Mann-Whitney U Test.pptx

Statistics Learning Materials

1. Mann-Whitney U Test Roseclyde D. Lucasan MTLED-Home Economics

2. What is Mann-Whitney U test? It tests whether there is a difference between two independent samples.

3. Example: Is there a difference between the reaction time of women and men ?

4. But the t-test for independent samples does the same. It also tests whether there is a difference between two independent samples.

5. The Mann-Whitney U Test is the non-parametric counterpart to the t-test for independent samples.

6. But there is an important difference between the two tests.

7. The t-test for independent samples tests whether there is a mean difference. For both samples, the mean value is calculated and it is tested whether these mean values differ significantly. - - - - - - - - - - - -

8. The Mann-Whitney U test, on the other hand, checks whether there is a rank sum difference.

9. How do we calculate the rank sum? For this purpose, we sort all persons from the smallest to the largest value.

10. This person has the smallest value, so gets rank 1,

11. this person has the second smallest value, so gets rank 2.

12. And this person has the third smallest value,

13. Now we have assigned a rank to each person. Then we can simply add up the ranks of the first group and the second group .

14. And in the second group a rank of 36. In the first group we get a rank of 42

15. Now we can investigate whether there is a significant difference between these rank sums.

16. The advantage of taking the rank sums rather than the difference in means is that the data need not be normally distributed.

17. So, in contrast to the t-test, the data in the Mann-Whitney U test do not have to be normally distributed.

18. What are the hypotheses of the Mann-Whitney U test? The null hypotheses is: In the two samples, the rank sums do not differ significantly. The alternative hypotheses is: In the two samples, the rank sums do differ significantly.

19. Gender Reaction time Female 34 Female 36 Female 41 Female 43 Female 44 Female 37 Male 45 Male 33 Male 35 Male 39 Male 42 Data are not normally distributed no t-Test But Mann-Whitney U Test

20. Gender Reaction time Rank Female 34 2 Female 36 4 Female 41 7 Female 43 9 Female 44 10 Female 37 5 Male 45 11 Male 33 1 Male 35 3 Male 39 6 Male 42 8 Calculation of the rank sums T₁ =2+4+7+9+10+5=37 T₂ =11+1+3+6+8=29 Null hypothesis: Both rank sums are the same.

21. Female Rank sum number of cases T₁ =37 n ₁ =6 =6 ∙5+6∙(6+1)/2 -37 =14 Male Rank sum number of cases T₂ =29 n₂ =5 = 6 ∙5+5∙(5+1)/2 -29 =16 U-value Expected value of U Standard error of U Z-value

22. Depending on how large the sample is, the p-value for the Mann-Whitney U test is calculated in different ways.

23. For up to 25 cases the exact values are used, which can be read from a table.

24. For large samples, the normal distribution of the U-value can be used as an approximation.

25. In our example, we would actually use the exact values, nevertheless, we assume a normal distribution.

26. The p-value of 0.855 is greater than the significance level of 0.055 and thus, the null hypothesis cannot be rejected based on this sample.