Somers' D as an Alternative for the Item–Test and Item-Rest Correlation Coefficients in the Educational Measurement Settings
Bibliographic record
Abstract
Pearson product–moment correlation coefficient between item g and test score X, known as item–test or item–total correlation (Rit), and item–rest correlation (Rir) are two of the most used classical estimators for item discrimination power (IDP). Both Rit and Rir underestimate IDP caused by the mismatch of the scales of the item and the score. Underestimation of IDP may be drastic when the difficulty level of the item is extreme. Based on a simulation, in a binary dataset, a good alternative for Rit and Rir could be the Somers’ D: it reaches the ultimate values +1 and –1, it underestimates IDP remarkably less than Rit and Rir, and, being a robust statistic, it is more stable against the changes in the data structure. Somers’ D has, however, one major disadvantage in a polytomous case: it tends to underestimate the magnitude of the association of item and score more than Rit does when the item scale has four categories or more.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.076 | 0.269 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.007 | 0.008 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".