Table 2.

Comparison of the product of coefficients and difference in coefficients estimators of the mediated effect under a correct probit and correct normality assumption

		Sample size
		50	100	200	500	1000	5000
${\widehat{\gamma }}_m{\widehat{\alpha }}_z$	μ = 0.281, σ = 0.258
	Mean (μn)	0.321	0.295	0.289	0.285	0.283	0.281
	Standard deviation (σn)	0.428	0.323	0.288	0.269	0.263	0.257
	Average squared distance	0.096	0.031	0.014	0.005	0.003	0.001
${\widehat{\beta }}_z-{\widehat{\gamma }}_z$
	Mean (μn)	0.149	0.156	0.159	0.161	0.160	0.160
	Standard deviation (σn)	0.301	0.222	0.194	0.180	0.174	0.170
	Average squared distance	0.057	0.019	0.008	0.003	0.002	0.000
${\widehat{\beta }}_z^{\text{probit}.\text{standard}}-{\widehat{\gamma }}_z$
	Mean (μn)	0.326	0.297	0.290	0.285	0.283	0.281
	Standard deviation (σn)	0.445	0.326	0.290	0.269	0.263	0.257
	Average squared distance	0.108	0.033	0.015	0.005	0.003	0.001