# Comparison of two curves

I have two measurements of something. You can think of them both as their own curve with known error on each point. They look quite similar, and if I calculate the R2 value it comes out to >0.9. But what I want to be able to calculate is a P value comparing these two curves (i.e., what is the probability that the difference i'm looking at is just due to noise?). Now I could easily do a student t-test at each point and come up with a P-value at each point, sure. But is there some way to come up with an over-all P value that uses all the points and not just one? Thanks very much for any help.

• This question appears to be off-topic because it is about statistics and thus belongs on Cross Validated. – Thomas Oct 23 '13 at 8:39
• It sounds like you have a pair of calibration curves generated by two different methods. If that is correct then you might want to look at the fixed and proportional bias in the measurements using the least products regression method detailed in this paper: molecularlab.it/public/data/TMax/… – Michael Lew - reinstate Monica Feb 3 '14 at 4:52

• To me, it seems that the connection is obvious, and frankly I am surprised that I should explain it. OK. Let actual values for curve 1 be $y_1$, ..., $y_N$, and for curve 2 be $z_1$, ... $z_N$ . Let observed values be $\hat y_1$ , ... , $\hat y_N$ for curve 1 and $\hat z_1$ , ... , $\hat z_N$ for curve 2. Let $d_i=y_i-z_i$, $\hat d_i=\hat y_i-\hat z_i$. The author wants to test the hypothesis that $d_i=0$ for all i. But $\hat d_i=d_i+(\hat y_i-y_i)-(\hat z_i-z_i)$ – user31264 Nov 4 '13 at 4:36