I have two sets of data with Y's linearly dependent on X's. I am trying to determine if the two sets of data are the same line or not. I've looked at literature and there are 2 ways to do this. 1. Compare the slopes and see if they are equal; then compare the intercepts and see if they are equal. Using the t-test to determine if the slopes and intercepts are equal. If both the slopes and intercepts are equal the lines are coincident.
2. Create a single model and with a dummy variable (Z) where Z = 1 for the first data set and Z = 0 for the second data set. Which would give y = a + bX +cZ + dXZ. Where a, b,c, d are coefficients, X is the independent variable, and Z is the dummy variable. You then perform a multiple partial F-test to determine if the lines are coincident by comparing the model with the Z and XZ terms to the model without those terms.
Is there an easy way to do either of these tests with the JMP software? So far I have fit a model with X, Z, and XZ (with the center polynomials checked). Looking at the effects tests the Z has an F ratio of 31 and Prob > F is <0.0001. The X*Z has an F ratio of 0.3178 and Prob > F is 0.5765. I am using 0.05 significance level with 21 and 18 degrees of freedom for the 2 sets of data.
I think you are on the right track using Analysis of Covariance. Your result indicates that the slopes do not differ significantly (XZ-term) but the levels ("intercept") differ between the two data sets (Z-term).
In JMP you do not need to explicitly create a 0/1 dummy variable to do this. You can just have a nominal variable with the name or ID of the two data sets.
See example under "Analysis of Covariance with Separate Slopes" in Chapter 12 in the manual (JMP Stat Graph Guide, page 250 for JMP 8)