Table 2.
Type I Error Rates for Dichotomous 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 | .08 | .07 | .05 | .05 | .09 | .08 | .06 | .05 | .10 | .08 | .06 | .06 | .11 | .09 |
| DIF size = 0.5 | .05 | .05 | .08 | .07 | .05 | .05 | .08 | .07 | .07 | .07 | .12 | .10 | .06 | .07 | .11 | .09 |
| DIF size = 0.7 | .05 | .04 | .07 | .07 | .05 | .05 | .08 | .07 | .08 | .07 | .15 | .13 | .07 | .07 | .13 | .11 |
| % DIF = 0.4 | ||||||||||||||||
| DIF size = 0.3 | .05 | .05 | .07 | .07 | .05 | .05 | .08 | .08 | .07 | .06 | .10 | .09 | .06 | .06 | .14 | .12 |
| DIF size = 0.5 | .05 | .06 | .07 | .07 | .05 | .06 | .05 | .05 | .09 | .08 | .15 | .13 | .08 | .07 | .10 | .08 |
| DIF size = 0.7 | .05 | .05 | .08 | .06 | .04 | .06 | .07 | .08 | .12 | .10 | .24 | .17 | .09 | .07 | .18 | .15 |
| Noncompensatory DIF | ||||||||||||||||
| % DIF = 0.2 | ||||||||||||||||
| DIF size = 0.3 | .02 | .02 | .02 | .03 | .02 | .02 | .02 | .02 | .03 | .03 | .06 | .05 | .03 | .03 | .03 | .04 |
| DIF size = 0.5 | .02 | .03 | .02 | .03 | .02 | .02 | .02 | .02 | .07 | .05 | .17 | .11 | .05 | .04 | .09 | .08 |
| DIF size = 0.7 | .02 | .03 | .02 | .03 | .02 | .02 | .02 | .02 | .15 | .10 | .33 | .23 | .10 | .07 | .21 | .17 |
| % DIF = 0.4 | ||||||||||||||||
| DIF size = 0.3 | .05 | .05 | .08 | .09 | .04 | .05 | .07 | .07 | .07 | .06 | .18 | .13 | .05 | .06 | .11 | .10 |
| DIF size = 0.5 | .11 | .11 | .19 | .17 | .10 | .10 | .16 | .14 | .23 | .17 | .55 | .40 | .19 | .15 | .38 | .32 |
| DIF size = 0.7 | .21 | .21 | .24 | .27 | .19 | .15 | .28 | .21 | .51 | .34 | .76 | .66 | .41 | .30 | .71 | .59 |
Note. DIF = differential Item Functioning; NR = number of respondents in reference group; NF = number of respondents in focal group; % DIF = percentage of DIF items.