Question on the merits of mediation analysis Vs another analysis (described within)


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I have a dataset involving an intervention (placebo versus real) - denoted as X, an outcome (Y), and a physiological variable (M) that I hypothesised would mediate the effect of X on Y.

I have shown that X did not significantly affect Y (as assessed using simple linear regression), but X significantly predicted M, and M, in turn, significantly predicted Y -- which based on the test of 'joint significance' provides evidence that M mediates the effect of X on Y. (MacKinnon et al., 2002).

Please note that I am aware of the debate about whether test of joint significance is sufficient evidence for mediation - with some arguing the you need to demonstrate that 95% of the bootstrapped distribution of the product of path a and path b does not overlap zero. However this is not the focus of my question.

My question pertains to whether there are any merits (in terms of rigour and inferences that can be made) to the mediation analysis described above compared to the analysis described below:

First I need to point out that it was a within subjects design. All subjects received both levels of the intervention (real and placebo) during two different testing sessions. During each testing session the physiological index and performance on the outcome measure were obtained following the administer of the intervention.

Analysis: Difference scores were obtained for values of the physiological index (Real - Placebo) and outcome measure (Real - Placebo). And a pearson's r correlation demonstrated a significant association between the difference scores.

Ideally I would like to try and build an argument for the merits of the mediation analysis over this correlation approach (which has been used more widely in the literature). But my intuition is that the diffscore sufficiently accounts for the effect of intervention (X) on M and Y, and that the mediation analysis isn't any more informative than the lateral analysis aside from perhaps being a bit more elegant.

I would greatly appreciate a stats experts input on this.

Many thanks in advance

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