Wilcoxon Signed-Rank Test Calculator Formula

Understand the math behind the wilcoxon signed-rank test calculator. Each variable explained with a worked example.

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Formulas Used

W-

w_minus = n * (n + 1) / 2 - w_plus

W Statistic

w_stat = min(w_plus, n * (n + 1) / 2 - w_plus)

Z Approximation

z_approx = (min(w_plus, n * (n + 1) / 2 - w_plus) - n * (n + 1) / 4) / sqrt(n * (n + 1) * (2 * n + 1) / 24)

Variables

VariableDescriptionDefault
nNon-Zero Pairs12
w_plusW+ (Positive Rank Sum)55

How It Works

Wilcoxon Signed-Rank Test

W = min(W+, W-)

Rank absolute differences, sum positive and negative ranks separately.

Worked Example

12 pairs, W+=55.

n = 12w_plus = 55
  1. 01W- = 78-55 = 23
  2. 02W = min(55,23) = 23

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