. Author manuscript; available in PMC: 2010 Apr 21.

Published in final edited form as: Clin Trials. 2007;4(5):499–513. doi: 10.1177/1740774507083434

Table 4.

Comparison of the product of coefficients and difference in coefficients estimators for the proportion mediated estimators under a correct logistic assumption and correct normal assumption

		Sample size
		50	100	200	500	1000	5000
${\hat{γ}}_{m} {\hat{α}}_{z} ∕ ({\hat{γ}}_{z} + {\hat{γ}}_{m} {\hat{α}}_{z})$	μ = 0.343, σ = 0.227
	Mean (μ_n)	–2.4 × 10¹¹	3.8 × 10¹¹	1.3 × 10¹⁰	0.358	0.280	0.349
	Standard deviation (σ_n)	1.7 × 10¹³	4.4 × 10¹³	2.3 × 10¹²	13.508	13.144	0.247
	Average squared distance	3.0 × 10²⁶	1.9 × 10²⁷	5.2 × 10²⁴	182.396	172.716	0.009
$1 - {\hat{γ}}_{z} ∕ {\hat{β}}_{z}$
	Mean (μ_n)	0.243	0.311	0.412	0.340	0.320	0.304
	Standard deviation (σ_n)	3.862	6.659	8.494	4.905	1.142	0.251
	Average squared distance	14.872	44.256	72.060	23.981	1.243	0.010
${\hat{γ}}_{m} {\hat{α}}_{z} ∕ {\hat{β}}_{z}$
	Mean (μ_n)	0.360	0.407	0.501	0.427	0.403	0.386
	Standard deviation (σ_n)	3.845	6.682	8.428	5.084	1.145	0.284
	Average squared distance	14.716	44.532	70.926	25.743	1.231	0.011
$1 - {\hat{γ}}_{z} ∕ {\hat{β}}_{z}^{logit . standard}$
	Mean (μ_n)	0.288	0.335	0.435	0.369	0.350	0.335
	Standard deviation (σ_n)	3.414	6.107	7.776	4.584	1.116	0.248
	Average squared distance	11.618	37.214	60.387	20.934	1.185	0.010
${\hat{γ}}_{m} {\hat{α}}_{z} ∕ {\hat{β}}_{z}^{logit . standard}$
	Mean (μ_n)	0.314	0.360	0.460	0.395	0.375	0.360
	Standard deviation (σ_n)	3.403	6.115	7.708	4.715	1.114	0.258
	Average squared distance	11.535	37.314	59.324	22.151	1.175	0.010