Table 1.
Root expected mean square error of equating, performance misclassifications, passing rates, and passing misclassifications between estimation and truth.
| Ability shift | True passing Rate (%) | Models | IRT scaling methodsa | REMSEEb | Classification Misclassifications (%)c |
Passing rates (%) | Passing misclassifications (%)d | |
|---|---|---|---|---|---|---|---|---|
| UC | OC | |||||||
| 0.00 | 50.72 | 3PL/2PL/GPC | FCIP | 0.04 | 5.99 | 6.20 | 50.82 | 0.09 |
| MS | 0.10 | 5.97 | 6.23 | 50.83 | 0.11 | |||
| SL | 0.04 | 5.94 | 6.25 | 50.85 | 0.12 | |||
| 2PL/2PL/GPC | FCIP | 0.16 | 5.88 | 6.46 | 50.55 | -0.18 | ||
| MS | 0.16 | 5.96 | 6.38 | 50.49 | -0.23 | |||
| SL | 0.15 | 5.85 | 6.49 | 50.58 | -0.14 | |||
| 1PL/1PL/PC | FCIP | 1.02 | 7.19 | 6.49 | 49.74 | -0.98 | ||
| MS | 0.35 | 6.45 | 6.48 | 50.04 | -0.68 | |||
| SL | 0.36 | 6.42 | 6.54 | 50.04 | -0.68 | |||
| 0.10 | 54.61 | 3PL/2PL/GPC | FCIP | 0.05 | 6.12 | 6.19 | 54.71 | 0.09 |
| MS | 0.09 | 6.06 | 6.26 | 54.74 | 0.12 | |||
| SL | 0.06 | 5.96 | 6.34 | 54.82 | 0.21 | |||
| 2PL/2PL/GPC | FCIP | 0.16 | 6.00 | 6.44 | 54.41 | -0.20 | ||
| MS | 0.18 | 6.04 | 6.40 | 54.34 | -0.27 | |||
| SL | 0.15 | 5.80 | 6.65 | 54.54 | -0.07 | |||
| 1PL/1PL/PC | FCIP | 1.04 | 7.57 | 6.23 | 53.62 | -1.00 | ||
| MS | 0.39 | 6.90 | 6.33 | 53.95 | -0.67 | |||
| SL | 0.37 | 6.65 | 6.41 | 53.95 | -0.67 | |||
| 0.25 | 60.59 | 3PL/2PL/GPC | FCIP | 0.05 | 6.23 | 6.11 | 60.60 | 0.01 |
| MS | 0.12 | 5.93 | 6.42 | 60.78 | 0.19 | |||
| SL | 0.12 | 5.86 | 6.48 | 60.85 | 0.26 | |||
| 2PL/2PL/GPC | FCIP | 0.16 | 6.12 | 6.35 | 60.29 | -0.30 | ||
| MS | 0.21 | 6.16 | 6.33 | 60.17 | -0.42 | |||
| SL | 0.15 | 5.66 | 6.83 | 60.53 | -0.06 | |||
| 1PL/1PL/PC | FCIP | 1.07 | 8.23 | 5.76 | 59.48 | -1.11 | ||
| MS | 0.48 | 8.08 | 5.69 | 59.82 | -0.77 | |||
| SL | 0.38 | 7.02 | 6.13 | 59.82 | -0.77 | |||
| 0.50 | 69.73 | 3PL/2PL/GPC | FCIP | 0.05 | 6.38 | 5.79 | 69.60 | -0.13 |
| MS | 0.17 | 5.83 | 6.34 | 69.89 | 0.15 | |||
| SL | 0.20 | 5.65 | 6.49 | 70.08 | 0.35 | |||
| 2PL/2PL/GPC | FCIP | 0.16 | 6.24 | 6.03 | 69.30 | -0.43 | ||
| MS | 0.27 | 6.24 | 6.04 | 68.76 | -0.98 | |||
| SL | 0.15 | 5.37 | 6.94 | 69.17 | -0.56 | |||
| 1PL/1PL/PC | FCIP | 1.11 | 9.07 | 4.91 | 68.54 | -1.19 | ||
| MS | 0.63 | 9.43 | 4.59 | 67.98 | -1.75 | |||
| SL | 0.43 | 7.44 | 5.53 | 68.89 | -0.84 | |||
aFCIP = separate calibration with linking and fixed common item parameter; MS = mean/sigma method; SL = Stocking and Lord characteristic curve method.
bREMSEE = Root Expected Mean Square Error of Equating.
cUC = under-classificationOC = over-classification.
dPassing misclassification = the difference between the estimated and the true passing rates, where a positive sign (+) represents an over-estimated passing rate and a negative sign (–) represents an underestimated passing rate.