Repeated measures ANOVA: Some new results on comparing trimmed means and means
Bibliographic record
Abstract
This paper considers the common problem of testing the equality of means in a repeated measures design. Recent results indicate that practical problems can arise when computing confidence intervals for all pairwise differences of the means in conjunction with the Bonferroni inequality. This suggests, and is confirmed here, that a problem might occur when performing an omnibus test of equal means. The problem is that the probability of rejecting is not minimized when the means are equal and the usual univariate F test is used with the Huynh-Feldt correction (epsilon) for the degrees of freedom. That is, power can actually decrease as the mean of one group is lowered, although eventually it increases. A similar problem is found when using a multivariate method (Hotelling's T2). Moreover, the probability of a Type I error can exceed the nominal level by a large amount. The paper considers methods for correcting this problem, and new results on comparing trimmed means are reported as well. In terms of both Type I errors and power, simulations reported here suggest that a percentile t bootstrap used with 20% trimmed means and an analogue of the epsilon-adjusted F gives the best results. This is consistent with extant theoretical results comparing methods based on means with trimmed means.
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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 | 0.027 | 0.129 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".