Transformation Tools
The Transformation Tools section is a library of 22 conversion utilities that solve a practical meta-analysis problem: studies report results in different forms, and you must harmonise them to a common metric before pooling. Each tool takes the form a paper actually reports and returns the form your meta-analysis needs.
The six categories
| # | Category | What it covers |
|---|
| 1 | Summary Statistics | Median to mean, SE to SD, CI to SD, variance to SD |
| 2 | Effect Sizes | OR/RR/HR conversions, log transforms, CI to SE, risk difference |
| 3 | Correlations | Correlation to Fisher's z, Cohen's d to correlation |
| 4 | Standardised Mean Differences | Cohen's d to Hedges' g, Glass's delta to Cohen's d |
| 5 | Diagnostic Tests | Sensitivity/Specificity to logit, DOR to log DOR |
| 6 | 2x2 Tables | OR/RR + marginals to 2x2 table reconstruction |
Summary Statistics conversions
| Tool | What it does |
|---|
| Median to Mean + SD | Estimates mean and SD from median and IQR (or median, min, max) |
| Standard Error to Standard Deviation | Converts using SD = SE * sqrt(n) |
| Confidence Interval to SD | Recovers SD from 95% CI and sample size |
| Variance to Standard Deviation | Bidirectional (SD = sqrt(variance)) |
Effect-size conversions
| Tool | What it does |
|---|
| Odds Ratio to Risk Ratio | Converts OR to RR (requires baseline event rate) |
| Odds Ratio to Log OR | Bidirectional between OR and ln(OR) |
| OR CI to SE | Recovers SE of OR from its 95% CI |
| Risk Ratio to Log RR | Bidirectional between RR and ln(RR) |
| RR CI to SE | Recovers SE of RR from its 95% CI |
| Hazard Ratio to Log HR | Bidirectional between HR and ln(HR) |
| HR CI to SE | Recovers SE of HR from its 95% CI |
| Hazard Ratio to Risk Ratio | Approximate conversion between HR and RR |
| Odds Ratio to Risk Difference | Convert OR to RD given baseline risk |
| Risk Ratio to Risk Difference | Convert RR to RD given baseline risk |
The log conversions and CI-to-SE conversions produce the inputs the meta-analysis engine needs when papers only report effects with CIs.
Correlation conversions
| Tool | What it does |
|---|
| Correlation to Fisher's z | z = 0.5 * ln((1+r)/(1-r)), stabilises variance before pooling |
| Cohen's d to Correlation | Convert between SMD and point-biserial correlation |
Standardised Mean Difference conversions
| Tool | What it does |
|---|
| Cohen's d to Hedges' g | Apply/remove Hedges' small-sample correction J |
| Glass's delta to Cohen's d | Convert between Glass's delta (one group SD) and Cohen's d (pooled SD) |
Diagnostic Test conversions
| Tool | What it does |
|---|
| Sensitivity/Specificity to Logit | For bivariate diagnostic meta-analysis |
| Diagnostic OR to Log DOR | Convert between DOR and ln(DOR) |
2x2 Table reconstructions
| Tool | What it does |
|---|
| OR + marginals to 2x2 Table | Reconstruct four cells from reported OR plus marginals |
| RR + marginals to 2x2 Table | Reconstruct cells from reported RR plus marginals |
Useful when papers report OR/RR with CI but not actual cell counts.
Typical preparation flow
Median + IQR -> Median to Mean + SD -> ready for MD/SMD
OR + 95% CI -> OR CI to SE -> ready for OR pooling
OR + baseline risk -> OR to RR -> pool on RR scale
Correlation r -> Correlation to Fisher's z -> ready for correlation pooling
Cohen's d -> Cohen's d to Hedges' g -> ready for SMD pooling
OR + marginals -> OR + marginals to 2x2 Table -> recovers cells
Take what the paper reports, transform to what the engine needs, then plug into Main Analysis, Subgroup Analysis, Meta Regression, or Network Meta-Analysis.
Reproducibility
Using named conversion tools and citing the conversion alongside the source study makes preparation transparent and replicable. The conversion used is documented, inputs/outputs are recorded, and a second reviewer can reproduce the same intermediate values.