stats

Wilcoxon Signed-Rank Test

Non-parametric paired test — W⁺/W⁻, exact critical values (n≤25), normal approx, difference dot plot.

Non-parametric alternative to the Paired T-Test — use when difference scores are not normally distributed.

Input

Hypothesis Tail

Hypothesized difference μ₀

(comma or space separated)

Results

Pairs (n) / used after zeros—

W⁺ (positive rank sum)—

W⁻ (negative rank sum)—

T = min(W⁺, W⁻)—

Z (normal approx, continuity correction)—

p-value—

Effect size r = |Z|/√n—

Conclusion α = 0.05—

Conclusion α = 0.01—

T = min(W⁺, W⁻) · Z = (T − n(n+1)/4 ± 0.5) / √(n(n+1)(2n+1)/24)

r = |Z| / √n · exact critical W for n ≤ 25, normal approx for n > 25