Approximately unbiased estimators of the inverse variance from sample summary statistics
Bibliographic record
Abstract
Background In meta-analysis, researchers often pool the results from a set of similar studies. A number of studies, however, often tend to report only the minimum and maximum values, median, and/or the first and third quartiles. Recently, many methods have been discussed for estimating the mean and standard deviation from those sample summaries. However, these methods may provide a substantially biased estimate of the inverse variance that is needed for the meta-analysis. Research Design We use Basu’s theorem to derive unbiased estimators for σ −2 from the most commonly used sample summaries from the normal distribution. While there are no closed formulas for these estimators, we use simulations to obtain simple approximations for the estimators. Results The proposed approximate estimators still show a little to no bias for normally distributed data and generally show smaller bias than the usual methods even for some non-normal distributions. The proposed estimators have lower mean squared error. Conclusions The proposed estimators are recommended for the purpose of obtaining inverse-variance weights, particularly in the context of meta-analyses.
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How this classification was reachedexpand
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 | 0.665 | 0.462 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.000 |
| Bibliometrics | 0.002 | 0.020 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.005 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; both teacher heads 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".