Equivalence tests for comparing correlation and regression coefficients
Why this work is in the frame
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Bibliographic record
Abstract
Equivalence tests are an alternative to traditional difference-based tests for demonstrating a lack of association between two variables. While there are several recent studies investigating equivalence tests for comparing means, little research has been conducted on equivalence methods for evaluating the equivalence or similarity of two correlation coefficients or two regression coefficients. The current project proposes novel tests for evaluating the equivalence of two regression or correlation coefficients derived from the two one-sided tests (TOST) method (Schuirmann, 1987, J. Pharmacokinet. Biopharm, 15, 657) and an equivalence test by Anderson and Hauck (1983, Stat. Commun., 12, 2663). A simulation study was used to evaluate the performance of these tests and compare them with the common, yet inappropriate, method of assessing equivalence using non-rejection of the null hypothesis in difference-based tests. Results demonstrate that equivalence tests have more accurate probabilities of declaring equivalence than difference-based tests. However, equivalence tests require large sample sizes to ensure adequate power. We recommend the Anderson-Hauck equivalence test over the TOST method for comparing correlation or regression coefficients.
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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 | 0.004 | 0.106 |
| 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 | 0.001 |
| 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