. 2017 Mar 17;17:44. doi: 10.1186/s12874-017-0322-8

Table 2.

Simulation results when X and Y are normally distributed

		Model A $\hat{Y} = \hat{α} + \hat{β} \cdot X$	Model B $\hat{Y} = \hat{α} + \hat{β} \cdot {log}_{b} (X)$	Model C $\hat{{log}_{a} (Y)} = \hat{α} + \hat{β} \cdot X$	Model D $\hat{{log}_{a} (Y)} = \hat{α} + \hat{β} \cdot {log}_{b} (X)$
Beta-hat coefficient and standard error from regression model		$\hat{β}$ = 0.995 se( $\hat{β}$ ) = 0.054	$\hat{β}$ = 9.587 se( $\hat{β}$ ) = 0.520	$\hat{β}$ = 0.020 se( $\hat{β}$ ) = 0.001	$\hat{β}$ = 0.193 se( $\hat{β}$ ) = 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
Absolute change in Y for an absolute change of c units in X	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
Absolute change in Y for a relative change of k times in X	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
Relative change in Y for an absolute change of c units in X	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
Relative change in Y for a relative change of k times in X	95% CI	(1.0178–1.0220)	(1.0163–1.0202)	(1.0179–1.0224)	(1.0165–1.0206)

Note: c = 1 and k = 1.1