# 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
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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 views: 255 posted: 2/26/2012 language: English pages: 23