In a mediation analysis, after establishing that the pairwise correlations are significant among the independent variable (X), the mediator (M) and the dependent variable (Y), what must occur in the final step to demonstrate that M is a significant full mediator of the relationship between X and Y?

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In mediation analysis, after establishing significant correlations among X, M, and Y, the key test for mediation quality lies in the behavior of the direct effect when the mediator is included in the model.
Option 1: 'The total effect of X on Y is greater than the direct effect.' While you may observe that the total effect can be larger than the direct effect due to the indirect pathway through M, this alone does not demonstrate full mediation; the distinction between total and direct effects is informative but not the definitive criterion for full mediation.
Option 2: 'All relationships tested in the last step remain significant.' This statement would indicate that the relationships persist even after including M, suggesting partial mediation at best. Full mediation requires the direct path to lose significance, not merely remain significant.
Option 3: 'The correlation between X and M is larger than between X and Y.' The relative magnitudes of the correlations tell us about associations but do not establish the mediating mechanism. A larger X-M correlation does not by itself prove that M transmits the effect from X to Y.
Option 4: 'The direct effect of X on Y becomes nonsignificant when M is included in the model.' This criterion is the classic definition of full (complete) mediation: once M accounts for the pathway, X no longer has a direct influence on Y independent of M. It reflects the idea that the effect of X on Y operates entirely through M, satisfying the standard test for full mediation.

To summarize, the crucial diagnostic for full mediation is the disappearance (becoming nonsignificant) of the direct X→Y path after introducing the mediator M, rather than reliance on broader comparisons of effect sizes, persistence of significance in all paths, or simple differences in X–M versus X–Y correlations. Each of the other statements either describes a different scenario (partial mediation) or misstates what the data imply about the mediating process.

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In a mediation analysis, after establishing that the pairwise correlations are significant among the independent variable (X), the mediator (M) and the dependent variable (Y), what must occur in the final step to demonstrate that M is a significant full mediator of the relationship between X and Y?

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