Table 5.
Pass Marks (%) Required to Detect 50% and 60% Knowledge for a 5-Question MC, with ≤5% of a False Positive Rate
| # items | Pass marks required for β=15.6%, probabilities and rates of guessing from the means of Table 5 (p=0.5324a) |
Column C: Type II error: Probability that a student with 50% knowledge fails (pass mark from Column A, p=0.5324) | Column D: Type I error: Probability that a student with no knowledge passes (pass mark=50%, p=0.421b) | |
|---|---|---|---|---|
| Column A: 50% Knowledge | Column B: 60% Knowledge | |||
|
| ||||
| 2 | – | – | – | 66.5% |
| 4 | – | – | – | 56.1% |
| 6 | – | – | – | 49.9% |
| 8 | 100.0% | – | 95.9% | 45.5% |
| 10 | 100.0% | 100.0% | 98.2% | 42.4% |
| 12 | 100.0% | 100.0% | 93.9% | 39.2% |
| 14 | 92.9% | 100.0% | 96.9% | 36.7% |
| 16 | 93.8% | 93.8% | 98.4% | 34.6% |
| 18 | 88.9% | 94.4% | 96.1% | 32.7% |
| 20 | 90.0% | 90.0% | 97.9% | 31.0% |
| 30 | 83.3% | 86.7% | 95.1% | 24.3% |
| 40 | 82.5% | 85.0% | 96.8% | 19.7% |
| 50 | 80.0% | 84.0% | 95.4% | 16.2% |
| 60 | 80.0% | 81.7% | 94.1% | 13.4% |
| 70 | 78.6% | 81.4% | 96.1% | 11.2% |
| 80 | 77.5% | 81.3% | 95.3% | 9.4% |
| 90 | 77.8% | 80.0% | 94.6% | 8.0% |
| 100 | 77.0% | 80.0% | 96.3% | 6.8% |
| 120 | 75.8% | 79.2% | 95.3% | 4.9% |
| 140 | 75.7% | 78.6% | 94.5% | 3.6% |
| 160 | 75.0% | 78.1% | 95.7% | 2.7% |
| 180 | 74.4% | 77.8% | 95.2% | 2.0% |
| 200 | 74.5% | 77.5% | 94.7% | 1.5% |
| 220 | 74.1% | 76.8% | 95.8% | 1.1% |
| 240 | 73.8% | 76.7% | 95.5% | 0.8% |
| 260 | 73.5% | 76.5% | 95.1% | 0.6% |
| 280 | 73.6% | 76.4% | 94.8% | 0.5% |
An Excel template used to for model the predicted test outcomes is provided in Supplementary Spreadsheet.
a
Weighted average combining the partial and least confident categories
b
Least confident category.