Great question. Let's use a hypothetical set of variables:

You have the Independent variable: grades

You have a mediator: self-esteem

You have a dependent variable: happiness

The effects of your independent variable on the mediator (you called this Path A), establishes that grades impact self esteem...cool, but that's probably not your theory.

The effects of your mediator on your dependent variable (you called this Path B), is the mediated effect, and it was significant...

You also found that the direct effect of grades on happiness was insignificant, there was an effect of your IV on or DV but only through your mediator.... Using the example, the effect of self esteem (induced by higher grades) increases happiness...but higher grades alone doesn't increase happiness.

So, what does this now mean?

Without the mediation analysis, you'd probably run a OLS regression. You'd probably include both grades and self esteem in the model. And, people would object because of the correlation between grades and self esteem...and your analysis would be weak sauce.

By conducting the mediation analysis, you observed the effects of grades on self-esteem, and found how much the self-esteem (induced by higher grades) affected happiness. The causal pathway you established is more credible, and the analysis is stronger...Since there's no direct effect, make sure your theory isn't that grades increase happiness. Instead, increased self esteem (stemming from higher grades) increases happiness.

Is there a mediation going on or not?

Yes, you found that academic success increases self esteem and the success induced self esteem increases happiness. And, you found that there is no direct effect of grades on happiness....hypothetically.

Cheers,

Ant

Thank you! This is a very clear explanation.

Cheers.

I am not sure Anthony's answer is correct. Can you please provide an output of your results?

Hi Rainer,

Thanks for being willing to help. I do not have the data set or the full output in front of me, just how it has been reported to me. So this is what I have to go on:

Direct effect of x on y: b=-0.16, se=0.12, p=.168

Total effect: b=-0.20, se=012, p=.096

Indirect effect: b=-0.02, boot se=0.03, CI [-0.12; 0.01]

but...

Direct effect of x on m: b=0.33, se=0.23, p

I think we have some problems with the terminology here. You are using the term "direct" effect not clearly. Typically, and according to Hayes the effect total effect (simple regression) x --> y = c. x --> m = a (simple regression), m --> y = b (regression weight, when x is also in the model!), direct effect x --> y = c' (regression weight, when m is also in the model), and the indirect effect of x --> = a*b = c - c'.

But your numbers somehow do not add up?! 0.16 + 0.02 does not add up to 0.2, nor is 0.33*0.11 equal to 0.2.

Thanks for pointing that out! I am clearly not an expert on Hayes' PROCESS. I have done mediation analyses in the past, but using the "old" Barron & Kenny approach, which would have ended any and all discussion of a possible mediation the moment the direct effect is not found. I also have some limited experience with PROCESS, but have never come across this type of a situation.

To give you a bit of a context, I am supposed to provide feedback on the interpretation of the results that were reported to me as I wrote them in the previous message. I am aware that the numbers do not add up. That is why I originally posted the question as a hypothetical, as I do not know what to generally do in situations in which the a and b path are the only ones reported as significant, and all the others are non-significant.

You cannot solely infer from the a and b paths (even if they are significant, respectivel) that the indirect effect a*b is also significant. There are several ways to test it, e.g. Sobel and Aioran test or bootstrapping the standard error of the indirect effect. The former two have the problem that they rely on the normality assumption for the standard error, which is often not the case for products of regression coefficients, and thats why today bootstrapping is the preferred option.

If the numbers do not add up, i would not trust the results. If you have no significant indirect effect, imho there is no evidence in the data to conclude a mediating effect (if the reported indirect effect of .02 is correct, the CI clearly indicates that zero is within the range of the CI).

My guess for the wrong numbers (and my initial statement about the terminology): I think the two reported "direct effects" x on m and m on y are both the bivariate regression weights, but for the indirect effect you need the regression coeffcient of m on y, when x is also in the model. Therefore, I think the reported b=.11 is wrong and should be much smaller and around 0.061 and possibly not significant.

Regarding PROCESS: this is not a method to do mediation! PROCESS is just a tool to conduct mediation this way.