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.
Define error as the difference between real and observed value.
Suppose your errors at different points are independent and normally distributed (i.e. no systematic error).
If you know the standard deviation of each error, you also know the standard deviation of difference between the value at two curves. Now you have the vector of differences, with known standard deviation of each difference. Divide each difference by its standard deviation, and you have vector of normalized values with standard deviation of 1 each. The null hypothesis is that they are distributed as N(0,1). Test it with any normality test.