Quantitative way to compare theoretical values to experimental values

[Whiteblooded]

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?..

 

[Vanadium 50]

It sounds like you are looking for a chi-squared test.

 

[Chestermiller]

You can scale either by the maximum sag, or by the area averaged sag. This will give you a much better shot at comparing the shapes. I would also recommend an area weighted square deviation, divided by the area (in case you are not using equal areas for the elements of surface). The big question is "why don't the predictions and observations match quantitatively." Another question would be "why would there be different theoretical model predictions to the same problem?"