Normal distribution necessary to assess moderating and mediating effects?

• Is linear regression only suitable for variables with a normal
distribution?
• If so, is there an alternative nonparametric test to test mediation or moderation?

For those not familiar with the language, moderation and mediation were both discussed in Barron and Kenny's influential article (free pdf).

Mediation

With regards to mediation, bootstrapping is often used where normality does not seem like a reasonable assumption.

Moderation

With regard to moderator regression, you could also explore bootstrapping options if you were concerned with the accuracy of the p-values you were obtaining.

• Thanks! I now have been able to perform the preacher and hayes test for mediation. I am not sure about the output though..I understand that ´boot´ is the estimation of the indirect effect, but is there also a significance p of this?
– user3119
Feb 10 '11 at 21:18
• Hi Renee, you might want to ask a separate question about interpretation of bootstrapping for mediation. However, as a simple rule that is often applied, if the bootstrapped 95% confidence interval of the indirect effect does not include zero, then the indirect effect is deemed to be statistically significant. Preacher and Hayes (2004) explains this in great detail: comm.ohio-state.edu/ahayes/BRMIC2004.pdf Feb 11 '11 at 1:20
• The last thing I am wondering about is what macro or test I can perform to assess moderation for non normal distributions. You mentioned bootstrapping, but I don´t know where to find it in SPSS or find a specific macro for that. It is very straightforward moderation I am looking for: 1 independent variable, 1 moderator and 1 dependent variable
– user3119
Feb 11 '11 at 8:00
• re moderation, check out this discussion on Preacher and Hayes' facebook page: facebook.com/topic.php?uid=44574520333&topic=15855 ; otherwise SPSS does have some bootstrapping support in the more recent versions, but I haven't tried it. Feb 11 '11 at 10:53

Many of us use linear regression in rough-and-ready fashion to learn about the relative importance of predictors, to assess the shape of relationships, and so on. But if one wants to make strict probabilistic inferences one needs to satisfy the set of standard assumptions entailed in such regression. The most important of these are random sampling and independent observations. Another one is that the regression residuals (not any particular X or Y variable) should be normally distributed. Without satisfying all of the standard assumptions, one cannot vouch for the accuracy of standard errors or p-values.