A correction factor for the impact of cluster randomized sampling and its applications.
Bibliographic record
Abstract
Cluster randomized sampling is 1 method for sampling a population. It requires recruiting subgroups of participants from the population of interest (e.g., whole classes from schools) instead of individuals solicited independently. Here, we demonstrate how clusters affect the standard error of the mean. The presence of clusters influences 2 quantities, the variance of the means and the expected variance. Ignoring clustering produces spurious statistical significance and reduces statistical power when effect sizes are moderate to large. Here, we propose a correction factor. It can be used to estimate standard errors and confidence intervals of the mean under cluster randomized sampling. This correction factor is easy to integrate into regular tests of means and effect sizes. It can also be used to determine sample size needed to reach a prespecified power. Finally, this approach is an easy-to-use alternative to linear mixed modeling and hierarchical linear modeling when there are only 2 levels and no covariates.
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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 | 0.121 | 0.525 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.019 | 0.004 |
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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".