How to interpret the estimate from Wilcoxon signed rank paired test? Suppose I do a Wilcoxon signed rank paired test such as:
a<-c(1.1, 2.2, 3.3, 4.4, 5.5)
b<-c(1.6, 1.0, 3.9, 2.2, 3.7)
wilcox.test(a,b,paired=TRUE,conf.int=TRUE)
    Wilcoxon signed rank test

data:  a and b
V = 12, p-value = 0.3
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
 -0.6  2.2
sample estimates:
(pseudo)median 
           0.8 

I am wondering how to interpret the sample estimates(pseudo) median 0.8? How this value has been calculated?
 A: From the documentation for the wilcox.test package:

Optionally (if argument conf.int is true), a nonparametric confidence interval and an estimator for the pseudomedian (one-sample case) or for the difference of the location parameters x-y is computed. (The pseudomedian of a distribution F is the median of the distribution of (u+v)/2, where u and v are independent, each with distribution F. If F is symmetric, then the pseudomedian and median coincide. See Hollander & Wolfe (1973), page 34.) Note that in the two-sample case the estimator for the difference in location parameters does not estimate the difference in medians (a common misconception) but rather the median of the difference between a sample from x and a sample from y.

The pseudomedian is informative in that it is an estimator of the location parameter for a shift alternative. Comparing it with the sample median can also be a heuristic measurement of symmetry.
I will add that I was under the impression the pseudomedian should be equivalent to the Hodges-Lehmann estimate of the median pairwise distance, yet calculating that using your data:
median(as.vector(outer(a,b,"-")))

gives me 0.7 rather than 0.8. Perhaps someone else will be able to provide illumination as to the discrepancy, there. 
