I have recorded the the rate at which water exits a tank on-site and through a video recording and it looks something like this:

Water Level Flow Rate (On-site) Flow Rate (Video)
0.60 1.70 1.62
0.61 1.43 1.38
0.62 1.50 1.41
... ... ...


I want to know if there is a statistically significant difference in the flow rate measured by the two different methods but I'm not quite sure what is the appropriate test.

I was told to use the kruskal-wallis test, which to my understanding is the wilcoxon rank sum test but for more than two groups. However, in my own opinion, I think the data can be paired so the wilcoxon signed rank test might be more appropriate.

I would like to know which is the correct test to use? Is it the wilcoxon rank sum test, wilcoxon signed rank test or some other test?

  • 1
    $\begingroup$ In the health field there is a literature on comparing two measurements. The archetypal paper was by Bland and Altman and we have a tag for bland-altman-plot which may be helpful to you $\endgroup$
    – mdewey
    Commented Jan 22, 2021 at 14:05

1 Answer 1


What you are really interested in are the differences between both measurement methods at the same water level. You are not interested, whether the mean or the median or the mode or any other measure of "common magnitude" is equal for both types of measurements but you are interested in differences at each water level. Thus the data are paired by water level and of those named in the original post the signed rank test is appropriate.


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