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Imagine I would like to test whether the blood oxygen saturation differs significantly between left and right arm. Now, imagine that:

  • All measurements are percentages
  • The differences between pairs show positive skewness and bimodality
  • The sample size is composed by 50 volunteers (50 left + 50 right = 50 pairs of measurements)
  • I have not to assume that the difference is clinically significant (only statistically)

My question is: is the Wilcoxon signed-rank test a good choice to test that, or are percentages not tested well by it?

(I use R)

I read those Q&A, but my doubts are still there mainly because I do not understand if a nonparametric test would be more appropriate and my data would be strictly percentages: Percentages from non binomial data: is ANOVA / Kruskal-Wallis appropriate?, Using ANOVA on percentages? and Wilcoxon signed-rank test for proportion variable response?

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    $\begingroup$ Non-statistician answer: As far as I know, data (in the dependent variable) are appropriate for nonparametric tests if they can properly ordered. That is you can rank each observation as larger, smaller, or equal to every other observation. I believe some of the tests start with the assumption that the data come from a continuous variable. So I don't see why percentages would cause any problem. But be careful to understand any additional assumptions in nonparametric tests, and especially interpretation. Be wary of sources telling you you are simply testing for a difference in medians. $\endgroup$
    – Sal Mangiafico
    Jan 20, 2018 at 13:13

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Wilcoxon signed rank test and all such univariate analyses (ANOVA, t-Test, etc.) can be analyzed using regression. You will probably need to do a log transformation in the percentages if they are your outcome (DV) and/or use logistic regression if the arm is a dichotomous variable.

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