Note on a Confidence Interval for the Squared Semipartial Correlation Coefficient
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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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 | 0.059 | 0.496 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.006 | 0.008 |
| Insufficient payload (model declined to judge) | 0.022 | 0.005 |
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".