I want one expression for the null hypothesis for the location tests (one-sample t-test and one-sample Wilcoxon test) can I write this for both tests $H_0:\mu=0$ as general expression?

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    $\begingroup$ Yes, you can, but you would first have to define what $\mu$ represents, which you have not done in your question. It might help people answer your question if you explained why you are worried that same null hypothesis might not be appropriate for the one-sample t-test and one-sample Wilcoxon. Are you for example worried that the Wilcoxon test hypothesis is about the median rather than the mean? $\endgroup$ Oct 16, 2022 at 22:15
  • $\begingroup$ @GordonSmyth Thank you for your comment, exactly that is what I worry about (Wilcoxon is about median not mean). $\endgroup$ Oct 17, 2022 at 8:20
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    $\begingroup$ The one-sample Wilcoxon test is only valid for symmetric distributions, for which median = mean. $\endgroup$ Oct 17, 2022 at 8:50
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    $\begingroup$ In general, the Wilcoxon signed rank test is not a test of the median. If you assume a symmetric distribution, then you can interpret it as a test of the median, which as GordonSmyth notes, would also make it a test of the mean. ... You could describe both tests are considering a hypothesis of Location = 0 , but in the case of the signed rank test, when the distribution of the values is not symmetric, it becomes difficult to describe what is meant by location. It may be the Hodges-Lehmann estimator (See, Wikipedia. $\endgroup$ Oct 17, 2022 at 18:24


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