Dear Sahiba / Apeksha
Regrets for the delay. I was struck in office work.
Moreover, I was wondering how to reply this as it needs a lot of typing :-(
Anyway, let me try. You shd also read it very patiently.
The story of mediation in social sciences starts somewhere from 1920-30s when physical sciences were at the boom and social scientists were trying to get the same status by claiming their area of study also as science, where we've procedure which on repeat experiments gave similar results.
Now this concept of Mediation was popularized by Barron & Kenny. Their approach was so simple and easy to understand. This is the reason that this approach was prevalent from 1980 to 2010 (30 Yrs). This conceptualized about the 4 type of results:
Step-1 Initial relation between X (IDV) and Y (DV) without Mediator (M)
2 possibilities: Sig relation or No Sig relation.
Step-2 Relation between X & M and M & Y
This step determined the presence or Absence of Mediation.
If both relations are significant-Any sort of medication present.
If any of the 2 relations is not sig, then No Mediation
If Sig relation in Step-1 then it'll be No mediation, Direct relation.
If No Sig relation in Step-1 then it'll be No mediation, No relation.
Step-3 Relation of X (IDV) and Y (DV) in the presence of Mediator (M)
This step determined the presence or type of Mediation.
Now there are 4 possibilities:
a) If Sig relation between X & Y in Step-1 and the No sig relation between X & Y now, it's Full Mediation.
b) If Sig relation between X & Y in Step-1 and the now too there is sig relation between X & Y, it's Partial Mediation.
c) If No Sig relation between X & Y in Step-1 and the now there is sig relation between X & Y, it's Indirect Effect (through the mediator).
d) If No Sig relation between X & Y in Step-1 and the now too there is no sig relation between X & Y, it's No Mediation No Relation.
These are the cases explained by Prof Gaskin (in the ppt refered by Sahiba).
Now after the year 2000, a lot of people started criticized Baron & Kenny approach for its flaws, the biggest of them was that two direct effects (between X & M and M & Y) do not constitute an indirect effect between X & Y. Prof Hayes criticized it to max and gave his Macro- Process.
Likewise, Prof Hair etc too criticized that.
Prof Hair says if there is no relation between X & Y (in the absence of Mediator) then there can't be any mediation possible.
So now mediation is only of 2 types: Partial and Full. Steps are the same 3 but the 2nd step is to check the Indirect effect (rather than checking 2 direct relations of X & M and M & Y).
The Sobel test is basically a specialized t test that provides a method to determine whether the reduction in the effect of the independent variable, after including the mediator in the model, is a significant reduction and therefore whether the mediation effect is statistically significant.
But now we do not need this test as Process, AMOS and Smart PLS, all provide calculations for this test.
Hope this will make the concepts somewhat clear.
Best wishes
Later this approach was