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I have a set of paired measurements which were collected before and after some trigger for a set of users. Users can react differently to trigger, i.e for some measurements before trigger are larger than measurements after the trigger, for others it's the opposite, for the some measurements after trigger could be still smaller than measurements before the trigger of other person. I want to show that on average the measurements after trigger will increase. Total amount of measurements is 140. The distribution from which data was sampled is most likely not normal.

On one hand, to prove that I can simply split measurements into two groups 'Before Trigger' and 'After Trigger', and do a t-test to compare means of two groups.

On the other hand, I can take differences for each user separately and perform wilcoxon signed rank (or some other paired test) test on those differences.

Which of the methods is more preferable and why?

Edit added QQ plots, first one for measurements, second one for difference

QQ plot for measurements before and after triggerQQ plot for differences

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This is a classic situation to use a paired test. You're interested in how the users change. Therefore, you examine the changes.

If you don't do this paired, then you're violating an assumption of independence: the "before" and "after" measurements most likely are related.

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  • $\begingroup$ Makes sense, but which paired test would be most suitable for this problem? $\endgroup$ – dmonkoff Aug 27 at 21:33
  • $\begingroup$ That will depend on your data and goal. What shape does your distribution of differences have? What do you want to test? The t-test will be robust to a lot of deviations from normality, particularly if you have a large sample size. $\endgroup$ – Dave Aug 28 at 1:35
  • $\begingroup$ Well, distribution of differences looks symmetric unimodal, I want to test if the measurements will increase after trigger and I have 140 samples. From the literature 30 samples is considered large enough for a lot of tests, but I'm not sure it would be large enough in this case. $\endgroup$ – dmonkoff Aug 28 at 1:55
  • $\begingroup$ The “30 is enough” is a common guideline, perhaps not a good one. But 140 observations is a pretty big sample size. How do the quantile-quantile plots look? It would help if you posted them. $\endgroup$ – Dave Aug 28 at 1:58
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    $\begingroup$ The QQ plot for the differences has that one worrying point at the top right, but it mostly looks quite normal to me. (That one point isn’t really even that worrying.) I think you’re safe to t-test the differences. $\endgroup$ – Dave Aug 28 at 2:35

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