Note on a Confidence Interval for the Squared Semipartial Correlation Coefficient
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Bibliographic record
Abstract
A squared semipartial correlation coefficient (ΔR 2 ) is the increase in the squared multiple correlation coefficient that occurs when a predictor is added to a multiple regression model. Prior research has shown that coverage probability for a confidence interval constructed by using a modified percentile bootstrap method with ΔR 2 was generally good with sample sizes that should not be too challenging for educational and psychological researchers. However, that research was limited to values of Δρ 2 = .00 or Δρ 2 ≥ .05. The present research investigates coverage probability when .01 ≤ Δρ 2 ≤ .04 and shows that the modified percentile bootstrap typically results in coverage probability in the [.925, .975] interval for a 95% confidence interval, provided the sample size is at least 50 if the number of predictors in the model with more predictors (i.e., the full model) is four or smaller, at least 150 if the number of predictors in the full model is five or six, and at least 200 and preferably 250 if the number of predictors in the full model is between seven and nine.
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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 | 0.005 | 0.043 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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