A Note on Determining the <b> <i>p</i> </b> -Value of Bartlett's Test of Homogeneity of Variances
Bibliographic record
Abstract
Bartlett's test for homogeneity of variances is rather nonrobust. However, when it is applicable, it is more powerful than various other tests. Dyer and Keating (1980 Dyer, D. D. and Keating, J. P. 1980. On the determination of critical values for Bartlett's test. J. Amer. Statist. Assoc., 75: 313–319. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) tabulate the exact critical values for Bartlett's test based on equal sample sizes from several normal populations. Moreover, they use these values to obtain highly accurate approximations to the critical values for unequal sample sizes. In this note, a simple and accurate method is proposed to obtain the p-value for Bartlett's test. Theoretically, the proposed method has third order accuracy. Numerical examples illustrate that it is extremely accurate even for very small sample sizes and a large number of populations. Furthermore, the proposed method can easily be implemented with standard statistical softwares.
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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 | 0.034 | 0.237 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.007 | 0.006 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.005 | 0.010 |
| Insufficient payload (model declined to judge) | 0.008 | 0.008 |
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".