When fitting data with regression, in many cases your main objective may be to compare the fits of different models, or to ask if an experimental intervention changed a parameter.

On the Compare tab of the Nonlinear regression dialog, Prism offers four choices:

For each data set, which of two equations (models) fits best?

Compare the fit of two models, taking into account differences in the number of parameters to be fit. Most often, you will want to compare two related equations. Comparing the fits of two unrelated equations is rarely helpful.

Example: Compare a one-phase exponential decay with a two-phase exponential decay.

Do the best-fit values of selected unshared parameters differ between data sets?

Compare the fit when the selected parameter(s) are shared among all datasets with the fit when those parameter(s) are fit individually to each dataset.

If you pick one parameter, you are asking whether the best-fit value of that one parameter differs among datasets.

If you pick all the parameters, you are asking whether a single curve adequately fits all the data points, or if you get a better fit with individual curves for each dataset.

Example: Fit a family of dose-response curves and compare the fit when the slope factor (Hill slope) is shared with the fit when each curve is fit individually. This is a way to test whether the curves are parallel.

For each dataset, does the best-fit value of a parameter differ from a theoretical value?

You may have theoretical reasons to believe that a parameter will have a certain value (often 0.0, 100, or 1.0). Compare the fit when the parameter is constrained to that value with the unconstrained fit.

Example: Test if a Hill Slope differs from 1.0 (a standard value).

Does one curve adequately fit all data sets?

This choice compares the fits of separate curves to each data set with the fit of a single curve fit to all the data sets. It asks whether there is evidence that the treatments did anything to shift the curves.

This choice is identical to choosing  "Do the best-fit values of selected unshared parameters differ between data sets?" and then selecting all the  parameters.