Converting Effect Sizes
The Rosetta Stone of Meta-Analysis
The Data Harmonization Problem
Every study reports results differently.
- Study 1: Means and SDs (\(d\))
- Study 2: F-test (\(d\)?)
- Study 3: Odds Ratio (\(d\)??)
To meta-analyze them, you must convert them all to a common metric (usually \(d\) or \(g\)).
1. The compute.es Workflow
The compute.es package acts as a universal translator. It takes almost any test statistic and returns \(d\), \(g\), \(r\), and their variances.
Interactive Conversion Lab
Try calculating an effect size from different inputs below.
Study reports: \(t(58) = 2.5\), \(N_{tx}=30, N_{ctrl}=30\).
Study reports: \(F(1, 58) = 6.25\). (Note: \(\sqrt{F} = t\))
Study reports: \(OR = 2.5\). Formula: \(d = \frac{\ln(OR) \sqrt{3}}{\pi}\)
2. Batch Conversion
In the real world, you do this for a whole dataframe.
3. The MAd Helper
The MAd package also has helper functions effectively wrapping these logic paths.