Do I need to worry about normality, if the DV is a 1-item 10point likert scale ?

#1
Dear all,

I hope you can help me with the following question

My design was a 2 x 2 with a single item measuring responsibility on a 10 point scale as my dv.

However, my data is not normally distributed, and a number of standard transformations did not seem to help out here. That's why I was looking at non-parametric alternatives.

I came across the ANOVA on ranks as a viable option. Here you rank your data and then redo the standard ANOVA. This approach is considered to be quite robust against all kinds of data violations.

However, now I think of it, my DV is already a 10-point ranked (ordinal) variable. Does that mean I do not need to worry about normality in this scenario?

Thanks for the information!
 

noetsi

Fortran must die
#2
In both regression and ANOVA it is the normality of the residuals that matter not the individual variables. You should run a QQ plot of the residuals to see if you have a problem before you do non-parametrics.
 
#3
Thanks for the quick response! I checked the residuals, and these are indeed not normally distributed.

So I have a 1-item dv, with a range from 1-10, that is not normally distributed. None of the standard transformations seem to help. An anova on ranks does not seem logical considering the dv is ordinal.

Thx for helping!
 

noetsi

Fortran must die
#4
One reason it might not be normal is that with only 10 levels an assumption of normality, that there is no limit to the range of the data and in practice that you have many levels is violated.

If no transformations work you might consider collapsing your DV into 2 levels and run logistic regression which does not assume normality. Or into a few levels (say 5) and run ordered logistic regression which also does not assume normality.