Too Small to Succeed: Small Samples and the p-Value Problem
Bibliographic record
Abstract
Determining an appropriate sample size is a critical planning decision in quantitative empirical research. In recent years, there has been a growing concern that researchers have excessively focused on statistical significance in large sample studies to the detriment of effect sizes. This research focuses on a related concern at the other end of the spectrum. We argue that a combination of bias in significant estimates obtained from small samples (compared to their population values) and an editorial preference for the publication of significant results compound to produce marked bias in published small sample studies. We then present a simulation study covering a variety of statistical techniques commonly used to examine structural equation models with latent variables. Our results support our contention that significant results obtained from small samples are likely biased and should be considered with skepticism. We also argue for the need to provide a priori power analyses to understand the behavior of parameter estimates under the small sample conditions we examine.
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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 | 0.576 | 0.903 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.007 | 0.003 |
| Bibliometrics | 0.008 | 0.009 |
| Science and technology studies | 0.005 | 0.030 |
| Scholarly communication | 0.010 | 0.015 |
| Open science | 0.009 | 0.007 |
| Research integrity | 0.012 | 0.019 |
| Insufficient payload (model declined to judge) | 0.005 | 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".