#StackBounty: Is it possible to get a CI for the difference in median response between two groups via Dunn test?

Bounty: 100

Dunn test for two groups is equivalent to Kruskal-Wallis. The null is the absence of stochastic dominance, but if we impose some more restrictions we can assume that the null is the equality of medians, \$H_0: M1 = M2\$.

Apparently, the Dunn test statistic is assumed Normal, but it is computed in rank terms, not in terms of the original observations. Therefore, we can obtain p-value for \$H_0\$, but no explicit CI for \$(M1 – M2)\$.

1) Is it ok to assume that \$(M1 – M2)\$ is also Normal? If yes, we can use the point estimate and p-value to derive the s.e. and construct a confidence interval.

2) This question is not related to 1). I would like to get p-value for \$H_0 : M1/M2 = 1\$. Let’s assume no ties. Then, using the fact that the Dunn p-value is invariant to a monotone transformation of the original response, \$Y\$, and that \$log(median(Y)) = median(log(Y))\$, it looks like the p-value for \$M1/M2\$ is exactly the same as for \$M1 – M2\$. Did I get that right?

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