Mann-Whitney U Test (Nonparametric Test).pptx

Mann-Whitney U Test (Nonparametric Test).pptx

1. Nonparametric Test Mann-Whitney U Test

2. LEARNING OBJECTIVES Determine when to use parametric to nonparametric tests Highlight the history and the assumptions of the Mann-Whitney U test. Differentiate t-test of independence to Mann-Whitney U test. Identify the critical values and hypothesis for Mann-Whitney U test. Calculate the U statistic and infer it.

3. What is U Test 01 Nonparametric Test

4. What can you say about the shape of the curves of the two figures above?

5. What can you say about the shape of the curves of the two figures above? bell-shaped curve off-centered curve normal distribution skewed distribution or not normal distribution

6. What can you say about the shape of the curves of the two figures above? bell-shaped curve off-centered curve normal distribution skewed distribution or not normal distribution Use NONPARAMETRIC TESTS analyze statistical data infer findings to in order to

7. Wilcoxon Signed Rank Test Spearman’s rho NONPARAMETRIC TESTS Mann-Whitney U Test Kruskal Wallis Test Friedman Test

8. NONPARAMETRIC TESTS Mann-Whitney U Test What is ?

9. Mann-Whitney U Test

10. Mann-Whitney U Test Both the one-sample signed rank and the two-sample rank sum test were devised by me as part of a significance test that opposed a point null hypothesis against its complementary alternative, or equal vs not equal. However, I only tabulated a few points for the equal-sample size situation in that work (although I provided larger tables in a later publication).

11. Mann-Whitney U Test In 1947, my student Donald Ransom Whitney and I published a paper that featured a recurrence that allowed us to compute tail probabilities for arbitrary sample sizes as well as tables for sample sizes of eight or fewer.

12. Mann-Whitney U Test

13. Mann-Whitney U Test The Mann-Whitney U test is the nonparametric counterpart to the t-test for independent samples Group A Group B

14. Assumptions,Critical Values and Hypothesis 02 Nonparametric Test

15. ASSUMPTIONS two independent samples at least ordinal scaled characteristic of groups not normally distributed

16. ASSUMPTIONS two independent samples Group A Group B

17. ASSUMPTIONS at least ordinal scaled characteristic of groups two independent samples

18. at least ordinal scaled characteristic of groups ASSUMPTIONS two independent samples Group A Group B comparing gender to salary

19. ASSUMPTIONS Group A Group B comparing gender to salary not normally distributed at least ordinal scaled characteristic of groups

20. FORMULA (if n ≤ 20 for both groups)   U statistic for the first group   U statistic for the second group final U statistic   Where: is the sum of the ranks of the first group, is the sample size of the first group, and is the sample size of the second group   Where: is the sum of the ranks of the second group, is the sample size of the first group, and is the sample size of the second group   the lower U value is the U statistic

21. CRITICAL VALUES for α = 0.05

22. HYPOTHESIS H : There is no difference (in terms of central tendency) between the two groups in the population. H 1 : There is a difference (in terms of central tendency) between the two groups in the population. if U > critical value if U ≤ critical value

23. Computing the U Statistic 03 Nonparametric Test

24. EXAMPLE Gender Response time female 34 male 33 male 35 female 37 female 44 male 45 female 36 male 39 female 41 female 43 male 42 A research was conducted to see if males and females have different response time (in seconds) when it comes to problems.

25. EXAMPLE Gender Response time female 34 male 33 male 35 female 37 female 44 male 45 female 36 male 39 female 41 female 43 male 42 Do a normality test not normally distributed

26. EXAMPLE Gender Response time female 34 male 33 male 35 female 37 female 44 male 45 female 36 male 39 female 41 female 43 male 42 Group the data according to gender group

27. EXAMPLE Gender Response time Rank female 34 female 36 female 41 female 43 female 44 female 37 male 45 male 33 male 35 male 39 male 42 Assign rank to each data starting from lowest to highest 1 2 3 4 5 6 7 8 9 10 11

28. EXAMPLE Gender Response time Rank female 34 female 36 female 41 female 43 female 44 female 37 male 45 male 33 male 35 male 39 male 42 Calculate the rank sums of each group and find the number of samples per group 1 2 3 4 5 6 7 8 9 10 11 R 1 =37 2+4+7+9+10+5=37 R 2 =29 11+1+3+6+8=29 n 1 =6 n 2 =5

29. EXAMPLE Find the critical value (CV) at 0.05 significance level n 1 =6 n 2 =5 CV = 3

30. EXAMPLE Find the U statistic for each group R 1 =37 R 2 =29 n 1 =6 n 2 =5     CV = 3        

31. EXAMPLE Find the U statistic and compare to CV CV = 3           H : if U > critical value H 1 : if U ≤ critical value

32. EXAMPLE Find the U statistic and compare to CV CV = 3           H : if U > critical value H 1 : if U ≤ critical value  

33. EXAMPLE Make conclusions based on the test statistic H : if U > critical value Accept H There is no difference between the males and females towards the response time when it comes to problems.