Skip to content

Explore Courses | Elder Research | Contact | LMS Login

Statistics.com Logo
  • Courses
    • See All Courses
    • Calendar
    • Intro stats for college credit
    • Faculty
    • Group training
    • Credit & Credentialing
    • Teach With Us
  • Programs/Degrees
    • Certificates
      • Analytics for Data Science
      • Biostatistics
      • Programming For Data Science – Python (Experienced)
      • Programming For Data Science – Python (Novice)
      • Programming For Data Science – R (Experienced)
      • Programming For Data Science – R (Novice)
      • Social Science
    • Undergraduate Degree Programs
    • Graduate Degree Programs
    • Massive Open Online Courses (MOOC)
  • Partnerships
    • Higher Education
    • Enterprise
  • Resources
    • About Us
    • Blog
    • Word Of The Week
    • News and Announcements
    • Newsletter signup
    • Glossary
    • Statistical Symbols
    • FAQs & Knowledge Base
    • Testimonials
    • Test Yourself
Menu
  • Courses
    • See All Courses
    • Calendar
    • Intro stats for college credit
    • Faculty
    • Group training
    • Credit & Credentialing
    • Teach With Us
  • Programs/Degrees
    • Certificates
      • Analytics for Data Science
      • Biostatistics
      • Programming For Data Science – Python (Experienced)
      • Programming For Data Science – Python (Novice)
      • Programming For Data Science – R (Experienced)
      • Programming For Data Science – R (Novice)
      • Social Science
    • Undergraduate Degree Programs
    • Graduate Degree Programs
    • Massive Open Online Courses (MOOC)
  • Partnerships
    • Higher Education
    • Enterprise
  • Resources
    • About Us
    • Blog
    • Word Of The Week
    • News and Announcements
    • Newsletter signup
    • Glossary
    • Statistical Symbols
    • FAQs & Knowledge Base
    • Testimonials
    • Test Yourself
Student Login

Wilcoxon – Mann – Whitney U Test

Wilcoxon – Mann – Whitney U Test

Wilcoxon - Mann - Whitney U Test:

The Wilcoxon-Mann-Whitney test uses the ranks of data to test the hypothesis that two samples of sizes m and n might come from the same population. The procedure is as follows:

  1. Combine the data from both samples
  2. Rank each value
  3. Take the ranks for the first sample and sum them
  4. Compare this sum of ranks to all the possible rank sums that could result from random rearrangements of the data into two samples.

If step 4 reveals that the rank sum for the observed first sample is larger (or smaller) than nearly all the random orderings, this indicates that the first sample is significantly different from the second sample.

Note: Hollander and Wolfe suggest that ties be resolved by using the average rank of the tied observations.

Here´s an example in Excel (in step 4, rather than comparing the observed sum of ranks to ALL POSSIBLE randomly ordered sums, thousands of randomly shuffled sums are used for comparison):

Is there a difference in the transfer of titrated water across a placental membrane between human fetuses at 12-26 weeks and at term? The permeability constant Pd of the membrane is used as the measure. (Source: Hollander & Wolfe, Nonparametric Statistical Methods, John Wiley and Sons, 1973)

Here are the data:

Here are the ranks; note the rank sum for the first sample is 30:

Here are the ranks, randomly shuffled using the Resampling Stats add-in for Excel (30-day trial available for download at https://resample.statistics.com/):

The column of 10,000 resulting values is sorted, and we see that 1291 of the 10,000 shufflings yielded a sum of ranks <= the observed value of 30. This translates into an estimated p-value of .1291 for a 1-sided test of the null hypothesis that the two samples might come from the same population (against the alternative that sample 1 is smaller than sample 2.)

Including the above method, there are several ways to determine this p-value:

  1. Compare the observed rank sum to the distribution of rank sums resulting from all possible orderings of the ranks (an exact permutation test)
  2. Compare the observed rank sum to repeatedly shuffled rank sums (an approximate or Monte Carlo permuitation test; the result approaches the result of #1 above as the number of repeats approaches infinity).
    This is the method described above.
  3. Transform the observed test statistic into an equivalent statistic, which is approximately normally-distributed.
  4. For certain sample sizes, you can consult tables of the exact distribution of the test statistic.

With the advent of high speed computing and the availability of resampling and permutation software, methods 1 and 2 have increasingly come to dominate 3 and 4. <!--

Special Offer for Statistics.com Users!

Buy the Resampling Stats Excel Add-In now and save $25 off the regular price!

Fax a copy of this printable order form to 703-522-5846 to take advantage of this special offer - $124 (regular price: $149) -->

This expanded glossary entry is sponsored by Resampling Stats.

Click here for more information on the Resampling Stats Add-In for Excel

Browse Other Glossary Entries

Courses Using This Term

Loading...
Biostatistics 1 – For Medical Science and Public Health
This course will teach you the principal statistical concepts used in medical and health sciences. Basic concepts common to all statistical analysis are reviewed, and those concepts with specific importance in medicine and health are covered in detail.
Return to Glossary Search

About Statistics.com

Statistics.com offers academic and professional education in statistics, analytics, and data science at beginner, intermediate, and advanced levels of instruction. Statistics.com is a part of Elder Research, a data science consultancy with 25 years of experience in data analytics.

 The Institute for Statistics Education is certified to operate by the State Council of Higher Education for Virginia (SCHEV)

Our Links

  • Contact Us
  • Site Map
  • Explore Courses
  • About Us
  • Management Team
  • Contact Us
  • Site Map
  • Explore Courses
  • About Us
  • Management Team

Social Networks

Facebook Twitter Youtube Linkedin

Contact

The Institute for Statistics Education
2107 Wilson Blvd
Suite 850 
Arlington, VA 22201
(571) 281-8817

ourcourses@statistics.com

  • Contact Us
  • Site Map
  • Explore Courses
  • About Us
  • Management Team

© Copyright 2023 - Statistics.com, LLC | All Rights Reserved | Privacy Policy | Terms of Use

By continuing to use this website, you consent to the use of cookies in accordance with our Cookie Policy.

Accept