I used a -4 to +4 Likert scale in one set of questionnaires and -3 to +3 for the same questionnaires, but gathered respondents in a different way. I want to rescale from -4 to +4 down to -3 to +3 for the second group.
How do I do this and secondly is there a referenced/accepted procedure for doing this?
Best Answer
Rescaling the variable as if it were continuous is easy enough. If it's centered on zero and the end points represent real extremes you can just just scale something like:
$$X_{SCALED} = X_{ORIG} \times MAX_{SCALED}/MAX_{ORIG}$$
That said, as was suggested in the answer to the other question linked in the comment above, scaling Likert scales is, for substantive reasons, not a great idea. Simple scaling with you result in non-integer answers which are impossible on either scale and might distort the substantive meaning that comes from scales where numbers represent real statements (e.g., 2 means "somewhat satisfied" while 0 means "neutral").
I'm generally hesitant to treat Likert scales as continuous in the first place. Look carefully at the distribution of answers on your two different scales to get a sense of any distortion that you have. It may make more substantive sense to do something other than scaling (i.e., collapsing categories in one or more of the scales and then comparing the variables as categorical).