Since there are three of them, m obt is equal to 3. Our hypotheses are the same. The statistical test for the Wilcoxon Signed Ranks Test is T . With 12 pairs of observations, and a one-tailed alpha of .01, we can go to the Wilcoxon T table and find that the critical value of T is 10. T crit , then, is 10, and our decision rule is to reject the null hypothesis if T obt is less than or equal to 10.
T is fairly simple to calculate.
We will go through the steps. First, subtract the first score from the second score, and record both the sign and the magnitude of this difference. Second, ignore the sign and rank order the difference scores assigning the rank of 1 to the lowest score. Replace the sign that was associated with that difference score. After recording the correct sign, sum the ranks of both the positive and negative signs.