Confidence Intervals for Squared Semipartial Correlation Coefficients: The Effect of Nonnormality
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Bibliographic record
Abstract
The increase in the squared multiple correlation coefficient (ΔR 2 ) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size was quite large (i.e., larger than 200). However, they also reported that probability coverage for the confidence intervals based on a bootstrap method was typically quite accurate, and moreover, this accuracy was obtained with relatively small sample sizes with six or fewer predictors. They further speculated that nonnormality would likely affect the accuracy of interval coverage. In the present study, the authors investigated the accuracy of coverage probability for confidence intervals obtained by using asymptotic and percentile bootstrap methodology when either predictors, residuals, or both are nonnormal. Coverage probability for asymptotic confidence intervals is poor, but adequate coverage probability can be obtained with reasonable sample sizes by using percentile bootstrap methodology. As well, the authors found that the width of these intervals was relatively precise (i.e., narrow) for the larger cases of sample size investigated.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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