Mann-Whitney U-Test

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					Mann-Whitney U-Test

             By:
Dr Wan Azlinda Wan Mohamed
          Mann-Whitney U test
• The Mann-Whitney U test, also called the rank
  sum test, is a non-parametric test that compares
  two independent (unmatched) groups.
• This means that either the data are at the ordinal
  level or data are at the interval/ratio level but not
  normally distributed.
• The test statistic is the U statistic. This is the test
  that you use if you cannot fulfill the assumptions
  of the t-test.
         Mann-Whitney U test
• This test is an alternative to the independent
  group t-test
• Assumption of normality or equality of variance
  is not met.
• Like many non-parametric tests, uses the ranks
  of the data rather than their raw values to
  calculate the statistic.
• Since this test does not make a distribution
  assumption, it is not as powerful as the t-test.
       Mann-Whitney U test
The hypotheses for the comparison of two
  independent groups are:
• Ho: The two samples come from identical
  populations / the sum of the ranks is
  similar
• Ha: The two samples come from different
  populations / the sum of the ranks is
  different
         Mann-Whitney U test
• The hypothesis makes no assumptions about
  the distribution of the populations. These
  hypotheses are also sometimes written as
  testing the equality of the central tendency of the
  populations.
• The test statistic for the Mann-Whitney test is U.
  This value is compared to a table of critical
  values for U based on the sample size of each
  group.
• If U is less than the critical value for U at some
  significance level (usually 0.05) it means that
  there is evidence to reject the null hypothesis in
  favor of the alternative hypothesis.
Procedure for Mann-Whitney U-Test
1. Why choose Mann-Whitney Test
2. Hypotheses Null and hypotheses
   Alternative
3. Assign ranks to all the scores in the
   experiment.
4. Compute the sum of the ranks for each
   group.
5. Compute the two version of the Mann-
   Whitney U. Fist compute U1 for Group 1
   using the formula:
   U1 = (n1)(n2) + n1 (n1 + 1) - Σ R1
  Procedure for Mann-Whitney U-
               Test
    Next compute U2 for Group 2 using the formula:
    U2 = (n1)(n2) + n2 (n2 + 1) - Σ R2
                         2
4. Determine the Mann_Whitney Uobt.
5. Find the critical value
6.Compare Uobt to Ucritt .
7. Intrepret, and make decision.
8. Draw conclusion
                  Example:
• Data shown are score on an algebra readiness
  test given to two math classes. Each class
  participated in a different math program during
  the past year. One class used a traditional
  program involving lots of paper/pencil and
  bookwork, and the other used a hands-on
  program with lots of tokens and objects that the
  students were required to move about in order to
  solve the problems. Determine if there is any
  difference in the test scores of the two types of
  classes at α = 0.05.
                 Solution:
• H0: There is no difference in the test
  scores for the two type of classes.
• H1: There is a difference in test score for
  the two type of classes (claim)
                 Solution:
U1 = (n1)(n2) + n1 (n1 + 1) - Σ R1
                     2
   = (18)(13) + (18)(19) – 208
                     2
   = 234 + 342 - 208
               2
   = 197
                 Solution:
U2 = (n2)(n1) + n2 (n2 + 1) - Σ R2
                     2
   = (13)(18) + (13)(14) – 288
                     2
   = 234 + 182 - 288
               2
   = 37
                   Solution:
To check your computation of U:
U1 + U2 = n1.n2        197 +37 = (18)(13)
                             234 = 234
It checks out, and because U is the smaller of U1
   and U2, U = 37
Critical value: Using n1 = 18 and n2 = 13, at a =
   0.05, the critical value is 67.
Reject null hypothesis , since Uobt less than Ucrit
There is a difference between the two classes on
   the algebra readiness test.
                Exercise:
• The managers of a company wants to
  know whether people who went through a
  training program designed and
  administered at a local community college
  are significantly better workers than those
  who did not participate in the program.
  The data are as shown.
                 Solution:
• H0: There is no difference in the in the job
  performance of people who went for
  training and no training.
• H1: People who went through a training
  program are significantly better workers
  than those who did not participate in the
  program (claim)
                 Solution:
U1 = (n1)(n2) + n1 (n1 + 1) - Σ R1
                     2
   = (11)(9) + (11)(12) – 141
                     2
   = 99 + 132 - 141
              2
   = 24
                 Solution:
U2 = (n1)(n2) + n2 (n2 + 1) - Σ R1
                     2
   = (11)(9) + (9)(10) – 69
                     2
   = 99 + 90 - 69
             2
   = 75
                   Solution:
To check your computation of U:
U1 + U2 = n1.n2        24 +75 = (11)(9)
                             99 = 99
It checks out, and because U is the smaller of U1
   and U2, U = 24
Critical value: Using n1 = 11 and n2 = 9, at a =
   0.05, the critical value is 27
Reject null hypothesis , since Uobt lesser than Ucrit
There is a difference in the in the job performance
   of people who went for training and no training.
.
Thank You

				
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posted:2/26/2012
language:English
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