Planning sample sizes when effect sizes are uncertain: The power-calibrated effect size approach.
Why this work is in the frame
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Bibliographic record
Abstract
Statistical power and thus the sample size required to achieve some desired level of power depend on the size of the effect of interest. However, effect sizes are seldom known exactly in psychological research. Instead, researchers often possess an estimate of an effect size as well as a measure of its uncertainty (e.g., a standard error or confidence interval). Previous proposals for planning sample sizes either ignore this uncertainty thereby resulting in sample sizes that are too small and thus power that is lower than the desired level or overstate the impact of this uncertainty thereby resulting in sample sizes that are too large and thus power that is higher than the desired level. We propose a power-calibrated effect size (PCES) approach to sample size planning that accounts for the uncertainty associated with an effect size estimate in a properly calibrated manner: sample sizes determined on the basis of the PCES are neither too small nor too large and thus provide the desired level of power. We derive the PCES for comparisons of independent and dependent means, comparisons of independent and dependent proportions, and tests of correlation coefficients. We also provide a tutorial on setting sample sizes for a replication study using data from prior studies and discuss an easy-to-use website and code that implement our PCES approach to sample size planning.
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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 | 0.037 | 0.623 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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