Just wanted to update the community: YES you can have a significant indirect effect (aka: mediation) if only one of the paths (a or b) are significant. The significant indirect effect is the a-path multiplied by the b-path. So regardless of whether one of the individual paths is insignificant, the indirect effect can be significant. 

"Introduction to Mediation, Moderation, and Conditional Process Analysis : A Regression-Based Approach" by Andrew F. Hayes. Page 92 in Chapter 4. 

If you apply the out-of-date Baron & Kenny's Causal Steps approach, it is not possible because you stop the analysis when "a" is not statistically significant.. But, since you mentioned about the significance of the indirect effect effect, you must not have employed Casual Steps. In modern methods, especially the ones that use bootstrapping, you can have statistically significant indirect effect even when one (or both) of the pathways that define the indirect effect is non-significant. 

Crystal -

This is not exactly my area, but if you are using the word "significance" in relation to p-values, please note that  p-value and "significance" represent incomplete information which is very often misleading and/or misunderstood.  Standard errors are likely less misunderstood, but note that both standard errors and p-values are functions of sample size, and change accordingly. 

Often in statistics, a researcher might want a statistic to give her/him a yes or no answer, when in reality everything is generally more of a matter of degree.  How close are you to one specific hypothesis are you as opposed to another?  Not, Is this hypothesis correct?  (No. Not exactly. Not ever.)  Not generally, Is there heteroscedasticity?  But, How much heteroscedasticity is there ... to some level of 'certainty'.  Not Does this model fit? But How well does it appear to fit.  (A la George Box:  Is your model useful?  It will never be 'exactly right.')

In many, perhaps virtually all cases, you are probably better expending your effort, if you have good test data, comparing alternative models/procedures, perhaps ones suggested by logic and subject matter expertise,  to see which alternative(s) appears best supported by your data, but also being aware that spurious results sometimes occur. 

Best wishes - Jim

This image can give you an easy approach to understand the mediation (Partial and Full)...moreover, you can view full presentation in the following web-page:

http://slideplayer.com/slide/5738913/

Just wanted to update the community: YES you can have a significant indirect effect (aka: mediation) if only one of the paths (a or b) are significant. The significant indirect effect is the a-path multiplied by the b-path. So regardless of whether one of the individual paths is insignificant, the indirect effect can be significant. 

"Introduction to Mediation, Moderation, and Conditional Process Analysis : A Regression-Based Approach" by Andrew F. Hayes. Page 92 in Chapter 4. 

Hi Crystal,

I'm in this same situation. Neither path a, direct effect or total effect are significant but path b and indirect effect ab are significant in my results. According to your own answer and to Hayes book, I see that you can claim mediation. But... how can you interpret the results? How can you explain that mediation exists when path a or path b are not significant?

Any help would be appreciated.

Thanks!

I am in a similar situation and the question is, " how can we interpret such mediation results?"

For those using the newly released 2018 edition of "Introduction to Mediation, Moderation, and Conditional Process Analysis : A Regression-Based Approach" by Andrew F. Hayes, this information now appears on page 116.

Just to make sure (I can´t access Hayes´ book at the moment) : So I can report a significant mediation as long as the indirect effect is significant, regardless of the fact that I have one path (e.g. Path a ) that is not significant. Did I understand the matter correctly?

Thanks in advance!

Short answer: yes.

Long answer: really depends on what your hypotheses are and what it is you're trying to investigate with the analysis and the like.

Should mediation analysis be conducted if a direct relationship is insignificant? My IV and DV has an insignificant relationship. Should I proceed with the mediation? Mediation provides a highly significant indirect relationship. Any source which can justify this will be highly appreciated.

Agha Agha

You can use the paper from Rucker et al. (2011). Mediation analysis in social psychology. Article Mediation Analysis in Social Psychology: Current Practices a...

Can i have significant relationship but VAF shows no mediation. How to interpret?

eg. significant at 0.011, but VAF is only 17%?

I am conducting a more complex study. I want to test if there's a mediation effect of two independent variables (congruence) on an outcome variable. Although, my congruence hypothesis to the outcome variable, and also to the mediator variable, path a, b, c is non-significant.

In general, most books and papers only talk about mediation for linear relationships. Please does anyone have a better idea about how to do mediated polynomial regression in SPSS? Or suggest any resource that could help. This would be very appreciated.

Hi all, I am working on a longitudinal high dimensional data, not sure how to test the mediation effect. Any suggestion would be appreciate.

My understanding regarding insignificant paths (i.e., a or b) and mediation effect is the same as Crystal's reply. Hayes (2018: 116): "Statistical significance of a and b are not requirements of mediation by current thinking." [Hayes, A.F. (2018). Introduction to Mediation, Moderation, and Conditional Process Analysis. The Guildford Press. New York. London.