Transformation Tools

The Transformation Tools section is a library of 23 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.