Table 6.
Type I Error Rates and Statistical Power for Product of Coefficients Methods
| Sample size |
|||||
|---|---|---|---|---|---|
| Effect size | 50 | 100 | 200 | 500 | 1,000 |
| First-order test (Sobel, 1982) | |||||
| Zero | 0 | 0 | .0020 | 0 | 0 |
| Small | .0060 | .0100 | .1220 | .5620 | .9760 |
| Medium | .3600 | .8620 | 1.000 | 1.000 | 1.000 |
| Large | .9020 | 1.000 | 1.000 | 1.000 | 1.000 |
|
Second-order test (Aroian, 1944) | |||||
| Zero | 0 | 0 | 0 | 0 | 0 |
| Small | .0060 | .0060 | .0920 | .5260 | .9740 |
| Medium | .3320 | .8540 | 1.000 | 1.000 | 1.000 |
| Large | .8920 | 1.000 | 1.000 | 1.000 | 1.000 |
|
Unbiased test (Goodman, 1960) | |||||
| Zero | .0160 | .0040 | .0140 | .0020 | .0100 |
| Small | .0080 | .0200 | .1420 | .6200 | .9820 |
| Medium | .3900 | .8700 | 1.000 | 1.000 | 1.000 |
| Large | .9120 | 1.000 | 1.000 | 1.000 | 1.000 |
|
Distribution of products test P = zαzβ (MacKinnon et al., 1998) | |||||
| Zero | .0620 | .0760 | .0420 | .0660 | .0400 |
| Small | .2220 | .3960 | .7180 | .9740 | 1.000 |
| Medium | .9180 | .9960 | 1.000 | 1.000 | 1.000 |
| Large | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
|
Distribution of αβ/σαβ (MacKinnon et al., 1998) | |||||
| Zero | .0560 | .0680 | .0400 | .0600 | .0420 |
| Small | .2060 | .3600 | .6920 | .9580 | .9960 |
| Medium | .9040 | .9960 | 1.000 | 1.000 | 1.000 |
| Large | .9980 | 1.000 | 1.000 | 1.000 | 1.000 |
|
Asymmetric distribution of products test (MacKinnon & Lockwood, 2001) | |||||
| Zero | .0040 | .0040 | .0020 | 0 | 0 |
| Small | .0300 | .0620 | .2740 | .7600 | .9880 |
| Medium | .5540 | .9200 | 1.000 | 1.000 | 1.000 |
| Large | .9400 | 1.000 | 1.000 | 1.000 | 1.000 |
|
Product of coefficients for standardized variables (Bobko & Rieck, 1980) | |||||
| Zero | .0020 | 0 | .0020 | 0 | 0 |
| Small | .0080 | .0160 | .1300 | .5700 | .9780 |
| Medium | .4200 | .8760 | 1.000 | 1.000 | 1.000 |
| Large | .9200 | 1.000 | 1.000 | 1.000 | 1.000 |
Note. For all analyses, α = β and τ′ = 0. Small effect size = .14, medium effect size = .36, and large effect size = .51. Tests are two-tailed, p = .05. For each method, values in the first row for each test are estimates of the empirical Type I error rate. Values in rows 2–4 represent empirical estimates of statistical power.