Tests of linear hypotheses using indirect information
Bibliographic record
Abstract
Abstract In multigroup data settings with small within‐group sample sizes, standard ‐tests of group‐specific linear hypotheses can have low power, particularly if the within‐group sample sizes are not large relative to the number of explanatory variables. To remedy this situation, in this article we derive alternative test statistics based on information sharing across groups. Each group‐specific test has potentially much larger power than the standard ‐test, while still exactly maintaining a target type I error rate if the null hypothesis for the group is true. The proposed test for a given group uses a statistic that has optimal marginal power under a prior distribution derived from the data of the other groups. This statistic approaches the usual ‐statistic as the prior distribution becomes more diffuse, but approaches a limiting “cone” test statistic as the prior distribution becomes extremely concentrated. We compare the power and ‐values of the cone test to that of the ‐test in some high‐dimensional asymptotic scenarios. An analysis of educational outcome data is provided, demonstrating empirically that the proposed test is more powerful than the ‐test.
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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 | 0.002 | 0.150 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".