=+Assume there are m X values and n Y values, where m n N and

=+Assume there are m X values and n Y values, where m þ n ¼ N and the X and Y value are independent. Show that the signed-rank test statistic Tþ calculated for these Di is equal to the sum of the ranks of the X observations in the combined ordered sample of mX’s and nY’s and also that Tþ  T is the sum of the X ranks minus the sum of the Y ranks. This sum of the ranks of the X’s is the test criterion for the Wilcoxon statistic in