ANOVA versus nonlinear fit I have a data set which looks something like this (not real data):
conc   Resp
0      5
0.1    18
0.2    20
0.3    23
0.4    24
0.5    24.5
0      5
0.1    17
..     ..

which happens to fit perfectly to the Michaelis-Menten equation:

Resp = max_value  *  conc / (conc_value_at_half_max + conc)

Even though it is something else entirely importantly, the response increases quickly with "conc" and then reaches a ceiling or max value of sorts. 
Anyway, I want to know how low I can go in "conc" before the value of "Resp" is not significantly lower than the max value. 
Using a simple ANOVA accomplices this nicely, but I was thinking: "should I not be exploiting the fact that the structure of the data is so nicely explained by a known equation?" Is there such a way?
I am using minitab for this because it is easier, but would work in R all the time.
 A: I think you should rethink the question. 
Why would it possibly matter to find the highest concentration where the response is far enough below the maximum plateau to give a P value less than some arbitrary threshold? 
If you added more concentrations, or collected replicate values, or obtained cleaner (smaller experimental error) data, then you'd reach a different conclusion about the largest concentration that gives a response "significantly" less than the plateau. So the answer to that question is partly determined by details of the experimental design that you can change. The answer tells you nothing fundamental about the system. 
As with most questions in statistics, I urge you to set aside the word "significant" and try to articulate the question you want answered in scientific terms. 
A: You could model it using nonlinear least squares regression, then use the modeled values and SE of the fit to determine the conc level that is "different" than the max. Once you fit the model, you could brute force search progressively lower thresholds until you reach a conc where Resp differs by a pre-specified alpha value from the max value and the estimated error around that.
So, fit a nls, then write a for loop to calculate the p values for, say, a t-test comparison, and search that for the critical conc value you're looking for.
