Imprecision in wilcox_effsize documentation #213
Description
TL;DR: the wilcox_effsize documentation states that for Wilcoxon two-sample paired signed-rank tests N should correspond to the number of pairs of observations involved in the test. However the source cited to support this notion and other literature actually suggest that N should be the total number of observations i.e. N = number of observations at test 1 + number of observations at test 2 = 2 * number of pairs.
This repository seems to be no longer under maintenance, however I will leave this issue as documentation.
In the documentation of wilcox_effsize it is stated that "N corresponds to total sample size for independent samples test and to total number of pairs for paired samples test." (emphasis is mine).
However, the cited source, i.e. the article "The need to report effect size estimates revisited. An overview of some recommended measures of effect size." by Maciej Tomczak and Ewa Tomczak actually states, for both the Mann Whitney U for independent samples and Wilcoxon signed rank tests for dependent samples, that N should be the "total number of observations on which Z is based". The Z statistic is based on the differences between samples at pre-test and post-test (see for example the documentation for scipy.stats.wilcoxon: Z is defined using T, which is based on the differences between observations at pre-test and post-test) so the number of observations on which it is based is actually the sum of observations at pre-test and post-test.
Note that this interpretation (N = 2 * number of pairs) is also reported in the book "SPSS survival manual: a step by step guide to data analysis using SPSS (4th edition)" by Julie Pallant, Chapter 16 "Non-parametric statistics", on the paragraph relative to "Wilcoxon signed rank test". Specifically the quote is "In this situation, N = the number of observations over the two time points, not the number of cases.", followed by practical examples.