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 | \( Z=\frac{\ln \left[ HR\right]}{SE\left(\ln \left[ HR\right]\right)} \) | \( {d}_{observed}=Z\times \sqrt{\frac{1}{n_A}+\frac{1}{n_B}} \) |