I would like to understand the differences between these tests for one sample median test and when to use each of them.

I have been searching information and this is what I got so far:

  • Sign test (in R sign.test) does not need a probability distribution symmetric but Wilcoxon (wilcox.test) does.
  • Wilcoxon is more powerful.

To check the symmetry in the prob distribution, I through an histogram right? What are the assumptions for each of them? When should I use them?

I am pretty lost here so any help is welcome.


1 Answer 1

  • One-sample sign test tests that the median in the population equals the value.
  • One-sample Wilcoxon test tests that the distribution in the population is symmetric around the value. More technically, that the sum of two randomly chosen deviations from the value has equal probability to occure positive or negative. Note that rejecting this null hypothesis does not preclude the value to be the mean or median of the population. The rejection implies two possible reasons: either the distribution is symmetric about some other value or the distribution is not symmetric at all.
  • So if we do assume symmetric shape of the population distribution then the Wilcoxon tests that the mean (=median) in the population equals the value (it is this test then is the nonparametric alternative to one-sample t-test which assumes normality). If you assume the symmetry and hence you test for mean (=median), then Wilcoxon is more powerful, as a median test, then the more universal sign test above.
  • $\begingroup$ Hi, thanks for your answer. It is very helpful. One more question: what happens if I use Wilcoxon with a non symmetric distribution? $\endgroup$ May 31, 2014 at 8:45
  • $\begingroup$ If the population distribution is believed to be asymmetric then there can be no value around which it is symmetric, and one-sample Wilcoxon is useless. $\endgroup$
    – ttnphns
    May 31, 2014 at 11:44

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