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The procedure for establishing mediation, i.e., determining that anindependent 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 shownthat the total-effect test can erroneously reject competitive mediation and issuperfluous for establishing complementary mediation. Little is known about thelast type, indirect-only mediation, aka "full" or "complete" mediation, inwhich the indirect (ab) path passes the statistical partition test while thedirect-and-remainder (d) path fails. This study 1) provides proof that thetotal-effect test can erroneously reject indirect-only mediation, includingboth sub-types, assuming least square estimation (LSE) F-test or Sobel test; 2)provides a simulation to duplicate the mathematical proofs and extend theconclusion to LAD-Z test; 3) provides two real-data examples, one for eachsub-type, to illustrate the mathematical conclusion; 4) in view of themathematical findings, proposes to revisit concepts, theories, and techniquesof mediation analysis and other causal dissection analyses, and showcase a morecomprehensive alternative, process-and-product analysis (PAPA).

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