The Effects of Nonnormality on Parametric, Nonparametric, and Model Comparison Approaches to Pairwise Comparisons
Bibliographic record
Abstract
Researchers in the behavioral sciences are often interested in comparing the means of several treatment conditions on a specific dependent measure. When scores on the dependent measure are not normally distributed, researchers must make important decisions regarding the multiple comparison strategy that is implemented. Although researchers commonly rely on the potential robustness of traditional parametric test statistics (e.g., t and F), these test statistics may not be robust under all nonnormal data conditions. This article compared strategies for performing multiple comparisons with nonnormal data under various data conditions, including simultaneous violations of the assumptions of normality and variance homogeneity. The results confirmed that when variances are unequal, use of the traditional two-sample t test can result in severely biased Type I and/or Type II error rates. However, the use of Welch’s two-sample test statistic with the REGWQ procedure, with either the usual means and variances or with trimmed means and Winsorized variances, resulted in good control of Type I error rates. The Kruskal-Wallis nonparametric statistic provided good Type I error control and power when variances were equal, although Type I error rates became severely inflated when variances were unequal. Furthermore, for researchers interested in eliminating intransitive decisions or comparing potential mean configuration models, a protected model-testing procedure suggested by Dayton provided good overall results.
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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 | 0.370 | 0.671 |
| Meta-epidemiology (narrow) | 0.005 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.004 |
| Bibliometrics | 0.006 | 0.009 |
| Science and technology studies | 0.004 | 0.023 |
| Scholarly communication | 0.007 | 0.011 |
| Open science | 0.007 | 0.010 |
| Research integrity | 0.004 | 0.019 |
| Insufficient payload (model declined to judge) | 0.007 | 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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".