### mannwhitney-180814080907.pdf

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: n1 n2 ( )( ) ( ) ( )( ) ( ) U n n n n R U n n n n R 1 1 2 1 1 1 2 1 2 2 2 2 1 2 1 2 = + + − = + + − ∑ ∑ Size of sample one Size of sample two
6. Mann Whitney U test: Where: ( )( ) ( ) ( )( ) ( ) U n n n n R U n n n n R 1 1 2 1 1 1 2 1 2 2 2 2 1 2 1 2 = + + − = + + − ∑ ∑ R1 ∑ Sum of sample one ranks R2 ∑ 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 n n = + ∑ 1 2 Check the rankings:
19. ( )( ) R R R = = = ∑ ∑ ∑ 12 13 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. ( )( ) ( ) U n n n n R 1 1 2 1 1 1 1 2 = + + − ∑ Step Three: Compute U1
23. ( )( ) ( ) ( )( ) ( ) U n n n n R U U U 1 1 2 1 1 1 1 1 1 1 2 6 6 6 7 2 265 36 21 265 305 = + + − = + − = + − = ∑ . . .
24. ( )( ) ( ) U n n n n R 2 1 2 2 2 2 1 2 = + + − ∑ Step Four: Compute U2
25. ( )( ) ( ) ( )( ) ( ) U n n n n R U U U 2 1 2 2 2 2 2 2 2 1 2 6 6 6 7 2 515 36 21 515 55 = + + − = + − = + − = ∑ . . .
26. U U U 1 2 305 55 55 305 55 = = < = . . . . . Step Five: Compare U1 to U2
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.