#
# Wilcoxon matched-pairs signed-rank test for small samples (n<=25), two-sided
# Script for R
#
# Syntax : wilcox.small (x,y)
#
# version: 0.3
# author : Christian Spannagel, University of Education Ludwigsburg
# website: http://www.christian-spannagel.de
# contact: cspannagel@web.de
#
# This work is licensed under the GNU General Public License, Version 2.
# http://www.gnu.org/licenses/gpl.html
# 

# tables taken from Vogel, A. (1977). Funktionentafeln und statistische Tabellen, p. 212
wilcox.table01 <- c(0,0,0,0,0,0,0,0,2,3,5,7,10,13,16,19,23,28,32,37,43,49,55,61,68)
wilcox.table05 <- c(0,0,0,0,0,1,2,4,6,8,11,14,17,21,25,30,35,40,46,52,59,66,73,81,90)

wilcox.small <- function (x,y) {
   wilcox.tieddiffs <- x-y
   wilcox.diffs = c()
   for (i in 1:length(wilcox.tieddiffs)) {
      if (wilcox.tieddiffs[i] != 0) {
         wilcox.diffs = c(wilcox.diffs, wilcox.tieddiffs[i])
      }
   }
   wilcox.ranks <- rank (abs(wilcox.diffs), ties.method="average")
   n=0;
   sumnegranks = 0;
   sumposranks = 0;
   for (i in 1:length(wilcox.ranks)) {
      if (wilcox.diffs[i] < 0) {
         sumnegranks = sumnegranks + wilcox.ranks[i]
         n = n + 1
      } else if (wilcox.diffs[i] > 0) {
         sumposranks = sumposranks + wilcox.ranks[i]
         n = n + 1
      }
   }
   cat ("Wilcoxon Matched-Pairs Signed-Rank test for small samples (n<=25), two-sided\n\n");
   cat ("n             =",n,"\n")
   cat ("sum neg ranks =",sumnegranks,"\n")
   cat ("sum pos ranks =",sumposranks,"\n\n")
   if (sumnegranks < sumposranks) {
      valuetocompare = sumnegranks
   } else {
      valuetocompare = sumposranks
   }
   if (n <= 25) {
      cat ("value to compare     : ",valuetocompare,"\n");
      cat ("critical value p=0,05: ",wilcox.table05[n],"\n");
      cat ("critical value p=0,01: ",wilcox.table01[n],"\n\n");
      if (valuetocompare <= wilcox.table01[n]) {
         cat ("Result: significant on level p=0,01\n")
      } else if (valuetocompare <= wilcox.table05[n]) {
         cat ("Result: significant on level p=0,05\n")
      } else {
         cat ("Result: not significant\n");
      }

   } else {
      cat ("Sample is too large (n=",n,")\n");
   }
}