Mann-Whitney U Test

Authors

Affiliations

Nathaniel Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

AKA:

• Wilcoxon Rank Sum test

Practical uses

• Non-parametric counterpart to the T-Test for independent samples

Definition

• An analog of the parametric Student’s t-test¹
• Compares the means between two independent groups with the assumption that the data is not in a normal distribution¹.
• Useful for numerical/continuous variables¹.

Example

For example, 2 different groups’ age or height (continuous variables), in a study with non-normally distributed data¹

Variables

Independent variables

Nominal/ordinal variable with 2 expressions

Examples

E.g. Meds: Drug & Placebo

Dependent variables

Metric/ordinal variable

Examples

E.G.: Salary, wellbeing, weight

Processing

Rank sum

Requirements

• Only 2 independent random samples
• At least ordinally scaled characteristics

Benefits

• Does not need to be normally distributed

Hypothesis

• Null hypothesis: There is no difference (in terms of central tendency) between the two groups in the population.
• Alternative hypothesis: There is a difference (with respect to the central tendency) between the two groups in the population

References

1.

Sundjaja JH, Shrestha R, Krishan K. McNemar And Mann-Whitney U Tests. In: StatPearls. StatPearls Publishing; 2023. Accessed October 3, 2023. http://www.ncbi.nlm.nih.gov/books/NBK560699/