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)),
• I'm using the fitting procedure from lmfit.Model to find the parameters. (why lmfit? The rest of our processing is already in python, and I couldn't get the statsmodels package to handle general model specifications with parameters; but identifying the statistical method is the primary reason for asking)

EDIT: additional context as requested in comment

• Overall aim: the dynamics of the network are for each node in the network to settle into a decision. The individuals can choose from one of two states, and we are interested in the conditions under which:
  • a) the fraction of nodes in network reaching the same state is maximised, and
  • b) how fast this happens.

Form of data: If we label the control experimental group #1 and the treatment group #2, the data looks like:

# time, average fraction of nodes with majority choice, experimental group

60,  0.52, 2
70,  0.53, 2
80,  0.55, 2
90,  0.54, 2
...

1200, 0.92, 2

• The "average fractions to majority choice" are averages across the replicates carried out.

• We have 15 replicates or more per treatment, and the analysis is on data already obtained.

• group #1 has lower average fractions by the end of the experiment (because they don't have the same level of agreement in general).

• The curve following a saturation equation (above) fits the data reasonably well and fits our hypotheses for the underlying dynamics. So we are not looking to select between models.

• However, we do want to say whether the `treatment' makes a difference.

So, the question here is whether difference between the fitted curves is statistically significant. What is the most appropriate way to test this?