Table 1.
Type I Error Rates for Polytomous Data.
| Iterative Wald approach |
Wald-2 approach |
|||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Scale length |
15 items |
30 items |
15 items |
30 items |
||||||||||||
| NR/NF | 500/500 | 750/250 | 1,000/1,000 | 1,500/500 | 500/500 | 750/250 | 1,000/1,000 | 1,500/500 | 500/500 | 750/250 | 1,000/1,000 | 1,500/500 | 500/500 | 750/250 | 1,000/1,000 | 1,500/500 |
| Compensatory DIF | ||||||||||||||||
| % DIF = 0.2 | ||||||||||||||||
| DIF size = 0.3 | .04 | .04 | .03 | .04 | .04 | .04 | .03 | .04 | .04 | .04 | .05 | .04 | .04 | .05 | .04 | .04 |
| DIF size = 0.5 | .04 | .04 | .04 | .04 | .03 | .04 | .03 | .04 | .05 | .05 | .07 | .06 | .05 | .05 | .06 | .05 |
| DIF size = 0.7 | .04 | .04 | .03 | .04 | .03 | .04 | .03 | .04 | .07 | .06 | .12 | .08 | .05 | .05 | .07 | .06 |
| % DIF = 0.4 | ||||||||||||||||
| DIF size = 0.3 | .04 | .04 | .03 | .04 | .03 | .04 | .03 | .04 | .05 | .05 | .06 | .05 | .04 | .05 | .05 | .05 |
| DIF size = 0.5 | .03 | .04 | .03 | .04 | .03 | .04 | .03 | .04 | .07 | .06 | .11 | .08 | .06 | .05 | .08 | .07 |
| DIF size = 0.7 | .03 | .04 | .03 | .03 | .03 | .03 | .03 | .03 | .13 | .08 | .21 | .14 | .08 | .06 | .13 | .09 |
| Noncompensatory DIF | ||||||||||||||||
| % DIF = 0.2 | ||||||||||||||||
| DIF size = 0.3 | .03 | .04 | .03 | .04 | .03 | .04 | .03 | .03 | .04 | .05 | .05 | .04 | .05 | .05 | .06 | .05 |
| DIF size = 0.5 | .03 | .04 | .03 | .04 | .03 | .04 | .03 | .04 | .05 | .05 | .06 | .06 | .05 | .06 | .06 | .07 |
| DIF size = 0.7 | .03 | .03 | .03 | .04 | .03 | .04 | .03 | .04 | .05 | .05 | .06 | .06 | .05 | .06 | .07 | .07 |
| % DIF = 0.4 | ||||||||||||||||
| DIF size = 0.3 | .03 | .04 | .03 | .04 | .03 | .04 | .03 | .04 | .06 | .06 | .11 | .10 | .07 | .07 | .12 | .11 |
| DIF size = 0.5 | .03 | .03 | .03 | .04 | .03 | .04 | .03 | .04 | .11 | .09 | .18 | .16 | .11 | .11 | .21 | .18 |
| DIF size = 0.7 | .03 | .04 | .03 | .04 | .03 | .04 | .03 | .04 | .09 | .10 | .18 | .19 | .12 | .11 | .21 | .22 |
Note. DIF = differential item functioning; NR = number of respondents in reference group; NF = number of respondents in focal group; % DIF = percentage of DIF items.