Table 4.
Mean Kendall's τ for 1,000 replications between the ordering based on the population test-score reliability and the ordering produced by the three item-score reliability methods and the corrected item-total correlation (CITC), for the bottom-up and the top-down procedure in the six different conditions.
| N = 200 | N = 1, 000 | |||||
|---|---|---|---|---|---|---|
| Small variance | Average variance | Large variance | Small variance | Average variance | Large variance | |
| of α | of α | of α | of α | of α | of α | |
| BOTTOM-UP PROCEDURE | ||||||
| Method MS | 0.44 (0.13) | 0.67 (0.08) | 0.80 (0.06) | 0.69 (0.08) | 0.83 (0.05) | 0.89 (0.04) |
| Method λ6 | 0.55 (0.11) | 0.75 (0.07) | 0.83 (0.05) | 0.80 (0.05) | 0.91 (0.03) | 0.94 (0.03) |
| Method CA | 0.58 (0.10) | 0.78 (0.06) | 0.87 (0.05) | 0.81 (0.05) | 0.92 (0.03) | 0.96 (0.02) |
| CITC | 0.58 (0.10) | 0.78 (0.06) | 0.87 (0.04) | 0.81 (0.05) | 0.92 (0.03) | 0.96 (0.02) |
| TOP-DOWN PROCEDURE | ||||||
| Method MS | 0.46 (0.14) | 0.64 (0.10) | 0.75 (0.08) | 0.61 (0.11) | 0.73 (0.09) | 0.80 (0.08) |
| Method λ6 | 0.55 (0.10) | 0.75 (0.07) | 0.83 (0.06) | 0.81 (0.05) | 0.91 (0.03) | 0.94 (0.03) |
| Method CA | 0.59 (0.10) | 0.78 (0.06) | 0.87 (0.05) | 0.81 (0.05) | 0.92 (0.03) | 0.96 (0.02) |
| CITC | 0.59 (0.10) | 0.78 (0.06) | 0.87 (0.04) | 0.81 (0.05) | 0.92 (0.03) | 0.96 (0.02) |
The Standard Deviation is in Parentheses.