# How do you calculate the effect size of one-sample Wilcoxon signed-rank test?

Can you / how do you calculate the effect of a one-sample Wilcoxon signed-rank test?

Is there a way to perform the calculation in SPSS or another software package?

• In SPSS see the NPTESTS procedure to calculate the Wilcoxon signed rank test for a pre-specified median. – Andy W Sep 2 '12 at 14:27

The Hodges-Lehmann statistic is the estimator associated with the Wilcoxon signed-rank test. Form the $n(n+1)/2$ pairwise averages $(x_i + x_j)/2$ for $i \leq j = 1, \dots, n$; take the median; and there you are.

I strongly suspect there's a procedure in SPSS for it, although a quick search of the web didn't turn up anything, and in R there's the exactRankTests package with wilcox.test in it, which function has an option that will return both the point estimate and a confidence interval.

Edit: I notice that although exactRankTests is still available, it's not being developed any more and the coin package is recommended instead. It, too, has wilcox.test, and the syntax looks the same.

The Hodges-Lehman estimator is only suitable if your distributions are symmetrical, i.e. not skewed source p35.

Another solution for a non-parametric effect size is z divided by the root of N (r=Z/SQRT(N)) as others have suggested.

Yet other suggestions are the standardised mean difference or the probability of superiority as described here

Important is that you check how your data is distributed and your data collection method as each of these solutions have slightly different assumptions.

As for SPSS I don't know because I use R for data manipulation, analysis and visualisation.