Why is the upper bound of the 95% CI infinity when using a one sample wilcoxon?

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.

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?

• Can you show the data or plot them? Oct 5, 2022 at 9:52
• Hi @rep_ho! Please see the above edit. Oct 5, 2022 at 10:23
• Could it be because you are doing only one sided test? Oct 5, 2022 at 11:09
• 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 Oct 5, 2022 at 18:03
• 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. Oct 6, 2022 at 9:44