I have two paired samples and I am running a paired Mann-Whitney test to determine whether they are different. In Matlab, this takes the form of p = signrank(x,y), which tests the null hypothesis that x-y comes from a population of median zero.
Unfortunately, Matlab doesn't give difference estimates for x-y or confidence intervals for this estimate.
In the past, to estimate the shift estimate for nonpaired samples, I used the Hodges-Lehmann estimate (see Difference of 'centers' of 2 non-normal samples with Mann-Whitney test & http://en.wikipedia.org/wiki/Hodges%E2%80%93Lehmann_estimator). This is essentially the median of all pairwise differences.
Here, since the samples are paired, I imagine that the HL estimate is incorrect. Intuitively, I was thinking of using the median of all paired differences.
In either case, my question is how to get the difference estimate for x-y and the confidence interval for that estimate.
Below is a picture of my data:
The top histogram shows both samples (correct & incorrect), the bottom histogram shows the pairwise differences. A boxplot of the data is on the right. The estimated p-Value for the paired MW test is above & is <.05. Thus the data is significantly difference with correct > incorrect (even though it admittedly is hard to see on the histogram. Any suggestions on how to make it more visualisable are greatly appreciated!)