# Normal distribution in multiple mediation?

I wonder if someone can help me. I'm running a multiple mediation (parallel model) using the preacher and hayes process script. I am no expert but it seems to be that the $a$ paths (IV to mediators) are essentially correlations, whilst the $b$ paths (mediators to DV controlling for the IV) are essentially a linear regression. I have checked this using correlations/linear regressions and the coefficients obtained are identical.

The snag in my data is that the dependent variable has a number of outliers and is not normally distributed. When running the simple regression it is only when my data is transformed and the outliers are removed that I meet the assumption of normality (of my residuals). What I am wondering, therefore, is whether I should be transforming this data (just the dependent variable, as I know there is no assumption of normality across $a*b$) before I run my multiple mediation? I believe that because it is based on bootstrapping these assumptions are not required, but the results obtained with the raw data (full mediation) are very different to the transformed/outliers removed data (akin to 'partial' mediation).

Question: Given this I am wondering what is most appropriate to use, the raw data or the transformed/cleaned data?

Background: The outliers are falling about 3-4 standard deviations above the mean and the overall data pattern is that the majority of people are good on the task (hence the negatively skewed distribution). And @gammer you are absolutely right the model we are using is $X \to M \to Y$ with 8 mediators (so 8 M's). We initially ran this as a multiple regression (hence why I had transformed my data to meet the assumptions of normality of residuals/removal of outliers) but I am now unsure whether to use normalised/raw data for my multiple mediation. All advice much appreciated.

• You need to explain what you are calling outliers. Also I do not know what you mean by mediation. – Michael R. Chernick Mar 28 '17 at 12:09
• @MichaelChernick, mediation analysis is when you you're trying estimate how a variable acts as an intermediary between the predictor and the outcome ( x --> M --> y ). This classically comes up in the context of determining the pathway through which a treatment is effective. These kinds of models are very common in the social sciences. You don't need to respond if you don't have any knowledge of what the OP is talking about. – gammer Mar 28 '17 at 12:49
• The outliers are falling about 3-4 standard deviations above the mean and the overall data pattern is that the majority of people are good on the task (hence the negatively skewed distribution). And @gammer you are absolutely right the model we are using is X -> M -> Y with 8 mediators (so 8 M's). We initially ran this as a multiple regression (hence why I had transformed my data to meet the assumptions of normality of residuals/removal of outliers) but I am now unsure whether to use normalised/raw data for my multiple mediation. All advice much appreciated. – JennyM Mar 28 '17 at 12:54