# PROPHET StatGuide: Mann-Whitney rank sum test

(The Wilcoxon rank sum test is equivalent to the Mann-Whitney U test.)

### Assumptions:

Within each sample, the values are independent, and identically
distributed.
(The Mann-Whitney rank sum test
is a nonparametric
test. We need not specify or know what the
distribution is,
only that all the values in each sample follow the same
continuous distribution.)

The two samples are independent of
each other.

The populations from which the two samples were taken
differ **only** in location.
That is, the populations may differ in their means or medians,
but not in their dispersions
or distributional shape (such as skewness).

Because the test statistic for the Mann-Whitney rank sum
is based only on the ranks
within each sample, the test can
be performed when the only data available are those relative ranks.

### Guidance:

**Ways to detect** before performing the
rank sum test whether your data violate any
assumptions.

**Ways to examine** rank sum test results to detect
assumption violations.

**Possible alternatives** if your data or rank sum test
results indicate assumption violations.

To properly analyze and interpret
results of the *rank sum test*, you should be familiar with the
following terms and concepts:

If you are not familiar with these terms and concepts, you are advised to
consult with a statistician. Failure to understand and properly apply the *
rank sum test* may result in drawing erroneous conclusions from your data.
Additionally, you may want to consult the following references:
- Brownlee, K. A. 1965.
*Statistical Theory and Methodology
in Science and Engineering.* New York: John Wiley & Sons.
- Conover, W. J. 1980.
*Practical Nonparametric Statistics.* 2nd ed.
New York: John Wiley & Sons.
- Daniel, Wayne W. 1978.
*Applied Nonparametric Statistics. *
Boston: Houghton Mifflin.
- Daniel, Wayne W. 1995.
*Biostatistics.* 6th ed.
New York: John Wiley & Sons.
- Hollander, M. and Wolfe, D. A. 1973.
*Nonparametric Statistical Methods. *
New York: John Wiley & Sons.
- Lehmann, E. L. 1975.
*Nonparametrics: Statistical Methods Based on
Ranks. * San Francisco: Holden-Day.
- Miller, Rupert G. Jr. 1986.
*Beyond ANOVA, Basics of Applied
Statistics.* New York: John Wiley & Sons.
- Rosner, Bernard. 1995.
*Fundamentals of Biostatistics.*
4th ed. Belmont, California: Duxbury Press.
- Sokal, Robert R. and Rohlf, F. James. 1995.
*Biometry.* 3rd. ed.
New York: W. H. Freeman and Co.
- Zar, Jerrold H. 1996.
*Biostatistical Analysis.* 3rd ed. Upper Saddle River, NJ:
Prentice-Hall.

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##### Last modified: March 18, 1997

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