How can we prove that kruskal-Wallis test and Jonckheere test is equivalent to Wilcoxon rank sum test when k = 2? And how can we prove that Friedman test and Page test is equivalent to sign test when k = 2?
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$\begingroup$ They're not equivalent in general. You would need to restrict consideration to the situations where those tests all apply at the same time, otherwise you'd be stuck with answering questions like "how do I do a rank sum test with 3 groups?" and discovering that Jonckheere is not equivalent to Kruskal-Wallis for three groups. $\endgroup$– Glen_bCommented Nov 23, 2021 at 22:42
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$\begingroup$ i forgot to comment that I was referring to when k equals to 2 $\endgroup$– wycCommented Nov 24, 2021 at 2:36
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$\begingroup$ An edit to make that explicit rather than implied would help your question. $\endgroup$– Glen_bCommented Nov 24, 2021 at 5:00
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