How to interprete and describe the results of a Wilcoxon Signed Rank test? I'm trying to learn about rank tests, and having doubts abouut how I should a result from a Wilcoxon Signed Rank test. Suppose, we are given:
Z = -2.201, r = - 0.845, P < 0.05,
then how should I interprete these three numbers and describe them in words?
 A: BBR Section 7.2 and especially 7.2.1 cover this.  It shows how to scale the signed rank statistic to [0,1] representing the probability that a randomly chosen pair of observations sum to a positive number.
Don't state P < 0.05. Give the P-value, and a proper conclusion is not reject/accept $H_0$ but rather, when P is small, that there is evidence against the supposition of no difference.
A: It is not that simple to explain what the signed-rank test actually tests for.  My best advice is read a few respected textbooks covering the test, and pay attention to how they state the null and alternative hypotheses.  However, be ware that some texts may simplify the language for these hypotheses, or may pull in additional assumptions to make interpreting the test easier.
Essentially, the signed rank test assesses whether the differences in pairs ---- or of the one-sample observations ---- is symmetric about zero. Except that the test uses the ranks after taking the differences.  You might say that it tests if the paired differences are systematically different than zero.
Various plots may be helpful.  A histogram of the paired differences.  Plotting group 1 vs. group two and superimposing a 1:1 line.
Beyond that, z and p are commonly reported statistics in the analysis of experiments.  r in this case is likely the z value divided by the number of pairs, and is an effect size statistic.  It more or less ranges from -1 to 1.   A negative r suggests that the second group has larger values than the first group. (But double check this, as software can reverse this !).  An absolute value of 0.8 for this statistic is likely a large value.
