Wilcoxon Signed Rank Test

The Wilcoxon signed-rank test is a nonparametric test of whether paired differences, or values in one sample, are centered on zero or a hypothesized value, based on the signs and ranks of the differences.

윌콕슨 부호순위 검정은 대응된 차이 또는 단일 표본의 값이 0이나 가설값을 중심으로 분포하는지를 차이의 부호와 순위로 검정하는 비모수 검정입니다.

How do I compare two related measurements when the differences are not normally distributed?

차이가 정규분포를 따르지 않을 때 서로 관련된 두 측정값은 어떻게 비교하나요?

The Wilcoxon signed-rank test compares paired measurements, such as before and after scores from the same people, without assuming the differences are normally distributed. It is the usual nonparametric alternative to the paired samples t test, especially for small samples, ordinal-like scales, or skewed differences.

When to use Wilcoxon Signed Rank Test

• Before-and-after scores from the same participants with skewed differences
• Matched pairs measured on an ordinal or non-normal continuous scale
• Testing whether a single sample's median differs from a hypothesized value

When to use something else

• Differences are approximately normal: use the paired samples t test
• Two independent groups rather than pairs: use the Mann-Whitney U test

Assumptions and requirements

• Paired observations, with pairs independent of one another
• Differences measured on a scale where their sizes can be meaningfully ranked
• Differences roughly symmetric around the median if the result is interpreted as a median shift

What the analysis reports

• Test statistic (W, V, or T) and standardized z
• p-value
• Effect size r
• Median of differences or Hodges-Lehmann estimate with confidence interval

How to report it

A Wilcoxon signed-rank test indicated that [outcome] was significantly higher at [time 2] than at [time 1], T = [value], z = [value], p = [value], r = [value].

Related methods

• Paired Samples t test
• Sign Test
• Mann-Whitney U Test

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