A | Expected B | B estimate | SEE | Relative frequency of bootstrap errors |
|---|
−2+ | −1 | 0 | 1 | 2+ |
|---|
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 1.9 | 2 | 0.316 | 0 | 0.05 | 0.9 | 0.05 | 0 |
12 | 18.3 | 18 | 0.81 | 0.025 | 0.225 | 0.5 | 0.225 | 0.025 |
20 | 35.4 | 35 | 0.91 | 0.025 | 0.317 | 0.317 | 0.317 | 0.025 |
- This table contains artificial values of equated scores from scale A to B, with different distributions of the bootstrap errors. For each raw score of A an estimated raw score of B is obtained. The SEE (Standard Error of Equating) is computed from the second half of the table, where, for each A raw score, 1000 bootstrapped B scores are estimated in 1000 bootstrap samples. The difference (error) between the B estimate and each of the bootstrapped B scores is computed. The number of errors of 0 points (no error), 1 point below (− 1), two or more points below (− 2+), 1 point above (1), and two or more points above (2+) the B estimates are collected. Then the Relative Frequencies (RF) of these errors are presented on the table, which allow to compute the SEE. Four theoretical bootstrap error distributions are presented. The first row shows an error free distribution, where RF(0) = 1 and therefore SEE = 0. The second row shows a plausible distribution, where RF(0) = 0.9, RF(− 1) = RF(1) = 0.05, and it follows that SEE= \( \sqrt{0.05+0.05} \) =0.316. The third row shows an acceptable distribution, where RF(0) = 0.5, RF(− 1) = RF(1) = 0.225, RF(− 2+) = RF(2+) = 0.025, and it follows that SEE= \( \sqrt{2\ast 0.225+2\ast 4\ast 0.025}=\sqrt{0.65} \) =0.81. The fourth row shows the worst case that could be regarded as acceptable, where RF(0) = RF(− 1) = RF(1) = 0.317, RF(− 2) = RF(2) = 0.025, and it follows that SEE is 0.91. We therefore consider a weighted SEE mean below 0.91 as acceptable
- Abbreviations: SEE Standard Error of Equating