The Power of Replicated Measures to Increase Statistical Power
Bibliographic record
Abstract
When running statistical tests, researchers can commit a Type II error, that is, fail to reject the null hypothesis when it is false. To diminish the probability of committing a Type II error (β), statistical power must be augmented. Typically, this is done by increasing sample size, as more participants provide more power. When the estimated effect size is small, however, the sample size required to achieve sufficient statistical power can be prohibitive. To alleviate this lack of power, a common practice is to measure participants multiple times under the same condition. Here, we show how to estimate statistical power by taking into account the benefit of such replicated measures. To that end, two additional parameters are required: the correlation between the multiple measures within a given condition and the number of times the measure is replicated. An analysis of a sample of 15 studies (total of 298 participants and 38,404 measurements) suggests that in simple cognitive tasks, the correlation between multiple measures is approximately .14. Although multiple measurements increase statistical power, this effect is not linear, but reaches a plateau past 20 to 50 replications (depending on the correlation). Hence, multiple measurements do not replace the added population representativeness provided by additional participants.
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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 | 0.485 | 0.816 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.009 | 0.012 |
| Bibliometrics | 0.008 | 0.009 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.009 | 0.013 |
| Open science | 0.005 | 0.008 |
| Research integrity | 0.006 | 0.008 |
| Insufficient payload (model declined to judge) | 0.010 | 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".