topic What does x_{i} mean in SAS documentation of Wilcoxon Signed Rank Test when we have paired data in Statistical Procedures

What does x_{i} mean in SAS documentation of Wilcoxon Signed Rank Test when we have paired data

pywils — Sun, 09 May 2021 00:28:14 GMT

Wikipedia's entry on the Wilcoxon Signed Rank Test says that the test is "used to compare two related samples, matched samples, or repeated measurements." In contrast, The SAS documentation of the Wilcoxon Signed Rank Test references x_{i} (a data value) and its rank, r_{i} as though we only had a single variable. How do I interpret x_{i} from SAS' documentation when I have paired data?

Thank you!

Re: What does x_{i} mean in SAS documentation of Wilcoxon Signed Rank Test when we have paired data

Reeza — Sun, 09 May 2021 01:46:24 GMT

Usually when you have paired data, you take the difference and assume the difference is the single array. Its possible it's different in this case, but I suspect it's the same.

Re: What does x_{i} mean in SAS documentation of Wilcoxon Signed Rank Test when we have paired data

StatDave — Sun, 09 May 2021 15:20:56 GMT

See the second paragraph on that documentation page. As described there, to perform the test to compare paired samples, you create a single variable that is the difference within each pair. The x_i are those differences and the r_ are the ranks.