Mann Whitney U test

This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.

1. Mann Whitney U test:
By: Dr. Ankit Gaur (B.Pharm, M.Sc, Pharm.D, RPh)

2. Use when:
• Data does not support means (ordinal)
• Data is not normally distributed.
Nonparametric tests:
Tests without population parameters
(means and standard deviations)

3. 1) Rank all data.
2) Evaluate if ranks tend to
cluster within a group.

4. Mann Whitney U test:
nonparametric equivalent of a t test
for two independent samples

5. Mann Whitney U test:
Where:n
1
n
2
()()
( )
()()
( )
Unn
nn
R
U nn
nn
R
1 1 2
11
1
2 1 2
22
2
1
2
1
2
= +
+
-
= +
+
-
å
å
Size of sample one
Size of sample two

6. Mann Whitney U test:
Where:
()()
( )
()()
( )
Unn
nn
R
U nn
nn
R
1 1 2
11
1
2 1 2
22
2
1
2
1
2
= +
+
-
= +
+
-
å
å
R
1å
Sum of sample one ranks
R
2å
Sum of sample two ranks

7. Evaluation of Mann Whitney U
1) Choose the smaller of the two U values.
2) Find the critical value (Mann Whitney table)
3) When computed value is smaller than the
critical value the outcome is significant!

8. group 1 group 2
24 28
18 42
45 63
57 57
12 90
30 68

9. group 1 group 2
24 28
18 2 42
45 63
57 57
12 1 90
30 68
Step One: Rank all data across groups

10. group 1 group 2
24 3 28 4
18 2 42
45 63
57 57
12 1 90
30 68

11. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63
57 57
12 1 90
30 5 68

12. Tied ranks:
• Find all values that are tied.
• Identify all ranks that would be
assigned to those values.
• Average those ranks.
• Assign that average to all tied values.

13. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63
57 57
12 1 90
30 5 68

14. 8th and 9th ranks would be used.
8+9 = 17 Averaging
17/ 2 = 8.5 ranks

15. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63
57 8.5 57 8.5
12 1 90
30 5 68

16. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63 10
57 8.5 57 8.5
12 1 90 12
30 5 68 11

17. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63 10
57 8.5 57 8.5
12 1 90 12
30 5 68 11
26.5 51.5
Step Two: Sum the ranks for each group

18. ( )
R
nn
=
+
å
1
2
Check the rankings:

19. ( )()
R
R
R
=
=
=
å
å
å
1213
2
156
2
78

20. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63 10
57 8.5 57 8.5
12 1 90 12
30 5 68 11
26.5 51.5

21. 26.5 + 51.5 = 78

22. ()()
( )
Unn
nn
R
1 1 2
11
1
1
2
= +
+
-å
Step Three: Compute U
1

23. ()()
( )
()()
()
Unn
nn
R
U
U
U
1 1 2
11
1
1
1
1
1
2
66
67
2
265
3621265
305
= +
+
-
= + -
=+-
=
å
.
.
.

24. ()()
( )
U nn
nn
R
2 1 2
22
2
1
2
= +
+
-å
Step Four: Compute U
2

25. ()()
( )
()()
()
U nn
nn
R
U
U
U
2 1 2
22
2
2
2
2
1
2
66
67
2
515
3621515
55
= +
+
-
= + -
=+-
=
å
.
.
.

26. U
U
U
1
2
305
55
55305
55
=
=
<
=
.
.
. .
.
Step Five: Compare U
1
to U
2

27. Critical Value = 5
This is a nonsignificant outcome

28. group 1 group 2
24 3 28 4
18 2 42 6
45 7 63 10
57 8.5 57 8.5
12 1 90 12
30 5 68 11

29. Thank you… “Believe in yourself
those who do not believe in
themselves cannot achieve
anything in their lives.