Agreement Between Two Ratings with Different Ordinal Scales
Bibliographic record
Abstract
Agreement studies, where several observers may be rating the same subject for some characteristic measured on an ordinal scale, provide important information. The weighted Kappa coefficient is a popular measure of agreement for ordinal ratings. However, in some studies, the raters use scales with different numbers of categories. For example, a patient quality of life questionnaire may ask ‘How do you feel today?’ with possible answers ranging from 1 (worst) to 7 (best). At the same visit, the doctor reports his impression of the patient’s health status as very poor, poor, fair, good, or very good. The weighted Kappa coefficient is not applicable here because the two scales have a different number of categories. In this paper, we discuss Kappa coefficients to measure agreement between such ratings. In particular, with R categories of one rating, and C categories of another, by dichotomizing the two ratings at all possible cutpoints, there are ( R −1)( C −1) possible (2×2) tables. For each of these (2×2) tables, we estimate the Kappa coefficient for dichotomous ratings. The largest estimated Kappa coefficients suggest the cutpoints for the two ratings where agreement is the highest and where categories can be combined for further analysis.
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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 | 0.036 | 0.119 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 0.006 |
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".