Skip to main content

Advertisement

Table 2 Simulation results when X and Y are normally distributed

From: Standardizing effect size from linear regression models with log-transformed variables for meta-analysis

  Model A
\( \widehat{Y}=\widehat{\alpha}+\widehat{\beta}\cdotp X \)
Model B
\( \widehat{Y}=\widehat{\alpha}+\widehat{\beta}\cdotp { \log}_b(X) \)
Model C
\( \widehat{{ \log}_a(Y)}=\widehat{\alpha}+\widehat{\beta}\cdotp X \)
Model D
\( \widehat{{ \log}_a(Y)}=\widehat{\alpha}+\widehat{\beta}\cdotp { \log}_b(X) \)
Beta-hat coefficient and standard error from regression model \( \widehat{\beta} \) = 0.995
se(\( \widehat{\beta} \)) = 0.054
\( \widehat{\beta} \) = 9.587
se(\( \widehat{\beta} \)) = 0.520
\( \widehat{\beta} \) = 0.020
se(\( \widehat{\beta} \)) = 0.001
\( \widehat{\beta} \) = 0.193
se(\( \widehat{\beta} \)) = 0.011
Absolute change in Y for an absolute change of c units in X Effect size 0.995 0.914 1.006 0.928
95% CI (0.889–1.101) (0.817–1.011) (0.895–1.118) (0.827–1.029)
Absolute change in Y for a relative change of k times in X Effect size 0.995 0.914 1.006 0.928
95% CI (0.889–1.101) (0.817–1.011) (0.895–1.118) (0.827–1.029)
Relative change in Y for an absolute change of c units in X Effect size 1.0199 1.0183 1.0201 1.0186
95% CI (1.0178–1.0220) (1.0163–1.0202) (1.0179–1.0224) (1.0165–1.0206)
Relative change in Y for a relative change of k times in X Effect size 1.0199 1.0183 1.0201 1.0186
95% CI (1.0178–1.0220) (1.0163–1.0202) (1.0179–1.0224) (1.0165–1.0206)
  1. Note: c = 1 and k = 1.1