Pairwise Multiple Comparison Tests when Data are Nonnormal
Bibliographic record
Abstract
Numerous authors suggest that the data gathered by investigators are not normal in shape. Accordingly, methods for assessing pairwise multiple comparisons of means with traditional statistics will frequently result in biased rates of Type I error and depressed power to detect effects. One solution is to obtain a critical value to assess statistical significance through bootstrap methods. The SAS system can be used to conduct step-down bootstrapped tests. The authors investigated this approach when data were neither normal in form nor equal in variability in balanced and unbalanced designs. They found that the step-down bootstrap method resulted in substantially inflated rates of error when variances and group sizes were negatively paired. Based on their results, and those reported elsewhere, the authors recommend that researchers should use trimmed means and Winsorized variances with a heteroscedastic test statistic. When group sizes are equal, the bootstrap procedure effectively controlled Type I error rates.
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How this classification was reachedexpand
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 | 0.003 | 0.047 |
| 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) | 0.004 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".