Analysis of frequency data: The ANOFA framework
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Analyses of frequencies are commonly done using a chi-square test. This test, derived from a normal approximation, is deemed generally efficient (controlling type-I error rates fairly well and having good statistical power). However, in the case of factorial designs, it is difficult to decompose a total test statistic into additive interaction effects and main effects. Herein, we present an alternative test based on the $G$ statistic. The test has similar type-I error rates and power as the former one. However, it is based on a total statistic that is naturally decomposed additively into interaction effects, main effects, simple effects, contrast effects, etc., mimicking precisely the logic of ANOVAs. We call this set of tools ANOFA (Analysis of Frequency data) to highlight its similarities with ANOVA. We also examine how to render plots of frequencies along with confidence intervals. Finally, quantifying effect sizes and planning statistical power are described under this framework. The ANOFA is a tool that assesses the significance of effects instead of the significance of parameters; as such, it is more intuitive to most researchers than alternative approaches based on generalized linear models.
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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 | 0.010 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 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