An exact bootstrap confidence interval for kappa in small samples
Bibliographic record
Abstract
Summary. Agreement between a pair of raters for binary outcome data is typically assessed by using the κ-coefficient. When the total sample size is small to moderate, and the proportion of agreement is high, standard methods of calculating confidence intervals for κ perform poorly. To improve the coverage of confidence intervals for κ, Lee and Tu formed an interval based on the profile variance of the estimate of the κ-coefficient, which requires the solution to a cubic polynomial. They showed in simulations that their method was the best available method with respect to the coverage probability and performs well except when the proportion of agreement is high and the sample size is small. Here, we propose a method that picks up where Lee and Tu's leaves off, namely when the proportion of agreement is high and the sample size is small. In particular, we propose the use of the bootstrap to form a confidence interval for κ. With a 2×2 table, and sample sizes less than 200, instead of a Monte Carlo bootstrap, one can easily calculate the ‘exact’ bootstrap distribution of the estimate of κ and use this distribution to calculate confidence intervals. We perform a simulation and show that the bootstrap gives slightly better coverage than Lee and Tu's method.
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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 | 0.057 | 0.413 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.007 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".