Bibliographic record
Abstract
Abstract Most classical multivariate procedures (e.g., multivariate analysis of variance, multivariate measures of effect size, classification procedures, and maximum likelihood factor analysis) require that the data follow a multivariate normal density function. Behavioral science researchers risk committing many more Type I errors, quantifying inaccurately the magnitude of effect sizes, missing treatment effects, establishing inaccurate confidence intervals, and so on by failing to consider whether their data conform to multivariate normality. This article discusses a number of options for assessing and dealing with nonnormal multivariate data including (i) testing for univariate normality among the p measures, (ii) transforming the data to achieve normality, (iii) univariate normal probability plots, (iv) multivariate measures of skewness and kurtosis, (v) computing squared distance statistics to locate outlying values, and (vi) adopting robust estimators with robust test statistics to circumvent the biasing effects of nonnormality. In addition, findings in the literature are discussed, which compared methods for detecting nonnormal data.
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How this classification was reachedexpand
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 | 0.005 | 0.360 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 teacher head, 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".