Dear Mike,

Let the (standardized) path coefficient from X (the independent variable) to M (the mediator) be x, the path from M to Y (the outcome) variable y, and the path from X to Y z. According to this model, the correlation between X and Y equals the indirect effect of X on Y plus the direct effect of M on Y, which is: r = x*y + z. [note that in the mediation model 'the correlation between X and Y' is not equivalent to 'the path coefficient from X to Y']. See e.g. http://ibgwww.colorado.edu/twins2002/cdrom/HTML/BOOK/node78.htm

We conclude that M mediates the relationship between X and Y when the assumption x*y = 0 does not hold.

If x*y = 0 does not hold, but the assumption z = 0 does (meaning that the direct path from X to M is absent) the formula reduces to r = x*y, we conclude that the relationship between X and Y is 'fully mediated' by M. If both assumptions x*y = 0 and z = 0 do not hold (so when there is an indirect effect as well as a direct effect), we conclude that the relationship between X and Y is 'partially mediated' by M.

In your latest example, in which - I assume - A is the independent variable, B the mediator, C the outcome variable: If "A has an indirect effect on C [via B]" it implies that "B mediates the effect of A on C'.

Kind regards,

Kees-Jan Kan

On Mon, Jun 1, 2015 at 4:28 PM, Mike <[log in to unmask]> wrote:

Hi Donald,

Thanks. I'm just curious because my analyses show that A is correlated with B (path coefficient x), B is correlated with C (path coefficient y), but A is not correlated with C. Intriguingly, when I put A, B, and C in a mediation analysis, the mediation path coefficient xy is also significant. So, in this case, I can just say "A has an indirect effect on C" rather than "B mediates the effect of A on C', right?

Mike