Correlation-adjusted standard errors and confidence intervals for within-subject designs: A simple multiplicative approach
Why this work is in the frame
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Bibliographic record
Abstract
In within-subject designs, the multiple scores of a given participant are correlated. This correlation implies that the observed variance can be partitioned into between-subject variance and between-measure variance. The basic confidence interval about the mean does not separate these two sources and is therefore of little use in within-subject designs. Two solutions have been proposed, one (Loftus and Masson) requires the computation of the interaction terms including the subject and all within-subject factors, the other (Cousineau and Morey) requires a two-step transformation of the data. As shown, these two methods are nearly equivalent. Herein, I present a correlation-adjusted method which requires the mean correlation across all pairs of measurements. This solution is shown to be similar to the other two for data satisfying the compound symmetry assumption. It is found to be too liberal for data having homogeneous correlations and heterogeneous variances but a Welch correction for heterogeneous variances can be used. Finally, it is inadequate for data that do not satisfy the compound symmetry assumption but satisfy the sphericity assumption. A statistical test of compound symmetry is discussed.
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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 | 0.004 | 0.001 |
| 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 | 0.000 |
| 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