Estimating Population Mean Power Under Conditions of Heterogeneity and Selection for Significance
Bibliographic record
Abstract
In scientific fields that use significance tests, statistical power is important for successful replications of significant results because it is the long-run success rate in a series of exact replication studies. For any population of significant results, there is a population of power values of the statistical tests on which conclusions are based. We give exact theoretical results showing how selection for significance affects the distribution of statistical power in a heterogeneous population of significance tests. In a set of large-scale simulation studies, we compare four methods for estimating population mean power of a set of studies selected for significance (a maximum likelihood model, extensions of p-curve and p-uniform, & z-curve). The p-uniform and p-curve methods performed well with a fixed effects size and varying sample sizes. However, when there was substantial variability in effect sizes as well as sample sizes, both methods systematically overestimate mean power. With heterogeneity in effect sizes, the maximum likelihood model produced the most accurate estimates when the distribution of effect sizes matched the assumptions of the model, but z-curve produced more accurate estimates when the assumptions of the maximum likelihood model were not met. We recommend the use of z-curve to estimate the typical power of significant results, which has implications for the replicability of significant results in psychology journals.
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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 | 0.370 | 0.759 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.008 | 0.013 |
| Bibliometrics | 0.009 | 0.009 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.007 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".