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Table 1 Calculations used on the extracted data to estimate the standardised observed effect size

From: A study of target effect sizes in randomised controlled trials published in the Health Technology Assessment journal

Observed effect size type Z-statistic calculation Re-arrangement to get standardised observed effect size
Mean difference, Difference in proportions, Regression coefficient, Absolute risk reduction, Analysis of variance/covariance (ANOVA/ANCOVA) coefficients \( Z=\frac{d}{SE(d)} \) \( {d}_{observed}=Z\times \sqrt{\frac{1}{n_A}+\frac{1}{n_B}} \)
Odds ratio \( Z=\frac{\ln \left[ OR\right]}{SE\left(\ln \left[ OR\right]\right)} \) \( {d}_{observed}=Z\times \sqrt{\frac{1}{n_A}+\frac{1}{n_B}} \)
Risk ratio \( Z=\frac{\ln \left[ RR\right]}{SE\left(\ln \left[ RR\right]\right)} \) \( {d}_{observed}=Z\times \sqrt{\frac{1}{n_A}+\frac{1}{n_B}} \)
Hazard ratio \( Z=\frac{\ln \left[ HR\right]}{SE\left(\ln \left[ HR\right]\right)} \) \( {d}_{observed}=Z\times \sqrt{\frac{1}{n_A}+\frac{1}{n_B}} \)