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Wilcoxon signed-rank test (one-sample)

The one-sample Wilcoxon signed-rank test compares a sample against a hypothesised median — the non-parametric alternative to a one-sample t-test.

What is Wilcoxon signed-rank test (one-sample)?

Subtract the null median μ₀ from each observation; rank the absolute differences; sum the ranks of the positive differences (V). Under H₀ (median = μ₀ and symmetric distribution), V is symmetric around n(n+1)/4.

Drop pairs where x = μ₀ exactly. Symmetry around the median is the key assumption — for skewed differences, the sign test is the simpler robust alternative (no symmetry needed).

When should I use Wilcoxon signed-rank test (one-sample)?

Single-sample test against a reference value when the data are clearly non-normal or n is small.
Ordinal data.

What data does it need?

One numeric column + hypothesised median μ₀.

What does it report?

V statistic + p + Hodges-Lehmann pseudo-median with CI.

What does it assume?

Independent observations.
Symmetric distribution around the true median (for the location-shift interpretation).

How do I interpret the result?

The Hodges-Lehmann pseudo-median is the natural effect estimate — robust and on the original scale. Report it alongside the p.