The replicates test

When evaluating a nonlinear fit, one question you might ask is whether the curve is 'too far' from the points. The answer, of course, is another question: Too far compared to what? If you have collected one Y value at each X value, you can't really answer that question (except by referring to other similar experiments). But if you have collected replicate Y values at each X, then you can ask whether the average distance of the points from the curve is 'too far' compared to the scatter among replicates.

Prism 5 and later does this calculation as part of nonlinear regression. Choose the replicates test in the Diagnostics tab. You can fit a linear model with Prism's nonlinear regression analysis, so the replicates test works with linear data too.

Prism does the calculations correctly, but the details in the Prism 5 Help  were incorrect in explaining the DF values.

Here is the correct explanation of how the df are computed:

• The degrees of freedom of the numerator (SD lack or fit) of the F ratio is number of X values minus the number of parameters fit.
• The degrees of freedom of the denominator (SD replicates, or 'pure error') of the F ratio equals the total number of data points minus the number of X values.

Prism 5 does the calculations correctly. The only error was in the description of the method in the Prism help. 

This Prism file shows an example from Draper and Smith. Prism reports the same results as shown in the text. The relevant pages of the text are shown on layout pages of this file.