Mann- Whitney Test.pptx

This is one of the test used in the statistical analysis of data

1. /Application

2. What is it? It is a non-parametric test used to test whether two independent samples were selected from population having the same distribution.

3. It allows you to draw different conclusions about your data depending on the assumptions you make about your data's distribution.

4. These conclusions can range from simply stating whether the two populations differ through to determining if there are differences in medians between groups. These different conclusions hinge on the shape of the distributions of your data.

5. & APPLICATION

6. The Mann-Whitney test is used as an alternative to a  t  test when the data are not normally distributed. A Mann-Whitney test is used when we have a continuous level variable measured for all observations in two groups and we want to test if the distribution of this variable is different in the two groups but we are unable to assume normality in both groups.

7. The test can detect differences in shape and spread as well as just differences in medians. It can also be used to compare an ordered categorical variable measured on two groups. It is the non-parametric equivalent of the independent-samples t-test but unlike the t-test it tests for differences in the overall distribution across groups rather than for differences in the mean.

8. Solution Steps: State the null and alternative hypothesis Non- directional : H0: μ 1  = μ 2 H1: μ 1  ≠ μ 2 Directional : H0: μ 1   μ 2 H1: μ 1   μ 2  

9. 2. Perform a ranking of all the observation. 3. Calculate the Rank Sums

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11. 6. Draw conclusion If Ustat < Ucrit Decision: Reject the null hypothesis Conclusion: There is significant difference … If Ustat > Ucrit Decision: Do not reject the null hypothesis Conclusion: There is no significant difference …

12. Example 1 A  researcher gave an aptitude test to 24 respondents, 12 were male and 12 of them were female. He recorded the scores for each of the respondents and tabulated it in the table below: At 5% level of significance, is there a significant difference between the ranks according to the sex category?

13. Solution Steps: State the null and alternative hypothesis H0: There is no significant difference between the ranks according to the sex category. H0: μ 1  = μ 2 H1: There is a significant difference between the ranks according to the sex category. H1: μ 1  ≠ μ 2

14. 2. Perform a ranking of all the observation Men Women 80 82 79 87 92 89 65 91 83 93 84 76 95 74 78 70 81 88 85 99 73 61 52 94

15. 2. Perform a ranking of all the observation Men Rank Women Rank 80 10 82 12 79 9 87 16 92 20 89 18 65 3 91 19 83 13 93 21 84 14 76 7 95 23 74 6 78 8 70 4 81 11 88 17 85 15 99 24 73 5 61 2 52 1 94 22

16. 3. Calculate the Rank Sums Men Rank Women Rank 80 10 82 12 79 9 87 16 92 20 89 18 65 3 91 19 83 13 93 21 84 14 76 7 95 23 74 6 78 8 70 4 81 11 88 17 85 15 99 24 73 5 61 2 52 1 94 22 Rank Sum (n1) 132 Rank Sum (n2) 168

17. 4. Calculate the U Statistic for the Two Groups Formula: Note: Use U stat with the smaller value between the two groups: U stat = 54 +

18. 5. Determine the Critical Value using the Mann-Whitney U Table *Since H1 is non-directional, use the two tailed testing. U crit = 37

19. 6. Draw conclusion U stat > U crit Decision: Do not reject the null hypothesis Conclusion: There is no significant difference between the ranks according to the sex category.

20. Note: In utilizing Mann-Whitney U Test in SPSS there is no need to sort and rank the given data. Directly input the data in the SPSS and analyze.

21. Thank you for listening.