---+ 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. 1 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 1 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): %$\frac{n1n2}{12(n^2-n)}(n^3-n-\sum{t_i^3-t_i})$% where %$t_i$% = how many values are tied in each tie 1 z: %$\frac{|W-n1\frac{n+1}{2}|-0.5}{\sqrt{Var}}\htmlimage{extrascale=1.5}$% * If z < 0, z = 0 1 P-value: %$2*(1-probt(z,n-1))$% -- Main.WillGray - 22 Jul 2004
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