Table 3.
Power 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 | .94 | .84 | 1.00 | .99 | .95 | .87 | 1.00 | 1.00 | .94 | .85 | 1.00 | .99 | .95 | .88 | 1.00 | 1.00 |
| DIF size = 0.5 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| DIF size = 0.7 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| % DIF = 0.4 | ||||||||||||||||
| DIF size = 0.3 | .93 | .82 | 1.00 | .99 | .95 | .87 | 1.00 | 1.00 | .94 | .83 | 1.00 | .99 | .96 | .88 | 1.00 | 1.00 |
| DIF size = 0.5 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| DIF size = 0.7 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Noncompensatory DIF | ||||||||||||||||
| % DIF = 0.2 | ||||||||||||||||
| DIF size = 0.3 | .94 | .88 | 1.00 | 1.00 | .96 | .90 | 1.00 | 1.00 | .94 | .89 | 1.00 | 1.00 | .96 | .90 | 1.00 | 1.00 |
| DIF size = 0.5 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| DIF size = 0.7 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| % DIF = 0.4 | ||||||||||||||||
| DIF size = 0.3 | .92 | .86 | 1.00 | .99 | .93 | .88 | 1.00 | .99 | .92 | .86 | 1.00 | .99 | .93 | .88 | 1.00 | .99 |
| DIF size = 0.5 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| DIF size = 0.7 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
Note. DIF = differential item functioning; NR = number of respondents in reference group; NF = Number of respondents in focal group; % DIF = percentage of DIF items.