Meta Analysis Calculations

Enter study effects, standard errors, variance, notes, and labels. Compare pooled estimates with heterogeneity checks. Download clear summaries for shared evidence review workflows today.

Advanced Meta Analysis Calculator

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Study 10

Example Data Table

This example uses natural effect estimates with standard errors.

Study Effect Estimate Standard Error Possible Meaning
Study A 0.18 0.060 Small positive effect
Study B 0.24 0.075 Moderate positive effect
Study C 0.11 0.055 Low positive effect
Study D 0.31 0.090 Higher positive effect
Study E 0.21 0.070 Stable positive effect

Formula Used

Variance: variance equals standard error squared.

Fixed weight: each study weight equals one divided by its variance.

Fixed pooled effect: multiply each effect by its fixed weight, add those values, then divide by total fixed weight.

Cochran Q: add weighted squared differences between each effect and the fixed pooled effect.

Tau squared: DerSimonian Laird variance equals max zero and Q minus degrees of freedom, divided by the correction term.

Random weight: each study weight equals one divided by study variance plus tau squared.

I squared: max zero and Q minus degrees of freedom divided by Q, then multiplied by 100.

Confidence interval: pooled effect plus or minus z value multiplied by pooled standard error.

How to Use This Calculator

Enter a clear study name for each row. Add the effect estimate from that study. Add the standard error for the same effect. Choose the natural scale for mean differences or standardized effects. Choose the log ratio scale for log odds ratios, log risk ratios, or log hazard ratios.

Press the calculate button. Review the fixed effect result first. Then compare it with the random effects result. Check Q, tau squared, and I squared. Use the CSV button for spreadsheet records. Use the PDF button for a simple report.

Meta Analysis Calculator Guide

Meta analysis helps researchers combine results from several studies. This calculator uses inverse variance methods to pool compatible effects. It accepts effect estimates and standard errors. These values may represent mean differences, standardized differences, or log ratios.

Why Pooled Evidence Matters

One study can be small or unstable. Several studies can show a clearer pattern. Pooling gives larger evidence weight to precise studies. It also reveals disagreement across results. That balance supports cautious interpretation.

Fixed Effect Model

The fixed effect model assumes one true effect. Every study estimates the same underlying value. Differences happen because of sampling error. Study weight equals one divided by variance. Smaller standard errors receive higher weights. This model is useful when studies are very similar.

Random Effects Model

The random effects model allows real differences between studies. It adds between study variance to each study variance. The DerSimonian Laird method estimates that extra variance. Wider confidence intervals often appear. This is expected when evidence varies.

Heterogeneity Review

Heterogeneity measures disagreement among studies. Cochran Q tests whether variation exceeds chance. I squared shows the percent of variation beyond sampling error. A higher I squared value suggests more inconsistency. It does not prove poor quality. It tells users to review design, population, and measurement differences.

Practical Use

Enter each study name, effect estimate, and standard error. Use log odds ratios or log risk ratios for ratio measures. Select the log scale option when ratios should be shown after exponentiation. Review fixed and random summaries together. Export the table when you need documentation.

Good Reporting Habits

Always mention the effect scale. State the number of included studies. Report the pooled estimate, confidence interval, tau squared, Q, and I squared. Explain any strong heterogeneity. Do not treat the pooled value as automatic truth. Check study quality, bias, and clinical meaning.

Limits

This tool supports generic inverse variance analysis. It does not replace specialist review. It also does not judge study eligibility. Users should prepare data carefully before entry. Consistent direction matters. Positive and negative effects must mean the same thing across all included studies. Careful preparation makes the summary stronger.

Use sensitivity checks when needed. Keep original extraction sheets available for review during peer review.

FAQs

What data do I need?

You need a study name, an effect estimate, and a standard error. The calculator uses these values for inverse variance weighting and pooled analysis.

Can I use odds ratios?

Yes. Enter log odds ratios and their standard errors. Then choose the log ratio scale. The result table will also show exponentiated ratio values.

What is a fixed effect model?

It assumes all studies estimate one true effect. Differences between studies are treated as sampling error, not real study-level variation.

What is a random effects model?

It allows true effects to differ across studies. It adds between study variance, so intervals are often wider when studies disagree.

What does I squared mean?

I squared estimates the percentage of observed variation that is beyond chance. Higher values suggest stronger inconsistency across study results.

What is tau squared?

Tau squared estimates between study variance. It is used in random effects weighting and helps describe heterogeneity in the evidence.

Can I export the results?

Yes. Use the CSV button for spreadsheet analysis. Use the PDF button for a simple printable summary of the calculated results.

Does this replace expert review?

No. It supports calculations only. You should still review study quality, bias, eligibility, outcome definitions, and interpretation before reporting results.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.