Table 6.

Comparison of the product of coefficients and difference in coefficients estimators of the mediated effect under an incorrect logistic and incorrect normality assumption (probit and χ²(2))

		Sample size
		50	100	200	500	1000	5000
${\widehat{\gamma }}_m{\widehat{\alpha }}_z$	μ = 0.484, σ = 0.447
	Mean (μn)	0.588	0.528	0.508	0.492	0.487	0.484
	Standard deviation (σn)	0.928	0.610	0.529	0.475	0.459	0.449
	Average squared distance	0.582	0.139	0.059	0.021	0.010	0.002
${\widehat{\beta }}_z-{\widehat{\gamma }}_z$
	Mean (μn)	0.418	0.386	0.377	0.368	0.365	0.364
	Standard deviation (σn)	0.630	0.460	0.411	0.377	0.368	0.361
	Average squared distance	0.215	0.062	0.027	0.010	0.005	0.001
${\widehat{\beta }}_z^{\text{logit}.\text{standard}}-{\widehat{\gamma }}_z$
	Mean (μn)	0.891	0.674	0.624	0.596	0.587	0.582
	Standard deviation (σn)	2.110	0.885	0.692	0.613	0.590	0.577
	Average squared distance	3.780	0.337	0.097	0.031	0.014	0.003