Example Data Table
| Scenario |
Effect Size |
Studies |
Average Sample |
Tau Squared |
Model |
| Small synthesis |
0.20 |
8 |
70 |
0.01 |
Random effects |
| Moderate evidence |
0.35 |
15 |
100 |
0.03 |
Random effects |
| Large review |
0.50 |
25 |
120 |
0.05 |
Fixed effect |
Formula Used
The calculator estimates the study level variance for a standardized effect with balanced or unbalanced groups.
Within variance: V = (n1 + n0) / (n1 × n0) + d² / [2 × (n1 + n0 - 2)]
Fixed effect meta variance: Vmeta = V / k
Random effects meta variance: Vmeta = (V + tau²) / k
Noncentral value: lambda = absolute effect / meta standard error
Two-sided power: Power = 1 - Phi(zcrit - lambda) + Phi(-zcrit - lambda)
These formulas use equal average study precision. Real projects may need study-specific weights.
How to Use This Calculator
Enter the expected effect size from past research, pilot data, or a clinically meaningful target. Add the planned number of studies and the average total sample per study. Choose fixed effect when one common effect is assumed. Choose random effects when true effects may differ across studies.
Use tau squared to represent heterogeneity. Higher tau squared usually lowers power. Enter manual standard error when you already know the expected study precision. Press calculate. The result appears above the form. Then export the table using CSV or PDF.
Power Planning for Meta Analysis
Power is the chance that a meta-analysis detects a real effect. It helps reviewers judge whether their planned evidence synthesis can answer the research question. A review with many studies can still have low power when effects are small, samples are limited, or heterogeneity is high.
Why Power Matters
Meta-analysis combines study estimates. The combined standard error usually becomes smaller as the number of studies increases. That improves the chance of statistical significance. Yet the gain is not automatic. Random effects models include between-study variation. This extra variance can reduce precision and widen the confidence interval.
Main Inputs
This calculator uses the expected effect size, study count, average sample size, alpha level, test direction, and heterogeneity. It also includes allocation ratio, dropout, design effect, and manual standard error. These options support early planning and sensitivity checks. They are useful before protocol registration, funding review, or final search completion.
Fixed and Random Effects
A fixed effect setting assumes one shared true effect. It often gives smaller standard errors. A random effects setting assumes the true effect may vary across studies. It adds tau squared to the variance. This is often more realistic for clinical, education, social, and policy evidence.
Interpreting Results
The estimated power is shown as a percentage. A common planning target is eighty percent. The calculator also reports the approximate number of studies needed to reach your target power. If the required number is very large, the assumed effect may be too small, heterogeneity may be too high, or the planned sample may be weak.
Practical Advice
Run several scenarios. Compare optimistic, expected, and conservative assumptions. Report the inputs with the final power estimate. Treat the output as a planning guide, not as final proof. For publication work, confirm assumptions with study-specific data and expert statistical review.
FAQs
What is meta-analysis power?
It is the probability that a meta-analysis will detect a true effect, given the selected effect size, variance, alpha level, and number of studies.
Should I use fixed effect or random effects?
Use fixed effect when studies estimate one common effect. Use random effects when true effects may vary across settings, samples, or methods.
What does tau squared mean?
Tau squared is between-study variance. Larger values show more heterogeneity. Higher heterogeneity usually increases uncertainty and reduces statistical power.
What effect size should I enter?
Use a value from pilot data, prior reviews, expert judgment, or the smallest effect that would matter for practice or policy.
Why does power fall with heterogeneity?
Heterogeneity adds extra variance in random effects analysis. Extra variance increases the meta-analysis standard error and lowers the chance of significance.
Can I use a manual standard error?
Yes. Select manual standard error when you already know the expected study-level standard error. This can be useful for generic effect measures.
What is a good target power?
Eighty percent is common. Some projects may require ninety percent when decisions are expensive, sensitive, or likely to affect policy.
Can this replace full statistical software?
No. It supports planning and sensitivity checks. Final analyses should use study-specific data, proper weighting, and a complete statistical workflow.