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I have a system where one property (delay) depends on its components, a valve $V$ and the piping $P$ in a hydraulic system: $d = f(V, P)$

I have reference measurements with one type of valve and piping: $d_1 = f(V, P_1)$. These measurements have some scatter, mainly due to the valve $V$, there is some inevitable production variation that influences performance. From these measurements I have average and standard deviation, I could also get the raw data to compute something else.

I now have a different piping $P_2$, and corresponding measurements $d_2 = f(V, P_2)$. How can I reliable compare these measurements to the reference $d_1$? So if I measure a smaller average delay, how can I be sure that it is because of the new piping and not just that I got lucky and the valves that I use now are slightly faster than the ones used for the reference measurement? (The valves used for the reference measurement are not available anymore)

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  • $\begingroup$ I think your concern is quite justified. But if you just have observations on the effect of pairs $(V,P_i)$ acting together, no statistic in the world can disentangle this. There are methods to disentangle the factors, but they all need data, which you do not seem to have. So, the only thing left is "prior knowledge". From your experience, is it possible/likely that valves are very different, and may they have sufficiently strong impact on the delay? If no, you can do some kind of t-test. If yes, you need to get new data. $\endgroup$
    – g g
    Commented Jul 16 at 6:31
  • $\begingroup$ Thanks g g , I'm afraid that I can't just disregard the effect of the valve and I need more measurements to assess the effect of the valves as well ... $\endgroup$
    – Ken Grimes
    Commented Jul 16 at 9:53
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    $\begingroup$ If you have not already done so have a look at design of experiments first so that you collect your data in the most efficient way. $\endgroup$
    – g g
    Commented Jul 16 at 11:55
  • $\begingroup$ You might look into generalizability theory. $\endgroup$
    – rolando2
    Commented Jul 19 at 12:46

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As long as there it no bias in the selection of the valves that you expect could favor $P_1$ or $P_2$, you can use any standard comparison of the two distributions. The default choice would be the the Welch t-Test as long as the data is almost Gaussian. If you have very non-gaussian data, then I would use a non-parametric test, but I'm not sure what would be the appropriate one in your case.

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  • $\begingroup$ Thanks Guillaume for the answer. Simply using a t-Test sound for me like disregarding the influence of the valve, which I'm afraid I can't do $\endgroup$
    – Ken Grimes
    Commented Jul 15 at 11:21
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    $\begingroup$ If the question is: "which pipe is better" then the Welch test can give you an answer for that. If the question is: "how do the valves impact the delay", then you need some form of regression model. $\endgroup$
    – Guillaume Dehaene
    Commented Jul 15 at 11:47
  • $\begingroup$ Thanks Gillaume, I'm afraid that you're right and I need more measurements to assess the effect of the valves as well ... $\endgroup$
    – Ken Grimes
    Commented Jul 16 at 9:52

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