Table 8.
Type I Error Rates of Mixed Effects for Difference in Coefficients Methods
| Sample size |
|||||
|---|---|---|---|---|---|
| α value/β value | 50 | 100 | 200 | 500 | 1,000 |
| τ – τ′ (Freedman & Schatzkin, 1992) | |||||
| Large/zero | .0440 | .0540 | .0500 | .0480 | .0380 |
| Medium/zero | .0460 | .0560 | .0460 | .0500 | .0480 |
| Small/zero | .0300 | .0560 | .0480 | .0440 | .0400 |
| Zero/large | .5680 | .5800 | .6000 | .5820 | .5980 |
| Zero/medium | .4720 | .6560 | .7100 | .7020 | .7080 |
| Zero/small | .1120 | .1980 | .3940 | .7520 | .8840 |
|
τ – τ′ (McGuigan & Langholtz, 1988) | |||||
| Large/zero | .0200 | .0380 | .0440 | .0440 | .0360 |
| Medium/zero | .0120 | .0280 | .0360 | .0440 | .0440 |
| Small/zero | 0 | .0020 | .0080 | .0080 | .0140 |
| Zero/large | .0300 | .0380 | .0400 | .0480 | .0320 |
| Zero/medium | .0120 | .0260 | .0420 | .0240 | .0440 |
| Zero/small | 0 | 0 | .0020 | .0100 | .0180 |
|
τ – τ′ (Clogg et al., 1992) | |||||
| Large/zero | .0460 | .0540 | .0500 | .0480 | .0380 |
| Medium/zero | .0460 | .0560 | .0460 | .0500 | .0480 |
| Small/zero | .0460 | .0640 | .0500 | .0440 | .0400 |
| Zero/large | .9800 | 1.000 | 1.000 | 1.000 | 1.000 |
| Zero/medium | .7740 | .9740 | 1.000 | 1.000 | 1.000 |
| Zero/small | .2020 | .2980 | .4900 | .8660 | .9860 |
|
Simple minus partial correlation (Olkin & Finn, 1995) | |||||
| Large/zero | .0340 | .0380 | .0480 | .0380 | .0364 |
| Medium/zero | .0160 | .0340 | .0380 | .0440 | .0500 |
| Small/zero | 0 | .0040 | .0080 | .0100 | .0160 |
| Zero/large | .0340 | .0380 | .0540 | .0520 | .0280 |
| Zero/medium | .0300 | .0400 | .0040 | .0280 | .0500 |
| Zero/small | 0 | .0060 | .0080 | .0140 | .0200 |
Note. For all analyses, τ′ = 0. Small value = .14, medium value = .39, and large value = .59. Tests are two-tailed, p = .05. For each method, values in each row are empirical estimates of the Type I error rate.