 88% | 88% | 83% | 78% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
| One-tailed p < .05 | ||||||||||||
| N | r = .01, d = .02 | r = .05, d = .10 | r = .10, d = .20 | |||||||||
| r ab | 0 | .10 | .30 | .50 | 0 | .10 | .30 | .50 | 0 | .10 | .30 | .50 |
| 50 | 6% | 6% | 6% | 6% | 9% | 9% | 9% | 8% | 15% | 14% | 11% | 12% |
| 100 | 6% | 6% | 6% | 6% | 12% | 14% | 12% | 10% | 23% | 22% | 23% | 20% |
| 150 | 6% | 6% | 6% | 6% | 14% | 14% | 14% | 12% | 29% | 30% | 29% | 26% |
| 200 | 7% | 7% | 7% | 6% | 18% | 16% | 17% | 15% | 39% | 38% | 36% | 31% |
| 250 | 7% | 7% | 7% | 7% | 18% | 20% | 17% | 17% | 46% | 45% | 39% | 38% |
| 300 | 7% | 7% | 6% | 6% | 20% | 20% | 18% | 15% | 48% | 50% | 47% | 42% |
| 350 | 7% | 7% | 7% | 7% | 22% | 20% | 22% | 19% | 56% | 54% | 53% | 48% |
| 400 | 7% | 7% | 8% | 7% | 25% | 23% | 22% | 21% | 63% | 59% | 59% | 52% |
| 450 | 7% | 7% | 7% | 7% | 25% | 26% | 22% | 23% | 67% | 67% | 63% | 56% |
| 500 | 7% | 8% | 7% | 8% | 30% | 29% | 29% | 22% | 70% | 70% | 67% | 63% |
| 750 | 9% | 8% | 9% | 8% | 36% | 36% | 34% | 29% | 86% | 84% | 80% | 77% |
| 1,000 | 9% | 9% | 9% | 8% | 46% | 48% | 40% | 34% | 93% | 91% | 91% | 85% |
| 2,500 | 12% | 12% | 11% | 11% | 76% | 78% | 74% | 67% | 100% | 100% | 100% | 100% |
| 5,000 | 17% | 18% | 17% | 16% | 97% | 97% | 96% | 92% | 100% | 100% | 100% | 100% |
| 7,500 | 24% | 22% | 19% | 17% | 100% | 99% | 99% | 98% | 100% | 100% | 100% | 100% |
| 10,000 | 24% | 23% | 22% | 22% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
| 100,000 | 93% | 94% | 90% | 86% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
Note: r and d values represent the effect size of the interaction term; rab represents the correlation between the continuous predictor and one of the dichotomous variables; we only provide estimates for a series of rab values given that rac and rbc would be = 0 since three-way interactions will likely include experimental conditions which are likely unrelated to the continuous predictor or gender; for the continuous predictors and the dependent variable, we assumed α = .85.