Mann-Whitney U Test

1
Mann-Whitney U Test

• Assoc. Prof. Chanchai Hosanguan
• Department of Community Dentistry
• Chulalongkorn University

2
(No Transcript)
3
?????????????????? Mann-Whitney U test

• Research question The difference between two
  population means
• Two independent samples
• Can not make necessary assumptions for t-test
• At least ordinal data

4
Review Assumptions

• Two random samples
• Samples are independent
• Normal distribution
• Population variances are equal

5
State hypothesis

• For 2-tail hypothesis
• HO M1 M2
• HA M1 ? M2
• where M1 median score of group 1
• M2 median score of group 2

6
State hypothesis

• For 1-tail hypothesis
• HO M1 ? M2
• HA M1 lt M2
• Or
• HO M1 ? M2
• HA M1 gt M2

7
Test statistic

• Let Un Rn - n(n1)
• 2
• Um Rm - m(m1)
• 2
• Choose U smaller of Un, Um as the test
  statistic.
• Where n number of observations in group 1
• m number of observations in group 2
• Rn sum of the ranks assigned to group 1
• Rm sum of the ranks assigned to group 2

8
State decision rule

• If U ? Ucritical
• then the difference is statistically significant
  at the ? level.
• Reject the null hypothesis

9
Calculation of U

• 1. Rank each observation of combined two samples
  in an ascending order, while keeping track of the
  sample.
• 2. For tied observations, assign a rank equal to
  the mean of the rank positions for which they are
  tied.
• 3. Compute sum of the rank values assigned to
  observations in the first and second groups.
  Label as Rn and Rm.
• 4. Compute Un and Um.

10
Example

• In an experiment designed to assess the impact of
  a CO2 Laser on enamel surfaces, 15 teeth were
  lased at low power laser (1W) and 10 teeth
  received higher power level (5W).

11
Example
12
Example Ranking of data
13
Example Calculation of U

• Un 145 - 15(151) / 2 25
• Um 180 - 10(101) / 2 125
• Choose Un 25 as the test statistic

14
Example Decision rule

• If U ? U0.05, 15, 10 (which is 39)
• then the difference is statistically significant
  at the 0.05 level.

15
Example Conclusion

• U (25) lt U0.05, 15, 10 (39)
• therefore the difference is statistically
  significant at the 0.05 level.

16
Example SPSS data file
17
Example SPSS Command
18
Example
19
Example Output interpretation
p-value lt 0.05
20
(No Transcript)