How to calculate study effect sizes for meta-analysis
Quick summary
- Meta-analysis software usually needs a study-level effect estimate plus a measure of uncertainty such as its SE or sampling variance.
- The appropriate calculation depends on what the paper reports: means and SDs, SEs, CIs, test statistics, event counts, ratio effects or pre/post data.
- The Blazon Study Effect Size Calculator shows the calculation, assumptions, analysis-ready
yi/sei/vivalues and reusable Methods wording. - The calculator prepares effect-size data; it does not pool studies or perform a meta-analysis.
What is a study-level effect size?
A study-level effect size describes the magnitude and direction of an effect in one study or comparison. Depending on the outcome and design, this may be a mean difference, standardized mean difference, risk ratio, odds ratio, hazard ratio or a transformed version such as log RR or log OR.
A meta-analysis then combines compatible study-level effects using appropriate statistical software. The effect-size calculation and the meta-analysis are therefore related but separate steps.
What information does meta-analysis software need?
A common structure is an effect estimate together with its sampling variance. In R’s metafor package these are often represented as yi and vi. The standard error sei is simply the square root of vi.
The Study Effect Size Calculator returns these analysis-ready values when they are appropriate for the selected effect measure.
Step 1: choose the type of data reported
The calculator separates four broad input types:
- Continuous — independent groups: for means, SDs, SEs, CIs, independent-samples t statistics or exact P values.
- Continuous — pre/post: for two-group studies with baseline and follow-up measurements.
- Binary: for event counts, odds ratios or risk ratios.
- Time-to-event: for hazard ratios and confidence intervals.
Step 2: enter the statistics exactly as reported
Avoid unnecessary rounding before entering values. The calculator keeps higher internal precision than it displays on screen, and the CSV export preserves analysis-ready numerical precision.
Step 3: choose the effect measure
For two independent continuous groups you may need a raw mean difference or a standardized effect. Hedges’ g is generally preferred over uncorrected Cohen’s d when a small-sample bias correction is appropriate.
For binary data, relative effects such as risk ratios and odds ratios are analysed on the natural-log scale. The calculator therefore shows both the familiar ratio and the corresponding log effect, SE and variance.
Step 4: inspect the calculation
Do not treat an online calculator as a black box. Expand Show calculation to see the formula, substituted values, intermediate results and the methodological references associated with the selected route.
Step 5: review Methods wording
The generated Methods text reflects the actual transformation used. For example, if an SD was reconstructed from an SE, the wording states that conversion. Adapt the wording to match your protocol, manuscript style and the complete analysis workflow.
Step 6: save and export results
Use Add to results table to assemble multiple study-level calculations. The table can be downloaded as CSV for use in R, RevMan, Stata, JASP or another analysis environment.
The calculator does not pool the exported rows. Study dependence, multi-arm trials, multiple outcomes and repeated time points still require appropriate handling in the subsequent meta-analysis.
How should pre/post studies be handled?
Pre/post studies require extra care because repeated measurements within the same participants are correlated. For controlled pre/post effects, the current calculator uses the difference between group mean changes as the numerator and, for standardized effects, the pooled baseline SD as the default standardizer. Change-score variability is used to quantify precision.
See Pre/post effect sizes for meta-analysis: baseline SD or change-score SD? for the rationale.
What if the SD of change is missing?
If baseline SD, follow-up SD and the within-person pre/post correlation are known, the SD of change can be reconstructed. See How to calculate SD of change from pre/post data and Pre/post correlation.
When should I not use the calculator?
The current calculator does not reconstruct effects for crossover trials, complex clustered designs, more than two repeated time points, Kaplan-Meier curves or dependent multi-arm effects. A valid numerical effect is not automatically a valid independent meta-analysis observation.
Related tools
- Pre/Post & Change-Score Calculator — reconstruct and convert pre/post summary statistics.
- Plot Data Extractor — extract numerical data from scientific plots.
Methodological references
- Cochrane Handbook, Chapter 6.
- Viechtbauer W. Conducting meta-analyses in R with the metafor package. Journal of Statistical Software. 2010.
- metafor effect-size calculation documentation.
Ready to calculate an effect? Open the Study Effect Size Calculator →