I guess this is the kind of question extremely hard to Google if you're lacking just the right word.
My situation is: I have some experimental data points, and I have two models: the "simple model" (null hypothesis, H0) and the more complex model (H1), with two more degrees of freedom. I try and fit each model separately to my data, and to assess how good the fit is, I compute a chi2 goodness-of-fit test.
I notice that chi2(H0) > chi2(H1), and I want to compute the p-value (a 3-sigmas significance allowing me to reject H0).
A colleague tells me that I can compute
chi2' = chi2(H0) - chi2(H1) and the corresponding degrees of freedom:
ndof' = ndof(H1) - ndof(H0) = 2. And then, I can integrate the chi2 distribution (with 2 d.o.f.) from
chi2' to infinity, which yields the p-value. The colleague says that taking the difference of chi2 values "comes from some theorem", which they ofc cannot find.
So far I have failed to find references to such method (nor help from anyone knowledgeable in statistics). Is that the right way of computing the significance?
If not, what would be a correct way of assessing by how much H1 is favoured over H0 ?