It seems that Wilcoxon Signed-Rank Test could be used not only for inference about the mean difference in a matched pairs, but can also be used for one sample setting. Now I have a dataset which is not normally distributed, and also is not matched pairs, so I suppose Wilcoxon Signed-Rank Test can be performed to test significance. My dataset is as follows. I want to test whether the language ability contributes to the grade (1 indicate passing the exam, and 0 indicate failing to the exam). My reasoning about Wilcoxon Signed-Rank Test for one sample setting is that, devide the dataset into two parts, which is grade =1 and grade =0, then compare the means of two groups, but it seems a bit weird. I checked online and found a lot of examples and explanation about Wilcoxon Signed-Rank Test used for matched pairs, but no one for one population. Could anybody have any suggestion for me about this?
If you're comparing the means of two groups, I don't think it makes sense to use a test for comparing one group to a specified location
You might look at a two group test (like a Mann-Whitney), except that I think the analysis would be better done with the response variable (grade) as the actual response in the model.
With that in mind, this looks to me like it would be best framed as something like a logistic regression problem.