Calculator Inputs
Example Data Table
Use this sample when you want to test the calculator quickly.
| Study | Group | Effect Size | Standard Error | Interpretation |
|---|---|---|---|---|
| Study A | Adults | 0.24 | 0.08 | Small positive effect |
| Study B | Adults | 0.31 | 0.10 | Moderate positive effect |
| Study C | Adults | 0.18 | 0.09 | Small positive effect |
| Study D | Mixed | 0.42 | 0.12 | Higher effect |
| Study E | Mixed | 0.27 | 0.07 | Moderate precision |
| Study F | Mixed | 0.35 | 0.11 | Moderate positive effect |
Formula Used
Variance: variance = SE²
Fixed effect weight: wᵢ = 1 / varianceᵢ
Random effects weight: wᵢ* = 1 / (varianceᵢ + tau²)
Pooled effect: pooled effect = Σ(wᵢ × effectᵢ) / Σwᵢ
Pooled standard error: SE pooled = √(1 / Σwᵢ)
Confidence interval: pooled effect ± z × pooled SE
Q statistic: Q = Σwᵢ(effectᵢ − pooled fixed effect)²
I²: I² = max(0, (Q − df) / Q) × 100
DerSimonian-Laird tau²: tau² = max(0, (Q − df) / C)
Prediction interval: random pooled effect ± z × √(tau² + random pooled SE²)
How to Use This Calculator
- Enter each study name, group, effect size, and standard error.
- If standard error is unavailable, enter lower and upper confidence limits.
- Select the effect scale that matches your research data.
- Choose fixed effect when one common effect is assumed.
- Choose random effects when studies may estimate different effects.
- Set the confidence level for the interval calculation.
- Press the calculate button to view pooled results.
- Download the CSV or PDF summary for reporting.
Meta Analysis Calculator Guide
What This Tool Does
A meta analysis calculator combines results from several studies. It helps researchers build one clear estimate from separate pieces of evidence. Each study can have a different sample size, precision level, and effect size. This tool gives more influence to precise studies. It gives less influence to uncertain studies. That makes the pooled result more balanced.
Why Weighting Matters
Study weighting is the heart of meta analysis. A study with a small standard error has a narrow confidence interval. It usually receives a larger weight. A study with a large standard error has less precision. It receives a smaller weight. This calculator shows both fixed effect weights and random effects weights. You can compare how assumptions change the final estimate.
Fixed and Random Models
A fixed effect model assumes all studies estimate one shared effect. This approach works best when the studies are very similar. A random effects model allows true effects to vary across studies. This is useful when designs, populations, or settings differ. The calculator estimates tau squared to measure between-study variation.
Understanding Heterogeneity
Heterogeneity shows how much study results differ. The Q statistic checks observed variation. I squared converts that variation into a percentage. Low I squared suggests consistent findings. High I squared suggests important differences. In that case, subgroup review may help. You can enter group names to compare separate evidence clusters.
Confidence and Prediction Intervals
The confidence interval describes uncertainty around the pooled result. A narrow interval suggests stronger precision. A wide interval suggests more uncertainty. The prediction interval is different. It estimates where a future study may fall. This is helpful when results vary across studies.
Practical Research Use
Use this calculator for planning, evidence reviews, academic reports, and clinical summaries. Check all input values before interpreting the output. Effect sizes must use the same scale. Log ratios should not be mixed with raw mean differences. When heterogeneity is high, explain possible causes. Good interpretation needs both statistics and subject knowledge.
FAQs
1. What is a meta analysis calculator?
It combines effect sizes from several studies. It calculates pooled estimates, confidence intervals, weights, and heterogeneity measures for research synthesis.
2. What effect size should I enter?
Enter the effect size reported by each study. Use one common scale across all studies, such as standardized mean difference or log odds ratio.
3. Can I use confidence intervals instead of standard errors?
Yes. Enter the effect size plus lower and upper confidence limits. The calculator estimates standard error from those limits.
4. When should I use a fixed effect model?
Use it when studies are very similar and you believe they estimate one shared true effect. It ignores between-study variation.
5. When should I use random effects?
Use it when study populations, methods, or settings differ. It includes between-study variation through the tau squared estimate.
6. What does I squared mean?
I squared estimates the percentage of total variation caused by heterogeneity rather than chance. Higher values suggest less consistent study results.
7. What is the prediction interval?
It estimates the range where a future similar study may fall. It is often wider than the pooled confidence interval.
8. Can I export the results?
Yes. After calculation, use the CSV or PDF buttons to save study weights, pooled estimates, and heterogeneity results.