Efficiency Evaluation of Statistical Tests for Homogeneity of Variances under Normal, Beta, and Weibull Distributional Frameworks
Bibliographic record
Abstract
This research endeavor aims to evaluate six test statistics relevant to assessing of homogeneity of variance (HOV): Bartlett’s (BL), Levene’s (LV), modified Levene’s (LVM), Klotz’s (KL), Layard’s (LY), and Samiuddin’s (SMD). Simulated datasets were generated under the frameworks of normal, Beta, and Weibull distributions, encompassing both three and four groups, while incorporating variations in sample sizes that were both equal and unequal. Each experimental condition was replicated 5,000 times to ensure the precision of statistical outcomes. In the context of the normal distribution, the BL, LY, and SMD statistics exhibited strong control over Type I error rates, with the BL and LY statistics achieving the highest statistical power among the tests classified as acceptable. Whereas the LV and LVM statistics demonstrated competence in error control, they were characterized by reduced power; conversely, the SMD statistic exhibited significantly low power. In contrast, the KL statistic consistently yielded inflated error rates, rendering it inappropriate for practical application. In the realm of the Beta distribution, the KL, LVM, and LY statistics emerged as the most proficient performers, adeptly preserving Type I error rates. The KL statistic, notwithstanding its mediocre performance under normal distribution conditions, demonstrated the greatest resilience within this specific context. The LVM statistic maintained a conservative approach; the LY statistic exhibited precision yet was somewhat less robust when faced with skewed data, the LV statistic demonstrated moderate effectiveness, the BL statistic was excessively cautious, and the SMD statistic was classified as unreliable. In relation to the Weibull distribution, the LY, SMD, KL, and LVM statistics consistently controlled the Type I error rates. The BL statistic performed satisfactorily but exhibited a slight inclination towards inflation of Type I error rates, whereas the LV statistic was assessed as unreliable. The BL statistic attained the highest statistical power, albeit with correspondingly elevated Type I error rates. The LVM and LY statistics demonstrated considerable power across diverse scenarios, with the LY statistic being preferentially utilized for small to medium sample sizes and the LVM statistic for larger sample sizes. The SMD and KL statistics consistently ranked lowest in terms of empirical power.
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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 | 0.140 | 0.476 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".