Total-effect test is superfluous for establishing complementary mediation

Mediation, which in social science literature means that an independent variable X affects a dependent variable Y through a mediator M, is a key concept in causal inference. For establishing mediation via data analysis, there is a long debate in the literature on whether we still require the “total effect” of X on Y to be statistically significant, given the significance of both the “mediated effect” and the “direct effect” of X on Y . In the last decade, it has been shown and widely accepted that total-effect test can erroneously reject “indirect-only mediation” and “competitive mediation” and should not be applied to establish mediation of these two types. For “complementary mediation”, however, the situation becomes more complicated and no consensus is reached so far. This article provides an explicit proof that the total effect has to be statistically significant whenever mediated effect and direct effect bear the same sign and are both significant, as long as the least square estimation (LSE) and F-tests are used to estimate and test mediation effects. We also show that the similar result can be obtained when the Sobel test is used in the place of the F-test. Our results support the growing consensus that the total-effect test should be abolished for establishing mediation.