How should I perform a statistical comparison between the model fitting results on two separate datasets? The same model is applied to both sets, but the data are from two conditions, e.g. control and treatment.

I read that I need an F-test. But the formula for the F statistic (from wikipedia),

$$ F = \frac{\frac{RSS_1 - RSS_2}{p_2-p_1}}{\frac{RSS_2}{n-p_2-1}} $$ with $p$ as the number of parameters in a model and $RSS$ as the sum of residuals.

But in this formula, the models are the same, so $p_2 - p_1$ = 0, and then the formula isn't valid. So where am I going wrong?

Context:

• My model equation is y = s-(s/((a+x)*b)),
• and I'm using lmfit.Model to find the parameters. The fitting procedure