**In the case of a dichotomous independent variable with the values 0 and 1: could a significant difference of the means of M between the two groups 0 and 1 be considered as a fulfilled precondition/significant association, so that carrying out a mediation analysis is justified?**

*My own thoughts on this question: Firstly, the term association confuses me. Unfortunately Hayes doesn’t give a definition of “association”. Other sources that I have consulted yet define association as covariation and link it to correlation and regression. The difference of means isn’t mentioned as a measure of association. But doesn’t the difference of means also indicate covariation in certain cases? For example, I have a dichotomous variable that indicates membership in a trauma survivor or a non-trauma group. If I find significant differences between the two groups in an outcome like depressive symptoms, I could interpret it as the following: depressive symptoms covary with trauma exposure; therefore the difference of means is an indicator of covariation. Furthermore the non-standardized regression coefficient in a linear regression model with an independent dichotomous variable (values 0,1) is the difference of the means of Y between 0 and 1. The regression coefficient is considered as a measure of association. As a result, in a regression-based simple mediation model with a dichotomous variable as X, the path coefficient from X to M is the difference of the means of M between 0 and 1.*

Thank you for your responses