Calculator
Example Data Table
| Study | Treatment n | Treatment mean | Treatment SD | Control n | Control mean | Control SD |
|---|---|---|---|---|---|---|
| Study A | 42 | 18.4 | 4.9 | 40 | 15.8 | 5.1 |
| Study B | 58 | 21.1 | 6.2 | 55 | 18.7 | 6.5 |
| Study C | 36 | 17.3 | 4.2 | 37 | 14.6 | 4.7 |
| Study | Treatment events | Treatment non events | Control events | Control non events |
|---|---|---|---|---|
| Trial 1 | 18 | 62 | 11 | 69 |
| Trial 2 | 26 | 54 | 15 | 65 |
| Trial 3 | 12 | 48 | 8 | 52 |
Formula Used
For continuous studies, the calculator supports Cohen d and Hedges g. Cohen d uses the mean difference divided by the pooled standard deviation. Hedges g multiplies d by a small sample correction factor, which reduces upward bias in smaller studies.
The pooled standard deviation is computed from both group variances. The sampling variance combines the group size term and the squared effect term. Individual study confidence intervals are calculated as effect size ± z × standard error.
For binary studies, the calculator supports log odds ratio, log risk ratio, and risk difference. Odds ratio and risk ratio are pooled on the log scale. Reported values are transformed back to the ratio scale after estimation.
Fixed effect pooling uses weight = 1 / variance. Random effects pooling uses weight = 1 / (variance + tau²). Tau² is estimated with the DerSimonian and Laird method. Heterogeneity statistics include Q, I², tau², and H.
The random effects prediction interval estimates the likely range for a future study effect. It combines between study variance with the uncertainty around the pooled random effects estimate.
How to Use This Calculator
Choose whether your studies are continuous or binary. Then select the effect measure that matches your outcome and reporting preference.
Enter one study per row. For continuous data, add treatment and control sample size, mean, and standard deviation. For binary data, enter events and non events for both groups.
Select fixed effect when studies are very similar and you want one shared underlying effect. Select random effects when study methods or populations differ and variation across studies matters.
Set your confidence level. If binary cells contain zeros, enable continuity correction so the ratio based estimates remain calculable.
Click the calculation button. The result section appears above the form and shows study level estimates, pooled effects, heterogeneity, a prediction interval, and a forest style plot.
Use the CSV option for spreadsheet review. Use the PDF option to export a report for sharing, documentation, or quick archiving.
About Meta Analysis Effect Sizes
Why effect sizes matter
Meta analysis combines evidence from several studies into one structured estimate. Effect sizes allow those studies to be compared on a common scale. That makes it possible to move beyond isolated findings and evaluate a broader pattern across research.
Choosing the correct measure
Continuous outcomes often use standardized mean differences such as Cohen d or Hedges g. These measures are useful when studies report similar constructs with different units or scales. Binary outcomes usually rely on odds ratios, risk ratios, or risk differences. The best choice depends on the way your outcome is measured and how you want readers to interpret results.
Understanding heterogeneity
Studies rarely match perfectly. They can differ in participants, interventions, settings, follow up periods, and measurement quality. Heterogeneity statistics help you understand whether variation across studies is larger than chance alone. Q tests overall dispersion. I² estimates the percentage of variability caused by real differences rather than sampling error. Tau² measures between study variance on the meta analytic scale.
Interpreting pooled estimates
A pooled effect is not the full story. You should inspect study level confidence intervals, weight patterns, and the prediction interval when using random effects. A narrow pooled interval with high heterogeneity may still hide important differences across settings. Strong reporting compares the pooled estimate with clinical or practical relevance, not only statistical direction.
FAQs
1. What does this calculator estimate?
It estimates study level effect sizes and then pools them with fixed effect or random effects meta analysis. It also reports heterogeneity, confidence intervals, weights, and a prediction interval for the random effects model.
2. When should I use Hedges g instead of Cohen d?
Use Hedges g when studies have smaller sample sizes. It applies a correction that reduces positive bias in standardized mean differences. With larger samples, Cohen d and Hedges g often become very similar.
3. Why are odds ratios and risk ratios pooled on the log scale?
Log transformation stabilizes the sampling distribution and makes variance formulas more appropriate for pooling. After estimation, the results are converted back to the ratio scale for easier interpretation.
4. What is I squared?
I squared estimates the percentage of observed variability that reflects real differences between studies rather than random error. Higher values suggest greater inconsistency across study results.
5. What is tau squared?
Tau squared is the estimated between study variance in a random effects meta analysis. It influences random effects weights and prediction intervals. Larger values indicate broader dispersion in true effects.
6. Why would I apply a continuity correction?
Ratio based binary measures can fail when one or more cells equal zero. A continuity correction adds a small constant, helping the study remain usable while preserving the overall analysis flow.
7. What is the prediction interval used for?
It estimates the plausible range for the true effect in a future study. This is especially helpful when heterogeneity exists and you want more than a single pooled average.
8. Can I use this output for a publication?
It is useful for planning, checking, and teaching. For publication, verify formulas, assumptions, inclusion rules, and reporting standards with your protocol, software validation steps, and statistical review.