I am looking at the cross-sectional shape of a sagging membrane. I have several theoretical models, neither of which fit perfectly. So rather than comparing values, I'm comparing shapes. One model fits fairly well, however I'm unsure of which quantity is correct to specify a 'goodness' of a model. I'm thinking of some sort of sum of squared deviations (the quantity which least-squared fits minimises). The main problem with this is that the sum of squared deviations on its own will not really tell us about how good the fit is - I think I'll need to divide it by something else?..