PHARM/PCS V5 · Procedure 45 Pairwise and Nonparametric
Mann-Whitney U-Test
Compare two independent groups without assuming normal data, by ranking every observation, when outliers or skew rule out a t-test.
What it computes
Nonparametric test for whether two independent samples come from the same distribution. Ranks all observations jointly, computes the U statistic, and for n2 > 8 uses the normal approximation for significance.
Inputs and outputs
You provide
- The values for each of the two groups, entered as two blocks
PHARM/PCS reports
- The rank sums R1 and R2
- The U statistic
- For larger samples, a z-score and its significance
- A plot of both groups with their medians
When to use it
The distribution-free alternative to the two-group t-test (Procedure 39); reach for it when data are ordinal, badly skewed, or carry outliers that make means and normal-theory tests untrustworthy.
Reading the results
Working on ranks, it tests whether one group tends to have larger values, not specifically whether the means differ; a significant result means a stochastic shift, subtly different from a mean difference. It sacrifices some power versus the t-test when the data really are normal, so don't default to it out of caution when parametric assumptions hold.
Ties handled for you
Tied values receive the average rank automatically. When the larger group has more than eight observations, the procedure uses the normal approximation with a continuity correction; for smaller samples, look up the exact probability in the book's Table A.10a.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.