# Wilcoxon Algorithm

Performed on a set of numbers and labels of size N. There must be two specific labels. Label 1 must be 1 and label 2 must be 2. There can also be any other labels that will be ignored.

#### Wilcoxon statistic

1. Sort the combined values in ascending order and assign numerical ranks starting with 1.
• For a tie, assign all tied values the average rank. For example: tied 2nd and 3rd values would recieve a rank of 2.5 each; tied 5th, 6th, and 7th values would receive a rank of 6 each.
2. Sum the ranks for each group.
• n1 = size of the smaller group
• n2 = size of the larger group
• sum1 = rank sum of the smaller group
• sum2 = rank sum of the larger group
• n = n1 + n2
3. The statistic is the sum of the smaller group or the smaller sum if the groups are of equal size.
• If n1 < n2, sum1
• If n1 = n2, least of sum1 and sum2

#### Wilcoxon probability

1. Variance (Var): where = how many values are tied in each tie
2. z: • If z < 0, z = 0
3. P-value: -- WillGray - 22 Jul 2004
Topic revision: r4 - 04 Jan 2010, JoanZhang

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