Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction
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Bibliographic record
Abstract
The standard Pearson correlation coefficient, r, is a biased estimator of the population correlation coefficient, ρ(XY) , when predictor X and criterion Y are indirectly range-restricted by a third variable Z (or S). Two correction algorithms, Thorndike's (1949) Case III, and Schmidt, Oh, and Le's (2006) Case IV, have been proposed to correct for the bias. However, to our knowledge, the two algorithms did not provide a procedure to estimate the associated standard error and confidence intervals. This paper suggests using the bootstrap procedure as an alternative. Two Monte Carlo simulations were conducted to systematically evaluate the empirical performance of the proposed bootstrap procedure. The results indicated that the bootstrap standard error and confidence intervals were generally accurate across simulation conditions (e.g., selection ratio, sample size). The proposed bootstrap procedure can provide a useful alternative for the estimation of the standard error and confidence intervals for the correlation corrected for indirect range restriction.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.016 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it