Can we Find Evidence for the Null in a Bayesian t-Test? Not Unless we Reconsider Bayes Factor Thresholds
Bibliographic record
Abstract
Within the fields of behavioural and psychological research, the use of Bayesian statistics has gathered increased interest. A statistical test commonly employed in behavioral and psychological research is the t-test. For the Bayesian t-test, a Bayes Factor (BF) can be computed which reflects evidence in favor of either the alternative hypothesis (H1) or the null hypothesis (H0). Even though the BF is a continuous measure of evidence, it is common to define specific thresholds for accepting the evidence in favor of either the H1 or the H0. Such evidence thresholds (e.g., BF > 3, BF > 6, BF > 10) are adopted by related scientific journals to define minimum publication or preregistration requirements. However, exceeding these thresholds is not analogous when H1 is true compared to when H0 is true. In turn, this disanalogy might require scientists to invest additional time and resources when H0 is true, as opposed to when H1 is true. In this study, we simulated 200 million BFs for various effect size, sample size, and variance assumptions, to demonstrate this disanalogy. Further, we show that despite having small shifts in the sample sizes required for exceeding various BF thresholds when H1 is true, when the H0 is true the probabilities of exceeding a BF > 6 or a BF > 10 are close to chance. As such, we recommend the use of a BF > 3 evidence threshold for the H0 independently of the evidence threshold set for H1.
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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 | 0.190 | 0.638 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.005 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.020 |
| Scholarly communication | 0.011 | 0.018 |
| Open science | 0.007 | 0.004 |
| Research integrity | 0.008 | 0.013 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".