A Comparison of Nonparametric Statistics and Bootstrap Methods for Testing Two Independent Populations with Unequal Variance
Bibliographic record
Abstract
The common parametric statistics used for testing two independent populations have often required the assumptions of normality and equal variances. Nonparametric tests have been used when assumptions of parametric tests cannot be achieved. However, some studies found nonparametric tests to be too conservative and less powerful than parametric tests. Bootstrap methods are also alternative tests when assumptions of parametric tests are violated, but they have small size limitations. Later, nonparametric tests when pooled with the bootstrap methods may overcome the powerful test and small sample sizes issue. Thus, the purpose of this study was to apply the bootstrap method together with nonparametric statistics and compare the efficiency of nonparametric tests and bootstraps methods when pooled with nonparametric tests for testing the mean difference between two independent populations with unequal variance. The Yuen Welch Test (YW), Brunner-Munzel Test (BM), Bootstrap Yuen Welch Test (BYW) and Bootstrap Brunner-Munzel Test (BBM) were studied via Monte Carlo simulation with non-normal population distributions. The results show that the probability of a type I error of all four test statistics could be controlled for all situations. The Brunner-Munzel test (BM) had the highest power and the best efficiency in the case of mean difference ratio increases. The Bootstrap Yuen Welch Test (BYW) had the highest power when the sample size was small.
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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 | 0.064 | 0.208 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".