Mann-Whitney U Test

The Mann-Whitney U test is a nonparametric rank-based test that compares two independent groups on an ordinal or continuous outcome without assuming normally distributed data.

맨-휘트니 U 검정은 정규분포를 가정하지 않고 순위를 이용해 두 독립 집단의 서열형 또는 연속형 결과변수를 비교하는 비모수 검정이다.

How do I compare two independent groups when the data are not normally distributed?

데이터가 정규분포를 따르지 않을 때 두 독립 집단을 어떻게 비교하나요?

The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups by ranking all observations and testing whether values in one group tend to be larger than in the other. It fits ordinal outcomes, small samples, or skewed continuous outcomes where an independent-samples t-test is doubtful.

When to use Mann-Whitney U Test

• Two independent groups measured on an ordinal scale such as Likert ratings
• A skewed continuous outcome with outliers in small samples
• Comparing distributions of one outcome between treatment and control

When to use something else

• The two measurements come from the same subjects: use the Wilcoxon signed-rank test
• There are three or more independent groups: use the Kruskal-Wallis test

Assumptions and requirements

• Observations are independent within and between groups
• The outcome is at least ordinal
• Interpreting it as a test of medians requires similarly shaped distributions in both groups

What the analysis reports

• U statistic (and/or standardized z)
• Exact or asymptotic p-value
• Mean ranks or medians per group
• Effect size such as rank-biserial correlation or r = z/√N

How to report it

A Mann-Whitney U test indicated that [outcome] was higher in [group 1] (Mdn = [value]) than in [group 2] (Mdn = [value]), U = [value], z = [value], p = [value], r = [value].

Related methods

• Wilcoxon Signed-Rank Test
• Kruskal-Wallis Test
• Independent Samples t-Test

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