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Nonparametric tests: Tests without population parameters (means and standard deviations)

Nonparametric tests: Tests without population parameters (means and standard deviations). Use when: Data does not support means (ordinal) Data is not normally distributed. 1) Rank all data. 2) Evaluate if ranks tend to cluster within a group. Mann Whitney U test:

cullen-jenkins
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Nonparametric tests: Tests without population parameters (means and standard deviations)

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  1. Nonparametric tests: Tests without population parameters (means and standard deviations)

  2. Use when: • Data does not support means (ordinal) • Data is not normally distributed.

  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: Size of sample one Size of sample two

  6. Mann Whitney U test: Where: Sum of sample one ranks 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. Step One: Rank all data across groups group 1 group 2 24 28 18 2 42 45 63 57 57 12 1 90 30 68

  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. Check the rankings:

  19. 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

  20. 26.5 + 51.5 = 78

  21. Step Three: Compute U1

  22. Step Four: Compute U2

  23. Step Five: Compare U1 to U2

  24. Critical Value = 5 This is a nonsignificant outcome

  25. 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

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