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I've been calculating 95% confidence intervals around the psuedomedian in a one sample wilcoxon signed rank tests, with a "greater" alternative and the mu = 0. That is, I have been exploring whether the group pseudomedian is greater than 0. I have several difference tests using this configuration. If it's relevant, I have completed this using wilcox_test() in the rstatix package in R.

The variable is always bounded. Values can only exist between -1 and 1. The reported lower bound of the confidence interval always has a specific value (e.g., -0.0172) but the upper bound always comes out as infinity. Why is this and is it accurate? I interpret this to mean that the true value exists somewhere between the lower bound and infinity but I don't understand why it doesn't vary across different tests I complete. The pseudomedian and distribution of the data is different for each test I run.

Further, when it comes to reporting an upper bound confidence interval like this, do I report it as infinity or as 1, because I know that logically the value cannot be greater than this value.

I hope this is enough information but please do let me know if further details would be helpful.

EDIT: As requested, I've added a plot showing the distribution of the data points. Each yellow diamond represents the median. Each violin represents a different wilcoxon test performed.

enter image description here

EDIT 2: I should also say, the upper CI value varies if the wilcoxon is two tailed instead of one tailed, so I think it might be something to do with that?

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  • $\begingroup$ Can you show the data or plot them? $\endgroup$
    – rep_ho
    Oct 5, 2022 at 9:52
  • $\begingroup$ Hi @rep_ho! Please see the above edit. $\endgroup$
    – Frewtea
    Oct 5, 2022 at 10:23
  • $\begingroup$ Could it be because you are doing only one sided test? $\endgroup$
    – rep_ho
    Oct 5, 2022 at 11:09
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    $\begingroup$ One-sided confidence intervals correspond to one-sided hypothesis tests (ie. alternative = "greater" or "less"). One end of a one-sided confidence interval is infinity. Matching Confidence limits with One-Sided Hypothesis tests $\endgroup$
    – dipetkov
    Oct 5, 2022 at 18:03
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    $\begingroup$ By "this" do you mean confidence intervals? Every intro stats should explain confidence intervals. The linked post does a fine job as well. I also like this online book: Improving Your Statistical Inferences. $\endgroup$
    – dipetkov
    Oct 6, 2022 at 9:44

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@dipetkov provided some helpful links to other questions with informative answers Matching Confidence limits with One-Sided Hypothesis tests and a textbook that covers confidence intervals well https://lakens.github.io/statistical_inferences/index.html

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    $\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Oct 6, 2022 at 10:06

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