Randomization test of mean is compuationally inaccessible when the number of groups exceeds two
Bibliographic record
Abstract
With the advent of fast computers, the randomization test of mean (also called the permutation test) received some attention in the recent years. Here we show that the randomization test is possible only for two-group design; comparing three groups requires a number of permutations so vast that even three groups of ten participants is beyond the current capabilities of modern computers. Further, we show that the rate of increase in the number of permutation is so large that simply adding one more participant per group to the data results in a computation time increased by at least one order of magnitude (in the three-group design) or more. Hence, the exhaustive randomization test may never be a viable alternative to ANOVAs.
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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 | 0.044 | 0.270 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".