I understand that in correlational studies it is fine to conclude that M mediates the association between X and Y even if the total effect (c) is not significant (Hayes, 2013) Does the same logic appliy when it comes to experimental designs? My experimental manipulation had significant effects on M, but not on Y. When I make a model, it works fine and bootstrapping shows that mediation exists. Can I conclude that experimental manipulation did not direct effects on Y, but it had indirect effects through M? Thank you!
Perfect mediation is defined when the effect from X to Y is entirely explained by the effect of X on M, so that a unit change in X results to a change in M, which in turn results to a change in Y. So, in the prototypical example, you start off with a substantial effect of X on Y, and examine if this is reduced or even eliminated when M is introduced. Thus what is compared is the effect of X on Y in two models: one with and one without M. If the coefficient is decreased there is mediation. If it is eliminated there is perfect mediation.
Statistical significance comes into play because you are estimating these effects from samples instead of the population. Thus the effects are interpreted as estimates: the effect from X to Y is a sample estimate of the population effect in the original model, the effects from X to M and from M to Y are sample estimates in the mediation model, and the direct effect from X to Y is a sample estimate in the mediation model. Then, instead of 'the effect becoming zero' we speak of 'the effect becoming non significant', i.e. its estimate value can come from a population with a zero effect, for 95% of all possible samples of this size.
So, the steps are:
a) Establish that there is a substantial effect from X to Y, without M. b) Introduce M in the model. c) Compare the effect from X to Y in the two models, before and after introduction of M.
In 'significance' terms, if the effect from X to Y is initially 'significant' and becomes 'non-significant' after introducing M, you have mediation. (But perhaps this is a more slippery version of the interpretation given above.)
If there is no substantial effect form X to Y to start with, perhaps a mediation model is not what fits the situation, conceptually.