Skip to main content

Advertisement

Table 4 Simulation results when Y has an asymmetric distribution

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 \( \widehat{\beta} \) = 0.625
se(\( \widehat{\beta} \)) = 0.254
\( \widehat{\beta} \) = 5.834
se(\( \widehat{\beta} \)) = 2.441
\( \widehat{\beta} \) = 0.011
se(\( \widehat{\beta} \)) = 0.005
\( \widehat{\beta} \) = 0.103
se(\( \widehat{\beta} \)) = 0.044
Absolute change in Y for an absolute change of c units in X Effect size 0.625 0.557 0.551 0.493
95% CI (0.128–1.122) (0.101–1.013) (0.100–1.006) (0.080–0.909)
Absolute change in Y for a relative change of k times in X Effect size 0.625 0.557 0.551 0.493
95% CI (0.128–1.122) (0.101–1.013) (0.100–1.006) (0.080–0.909)
Relative change in Y for an absolute change of c units in X Effect size 1.0125 1.0111 1.0110 1.0099
95% CI (1.0026–1.0224) (1.0020–1.0203) (1.0020–1.0201) (1.0016–1.0182)
Relative change in Y for a relative change of k times in X Effect size 1.0125 1.0111 1.0110 1.0099
95% CI (1.0026–1.0224) (1.0020–1.0203) (1.0020–1.0201) (1.0016–1.0182)
  1. Note: c = 1 and k = 1.1