Wilcoxon signed ranked test

Comments

• statisticum

  May 2020

  In my last comment, I forgot to bring another point. The matched rank biserial correlation is suppose to be the difference between the number of the number of + ranks/total number of ranks minus the number of - ranks / total number of ranks. The result of 4/6 minus 2/6 is supposed to give 0.333. In the ouptut, I have 0.619.

  Thanks again for your attention
• eduard

  May 2020

  Hi, I suppose this question is over JASP? I will move the question to the proper subforum.

  Eduard

  
• JohnnyB

  May 2020

  Hi Statisticum,

  
  

  Which test are you running in SPSS and Simstat? Do these programs give the Z value by default for the wilcoxon signed rank test?

  In any case, I checked the data in R, and the wilcox.test gives the same result as JASP for paired observations (see the code below).

  As for the effect size, the method you describe is for the sign test, where you do not take into account the ranks of the absolute difference. For the signed rank test, the magnitude of the difference also matters for the effect size. We follow the procedure as described in Kerby (2014), who writes it as follows:

  "The result is that the matched-pairs rank-biserial correlation can be expressed r = (SF/S) – (SU/S), a difference between two proportions."

  In R, this can be calculated:

  pre <- c(63, 75, 75, 74, 65, 63) 
  post <- c(70, 48, 65, 60, 68, 57)
  
  wilcox.test(pre, post, paired = TRUE) # V = 17, p-value = 0.2188
  
  diffs <- pre - post
  ss <- sign(diffs)
  absRanked <- rank(abs(diffs))
  
  posDiffsRankSum <- sum(absRanked[ss == 1])
  negDiffsRankSum <- sum(absRanked[ss == -1])
  (posDiffsRankSum - negDiffsRankSum) / sum(absRanked) # 0.6190476
  

  Which reproduces the JASP results.

  Kind regards,

  Johnny