Testing Repeated Measures Hypotheses When Covariance Matrices are Heterogeneous: Revisiting the Robustness of the Welch-James Test Again
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Bibliographic record
Abstract
The Welch-James and Improved General Approximation tests were examined in between-subjects × within-subjects repeated measures designs for their rates of Type I error when data were nonnormal, nonspherical, and heterogeneous and when group sizes were unequal as well. The tests were computed with either least squares or robust estimators of central tendency and variability and assessed with critical values that were obtained either theoretically or through a bootstrapping method. Prior findings indicated that one could only obtain a robust test of the interaction effect with the Welch-James procedure when sample sizes were very large. This study’s results indicate that a robust test of the interaction effect can be obtained with reasonable sample sizes when the Welch-James test is computed with trimmed means and Winsorized covariance matrices.
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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 | 0.001 | 0.008 |
| 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