Testing treatment effects in repeated measures designs: Trimmed means and bootstrapping
Bibliographic record
Abstract
Non-normality and covariance heterogeneity between groups affect the validity of the traditional repeated measures methods of analysis, particularly when group sizes are unequal. A non-pooled Welch-type statistic (WJ) and the Huynh Improved General Approximation (IGA) test generally have been found to be effective in controlling rates of Type I error in unbalanced non-spherical repeated measures designs even though data are non-normal in form and covariance matrices are heterogeneous. However, under some conditions of departure from multisample sphericity and multivariate normality their rates of Type I error have been found to be elevated. Westfall and Young's results suggest that Type I error control could be improved by combining bootstrap methods with methods based on trimmed means. Accordingly, in our investigation we examined four methods for testing for main and interaction effects in a between- by within-subjects repeated measures design: (a) the IGA and WJ tests with least squares estimators based on theoretically determined critical values; (b) the IGA and WJ tests with least squares estimators based on empirically determined critical values; (c) the IGA and WJ tests with robust estimators based on theoretically determined critical values; and (d) the IGA and WJ tests with robust estimators based on empirically determined critical values. We found that the IGA tests were always robust to assumption violations whether based on least squares or robust estimators or whether critical values were obtained through theoretical or empirical methods. The WJ procedure, however, occasionally resulted in liberal rates of error when based on least squares estimators but always proved robust when applied with robust estimators. Neither approach particularly benefited from adopting bootstrapped critical values. Recommendations are provided to researchers regarding when each approach is best.
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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 | 0.196 | 0.499 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.004 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.006 | 0.003 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".