A robust effect size measure <i>A<sub>w</sub></i> for MANOVA with non-normal and non-homogenous data
Bibliographic record
Abstract
A common research question in psychology entails examining whether significant group differences (e.g. male and female) can be found in a list of numeric variables that measure the same underlying construct (e.g. intelligence). Researchers often use a multivariate analysis of variance (MANOVA), which is based on conventional null-hypothesis significance testing (NHST). Recently, a number of quantitative researchers have suggested reporting an effect size measure (ES) in this research scenario because of the perceived shortcomings of NHST. Thus, a number of MANOVA ESs have been proposed (e.g. generalized eta squared [Formula: see text], generalized omega squared [Formula: see text]), but they rely on two key assumptions—multivariate normality and homogeneity of covariance matrices—which are frequently violated in psychological research. To solve this problem we propose a non-parametric (or assumptions-free) ES ( Aw) for MANOVA. The new ES is developed on the basis of the non-parametric A in ANOVA. To test Aw we conducted a Monte-Carlo simulation. The results showed that Aw was accurate (robust) across different manipulated conditions—including non-normal distributions, unequal covariance matrices between groups, total sample sizes, sample size ratios, true ES values, and numbers of dependent variables—thereby providing empirical evidence supporting the use of Aw, particularly when key assumptions are violated. Implications of the proposed Aw for psychological research and other disciplines are also discussed.
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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 | 0.042 | 0.222 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.028 | 0.011 |
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".