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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.063 | 0.340 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.024 | 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".