I need a reference to justify standardizing non-normal data. I will first explain what I am doing.
I had a survey with ~30 questions. The answers to the questions were numeric; the range of possible answers to these questions all had a minimum of 0 but the maximum was not all the same (for example, the range for some questions was 0-30, for others it was 0-4). I then divided the questions into two separate categories to create 2 scales. The questions were not in equal groupings; one scale has ~20 questions, the other has ~10. For each individual respondent I summed the answers to each question to create a score for each scale. Obviously the maximum possible score was much greater for the scale with ~20 questions than that of the scale with ~10 questions. The distribution of the scores for each scale has a heavy right skew.
I am using these scale in logistic regression. Each scale is being used in a separate model. The scale is the predictor variable of interest and is the only continuous variable, I have several control variables that are all either binary or categorical "dummy" variables and are the same in each model. Both models have the same dependent variable, in other words, both models are being used to predict the odds of the same event occurring.
I have chosen to standardize these scales in the usual way ((x-mean)/sd) so that when I draw conclusions about the models, I can say something along the lines of "for a 1 unit change in scale A, holding all other variables constant, there was a such and such change in odds of event Y, whereas for a 1 unit change in scale B, again holding all other variables constant, there was a such and such change in odds of event Y."
I have read conflicting reports on whether it is acceptable (by acceptable I mean that when I submit my paper for publication, the reviewers will accept my methods as legitimate) to standardize non-normally distributed variables. What I have been scouring the search engines, databases, and online texts for is a solid reference (could be a book or a published paper) that supports my decision of standardizing a non-normal variable. I have not had much luck and would very appreciative if anyone has suggestions for articles or texts that would help me achieve my goal.