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I have generated a set of ground displacements at certain points using two different methods. I am now trying to find a good method of statistical analysis to compare how similar the results of the two methods are.

I only have two measurements for each point but I have over 1 million different points. Is there a method of analysis that I can use to compare the similarity of the displacement generated by both of the methods at each of the different points which will then allow me to calculate the similarity of the overall data set?

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It sounds like a natural method to analyze your data would be a paired t-test. For each point, you compute the difference $d_i$ between the two measurements, $d_i=x_{i1}-x_{i2}$ where $x_{i1}$ is the measurement using method 1 and $x_{i2}$ is the measurement using method 2. Once you have your 1 million $d_i$'s, you could perform a one sample t-test on the $d_i$'s to see if they are statistically significant from zero (which is almost guaranteed since you have 1 million pairs of points). You could also construct a confidence interval to estimate the mean difference between the two methods. Without more context, it's hard to know what kind of similarity measure would be useful. Perhaps there are magnitudes of discrepancies between the two measurements that would be meaningful? In such a case, it could be interesting to report what proportion of differences are within an interesting absolute range or perhaps measurements that are within some relative percent of the other. You could also report summary measures as simple as what proportion of the time the difference is positive.

Other potentially interesting methods of analysis would be to regress the measurements from method 2 on method 1 to explore the shape of the relationship. Things to look for could that would be relevant include a non-linear relationship or heteroskedasticity. If the relationship appears linear, the correlation could be a nice summary measure of how strongly correlated the two measurements are.

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