Analytic Permutation Testing for Functional Data ANOVA
Why this work is in the frame
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Bibliographic record
Abstract
Analysis of variance is a cornerstone of statistical hypothesis testing. When data lies beyond the assumption of univariate normality, nonparametric methods including rank based statistics and permutation tests are enlisted. The permutation test is a versatile exact nonparametric significance test that requires drastically fewer assumptions than similar parametric tests. The main downfall of the permutation test is high computational cost making this approach laborious for comparing multiple samples of complex data types and completely infeasible in any application requiring speedy results such as high throughput streaming data. We rectify this problem through application of concentration inequalities and thus propose a computation free permutation test—that is, a permutation-less permutation test. This general framework is applied to multivariate and matrix-valued, but with a special emphasis on functional data. We improve these concentration bounds via a novel incomplete beta transform. Our theory is extended from two-sample to k-sample testing through the use of weakly dependent Rademacher chaoses and modified decoupling inequalities. Our methodology is tested on classic functional datasets including the Berkeley growth curves and the phoneme dataset. We further analyze a novel dataset of 12 spoken vowel sounds that was collected to illustrate to power of the analytic permutation test. Supplementary materials for this article are available online.
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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 | 0.000 |
| 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