I am working with some data that vary along an arbitrary scale of -1 to 1. More specifically, this scale refers to a difference between two scores (with 0 meaning no difference, 1 being the maximum possible difference when A>B, and -1 being the maximum possible difference when B>A)
I think it could be useful to express the observed scores as POMPs (Percent Of Maximum Possible score; Cohen, P., Cohen, J., Aiken, L. S., & West, S. G. (1999). The problem of units and the circumstance for POMP. Multivariate behavioral research, 34(3), 315-346). These scores are easy to calculate through the provided formula
100*[(observed-minimum)/(maximum-minimum)], where maximum/ minimum refers to the boundaries of the scale.
However, I am uncertain whether I should set minimum score = 0 (so score=0 retains the original meaning of no difference and the sign indicates the sign of the difference) or, to the contrary, I should calculate the POMP score considering minimum= -1 (in which case, 0 scores would become 50% of the maximum possible difference).
I thank you in advance for any possible answer