Hi Nicolai -

Does this mean you have categorical data?  So you have taken differences in variance into account, to avoid letting that falsely indicate an outlier, and now you want to know if normality is a consideration, right?  I'm not familiar with your references or bisquare weighting, but have used iterated reweighted least squares to identify the coefficient of heteroscedasticity in regression with continuous data.  But there the estimated residuals are what you would like to be approximately 'normally' distributed, though it is not very crucial, and the data can be from any distribution.  With categories, or ANOVA, the data are already conditionally distributed, y|x, where the x are the categories, so normality of those data is analogous to normality of estimated residuals.  

So, I'm not familiar with what you are doing, and I have generally never paid (much) attention to "normality," and i worked with a lot of highly skewed data, but I'm guessing that maybe you need to consider normality here.  If so, I wonder if it is very crucial?  Perhaps a simulation study, or even just a few changes to your data to see the impact, i.e., study the sensitivity of results to nonnormality, might be of interest to you. 

Cheers - Jim

Hi Jim,

Thanks a lot for your answer. I'm considering continuous data here. Another way to phrase the question is the following: The Pearson correlation coefficient measures the strength of the linear relationship between normally distributed variables, while the Spearman rank correlation method does not assume that the variables are normally distributed. What I'm wondering now is how the robust method relates to these - does it still assume normality, like Pearson?

That's a good suggestion, I could investigate this in some simulations.

Best,

Nicolai