Comprehensive study of tests for normality and symmetry: extending the Spiegelhalter test
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Bibliographic record
Abstract
Statistical inference in the form of hypothesis tests and confidence intervals often assumes that the distribution(s) being sampled are normal or symmetric. As a result, numerous tests have been proposed in the literature for detecting departures from normality and symmetry. This article initially summarizes the research that has been conducted for developing such tests. The results of an extensive simulation study to compare the power of existing tests for normality is then presented. The effects on power of sample size, significance level, and in particular, alternative distribution shape are investigated. In addition, the power of three modifications to the tests for normality proposed by Spiegelhalter [Spiegelhalter, D.J., 1977, A test for normality against symmetric alternatives. Biometrika, 64, {415–418}; Spiegelhalter, D.J., 1980, An omnibus test for normality for small samples. Biometrika, 67, 493–496.], which are tailored to particular shape departures from the normal distribution is evaluated. The test for normality suggested by Spiegelhalter [Spiegelhalter, D.J., 1980, An omnibus test for normality for small samples. Biometrika, 67, 493–496.] is also extended here to serve as a test for symmetry. The results of a simulation study performed to assess the power of this proposed test for symmetry and its comparison with existing tests are summarized and discussed. A key consideration in the assessment of the power of these various tests for symmetry is the ability of the test to maintain the nominal significance level.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.020 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it