Total-effect Test May Erroneously Reject So-called "Full" or "Complete" Mediation

The procedure for establishing mediation, i.e., determining that an independent variable $X$ affects a dependent variable $Y$ through some mediator M, has been under debate. The classic causal steps require that a ``total effect'' be significant, now also known as statistically acknowledged. It has been shown that the total-effect test can erroneously reject competitive mediation and is superfluous for establishing complementary mediation. Little is known about the last type, indirect-only mediation, aka ``full" or ``complete" mediation, in which the indirect (ab) path passes the statistical partition test while the direct-and-remainder (d) path fails. This study 1) provides proof that the total-effect test can erroneously reject indirect-only mediation, including both sub-types, assuming least square estimation (LSE) F-test or Sobel test; 2) provides a simulation to duplicate the mathematical proofs and extend the conclusion to LAD-Z test; 3) provides two real-data examples, one for each sub-type, to illustrate the mathematical conclusion; 4) in view of the mathematical findings, proposes to revisit concepts, theories, and techniques of mediation analysis and other causal dissection analyses, and showcase a more comprehensive alternative, process-and-product analysis (PAPA).