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Wilcoxon procedure

We refer to Siegel and Castellan book called Nonparametric statistics for the behavioral science and Inferential statistics for more details about the procedures.

Step 1 - For each matched pair of observations, X_i and Y_i, determine the signed difference d_i = X_i - Y_i between the two variables
Step 2 - Rank these d_i's without respect to the sign. For tied d_i's, assign the average of the tied ranks
Step 3 - Affix to each rank the sign (+ or -) of the d which it represents
Step 4 - Determine N, the number of non-zero d_i's
Step 5 - Determine W⁺, the sum of the ranks which have a positive sign.
Step 6 - Determine whether two samples come from the same population or not, according to the size of N.