Table 3.

Comparison of the product of coefficients and difference in coefficients estimators of the mediated effect under an incorrect logistic and correct normality assumption

		Sample size
		50	100	200	500	1000	5000
${\widehat{\gamma }}_m{\widehat{\alpha }}_z$	μ = 0.475, σ = 0.442
	Mean (μn)	0.548	0.501	0.490	0.482	0.478	0.475
	Standard deviation (σn)	0.741	0.560	0.499	0.464	0.454	0.444
	Average squared distance	0.288	0.095	0.042	0.016	0.008	0.002
${\widehat{\beta }}_z-{\widehat{\gamma }}_z$
	Mean (μn)	0.218	0.229	0.234	0.236	0.235	0.235
	Standard deviation (σn)	0.512	0.369	0.320	0.294	0.285	0.278
	Average squared distance	0.168	0.055	0.024	0.009	0.004	0.001
${\widehat{\beta }}_z^{\text{probit}.\text{standard}}-{\widehat{\gamma }}_z$
	Mean (μn)	0.483	0.435	0.424	0.416	0.413	0.410
	Standard deviation (σn)	0.707	0.508	0.448	0.414	0.403	0.394
	Average squared distance	0.284	0.082	0.037	0.013	0.007	0.001