Enter study data
Provide one label, one effect size, and one standard error for each study. Spaces, commas, or new lines are accepted for numeric fields.
Example data table
| Study | Effect Size | Standard Error | Interpretation Hint |
|---|---|---|---|
| Study A | 0.12 | 0.05 | More precise study |
| Study B | 0.18 | 0.06 | More precise study |
| Study C | 0.21 | 0.07 | More precise study |
| Study D | 0.25 | 0.08 | More precise study |
| Study E | 0.3 | 0.09 | More precise study |
| Study F | 0.32 | 0.1 | Less precise study |
| Study G | 0.38 | 0.11 | Less precise study |
| Study H | 0.45 | 0.13 | Less precise study |
| Study I | 0.5 | 0.16 | Less precise study |
| Study J | 0.62 | 0.2 | Less precise study |
Formula used
Fixed-effect pooled estimate: θ̂ = Σ(wᵢyᵢ) / Σwᵢ, where wᵢ = 1 / SEᵢ².
Random-effects variance: τ² = max(0, [Q - (k - 1)] / [Σwᵢ - (Σwᵢ² / Σwᵢ)]), with Q = Σ[wᵢ(yᵢ - θ̂fixed)²].
Random-effects pooled estimate: replace each weight with 1 / (SEᵢ² + τ²) and recompute the weighted mean.
Filled study mirror: each imputed estimate uses yᵢ(filled) = 2θ̂trimmed - yᵢ with the same standard error as its trimmed partner.
Practical trim rule in this calculator: the algorithm repeatedly checks the least precise studies, detects side imbalance, trims one extreme study from the excess side, recomputes the center, then mirrors trimmed studies around the final trimmed estimate.
How to use this calculator
- Paste study labels, effect sizes, and standard errors in matching order.
- Choose fixed effect or random effects, depending on your synthesis plan.
- Leave missing side on auto for exploratory screening, or force left or right when theory supports one direction.
- Adjust the least precise share when you want the asymmetry check to focus on a broader or narrower small-study set.
- Press calculate to view the observed estimate, adjusted estimate, trim path, and funnel plot.
- Use the CSV or PDF buttons to export the table and summary for reporting.
FAQs
1. What does trim and fill estimate?
It screens a meta-analysis for funnel asymmetry that may reflect publication bias or small-study effects. The method trims studies from an overrepresented side, estimates a new center, then fills mirrored studies to show an adjusted pooled effect.
2. Does a filled study represent real observed evidence?
No. A filled study is an imputed value created to restore funnel symmetry under the selected assumptions. It is a sensitivity device, not a replacement for a real trial or observational study.
3. When should I use random effects here?
Use random effects when true effects likely vary across studies because of populations, interventions, follow-up periods, or methods. Fixed effect is more suitable when one common effect is a reasonable simplifying assumption.
4. Why can the adjusted pooled effect move a lot?
Large movement usually means the algorithm found notable side imbalance among less precise studies. The shift also grows when trimmed studies are far from the pooled center or carry meaningful influence after filling.
5. Can this method prove publication bias?
No. Funnel asymmetry can arise from heterogeneity, outcome scaling, chance, poor study quality, or true small-study effects. Treat trim and fill as one sensitivity check beside clinical judgment and other bias diagnostics.
6. Why does the calculator need standard errors?
Standard errors determine study precision and weights. They also shape the funnel plot because smaller standard errors place studies higher and usually closer to the pooled effect under symmetric sampling variation.
7. What does the least precise share control?
It sets how much of the lower-precision portion is examined for asymmetry during each trim step. A higher share makes the imbalance check broader, while a lower share targets the noisiest studies more tightly.
8. Is this calculator suitable for final publication?
It is useful for transparent screening, teaching, and fast sensitivity analysis. For a final manuscript, verify assumptions and reproduce findings with dedicated meta-analysis software and documented statistical decisions.