What type of statistical test to use on ordered (e.g., time or position) observations? I have 2 samples where one is using water as treatment (in black) and one using a test treatment (teal).  The x axis is position on a gene and y axis is the coverage which is basically the number of times that region had a hit on the detecter.
Is there a statistical test I can use to say the test treatment has higher or lower coverage than the water treatment?  I guess a t-test or wilcoxon could technically work but it's not incorporating the position information which I think is important.
Also, is there a way to incorporate segments? For example, is the (mean/median) "coverage" on region X to Y significantly different between the 2 samples compared to the other regions?
Are there any tests that come to mind when looking at this type of data? These types of plots remind me of time series data so I feel that tests used on time series data would be applicable here.

 A: You say "I guess a t-test or wilcoxon could technically work but it's not incorporating the position information which I think is important". Why do you believe position is important? Does the position on the gene actually affect the means by which you are measuring coverage? In other words, does the fact that (arbitrary) position 200 has 10 coverage have any impact on whether position 201 has, e.g., 9 coverage? Or is it possible for bp 201 to have 1 coverage while position 200 has 100 coverage given the general trends we're seeing here? In other words, are the coverages of individual base pairs independently and identically distributed? Even if there is a dependency, you only lose power by treating them as independent, but won't increase your risk of Type 1 errors.
I am noticing some error bars on your plot. What do they represent? 2*Standard error? If so, then the statistics are being done for you. Base pairs around positions 420 and 720 have non-overlapping error bars between conditions, and are hence statistically different if these are indeed standard error bars plotted.
It appears you should also be concerned with correction for multiple comparison since each base pair is a separate (hopefully independent) statistical test. False discovery rate (FDR) is a well enough correction if you have the p-values, or you can construct the p-values from the (presumably average) coverage values and their standard errors at each base pair.
