. Author manuscript; available in PMC: 2016 Aug 18.

Published in final edited form as: Struct Equ Modeling. 2011 Nov 14;18(2):195–211. doi: 10.1080/10705511.2011.557334

Table 1. Three Methods for Testing Mediated Effects Examined in the Current Simulation Study.

Method

Estimate of Mediated Effect

Test of Significance

First-order solution (Sobel, 1982)

α̂β̂

z = \frac{\hat{α} \hat{β}}{\sqrt{{\hat{α}}^{2} {\hat{σ}}_{β}^{2} + {\hat{β}}^{2} {\hat{σ}}_{α}^{2}}}

Asymmetric confidence interval (MacKinnon & Lockwood, 2001)

α̂β̂

\hat{α} \hat{β} \pm C L \sqrt{{\hat{α}}^{2} {\hat{σ}}_{β}^{2} + {\hat{β}}^{2} {\hat{σ}}_{α}^{2}}

Joint significance test (Cohen & Cohen, 1983)

None

t = \frac{\hat{α}}{{\hat{σ}}_{α}}; t = \frac{\hat{β}}{{\hat{σ}}_{β}}