Which Test?

Draft: This page has not been reviewed by a statistician yet. Use it as a starting point and check important choices with a statistician.

Mann-Whitney U test

Compares a skewed measurement or an ordered score between two independent groups using ranks instead of raw values.

Clinical example

Length of stay in days compared between two wards. A few patients stayed very long, so the values are strongly skewed. Each patient was on one ward only.

When to use it

  • The outcome is a skewed measurement or an ordered score such as a pain score.
  • You compare exactly two groups, and each patient is in only one of them.
  • You don't need to adjust for other variables.

Assumptions to check

Independent observations

One value per patient. Repeated measurements or clustered patients need a mixed model.

It compares whole distributions

The test asks whether values in one group tend to be higher than in the other. It is a comparison of medians only when the two distributions have a similar shape.

Check first

  • Consider a log transform first if the data are right-skewed and you also plan regression analyses; keep one approach throughout the paper

What to report

  • Median with interquartile range per group
  • Hodges-Lehmann estimate of the shift with 95% CI
  • The exact p-value, not just "p < 0.05"

Common mistakes

Don't run a normality test to decide

With small samples it rarely flags a problem; with large ones it flags harmless deviations. Look at the histograms and think about the measurement instead.

Report the effect, not just the p-value

Give the estimate (difference, ratio) with its 95% confidence interval and the exact p-value.

Be careful treating a score as a measurement

The steps of an ordinal score aren't necessarily equal. Means and t-tests assume they are.

Don't dichotomize a measurement

Cutting a continuous variable into high and low ("BP above 140") throws away information and power, and the cut-off is often arbitrary.

Alternatives

If your situation is…Use
Roughly symmetric data or larger groupsWelch's t-test
Ordered score and you need to adjust for other variablesProportional odds (ordinal logistic) regression

In your software

R
# R
wilcox.test(los_days ~ ward, data = trial, conf.int = TRUE)
SPSS
NPTESTS
  /INDEPENDENT TEST (los_days) GROUP (ward) MANN_WHITNEY.

Sources