MANN WHTNEY U TEST.pptx

EDUCATIONAL PURPOSES

1. A D V A N C E STATISTICS MTH - 11 4 INSTR: VINCENT B. VALLEJO

2. MANN- WHITNEY U TEST - The Mann–Whitney  U  Test is a popular test for comparing two independent samples. It is a nonparametric test, as the analysis is undertaken on the rank order of the scores and so does not require the assumptions of a parametric test.

3. MANN- WHITNEY U TEST - It was originally proposed by Frank Wilcoxon in 1945 for equal sample sizes, but in 1947 H. B. Mann and D. R. Whitney extended it to unequal sample sizes (and also provided probability values for the distribution of  U , the test statistic).

4. MANN- WHITNEY U TEST - The  Mann–Whitney  U  test  is the non-parametric alternative to the Independent-samples t-test. The test is used to test for differences between two independent groups on ordinal data or non-normal continuous data .

5. MANN- WHITNEY U TEST Instead of comparing the means of the two groups, as in the case of the t-test, the Mann-Whitney U Test compares medians . It then evaluates whether the ranks for the two groups differ significantly. As the scores are converted to ranks, the actual distribution of the scores does not matter. - Known as Wilcoxon Rank Sum Test or Wilcoxon -Mann-Whitney Test .  

6. Examples: 1. A company Quality manager would like to know if there is a difference in the service quality received by Suppliers and Customers. Few scenarios in which you could use the Mann-Whitney  U  test Examples: 2. A market researcher would like to investigate if there are differences in attention to Social Media differs between Male and Female. Examples: 3. An HR Manager would like to investigate if the compensation offered to the two departments (Finance & HR) is significantly different. So the HR manager collected data from 10 personnel from each department. Examples: 4. An educationist would like to evaluate the difference in attentiveness of male and female students.

7. 1. The sample drawn from the population is random. ASSUMPTIONS IN MANN-WHITNEY U TEST 2. Independence within the samples and mutual independence is assumed. 3. Measurement scale is at least ordinal. 4. If the two populations are different, their difference lied only in location – meaning the two population have the same variations.

8. 1 . Set up the hypothesis: H0: Population are identical. H1: Population are not identical.   OR; PROCEDURE FOR MANN-WHITNEY U TEST 1 . Set up the hypothesis: H0: All the population distribution functions are identical. H1: At least one of the populations tends to yield a larger observation than the least one of the other population.

9. 2. Compute the value of Mann-Whitney U Test; PROCEDURE FOR ONE SAMPLE T-TEST

10. PROCEDURE FOR ONE SAMPLE T-TEST

11. PROCEDURE FOR ONE SAMPLE T-TEST

12. An entrepreneur with loading business is interested to determine if there is a difference in the amounts spent in mobile phone loads by men and women. A sample of 7 men and 8 women is selected. Each person is asked to keep a record of the amount they spend for mobile phone loads in a week. The result are as follows Examples: Amounts Spent by Men 100 90 120 145 60 75 100 Amounts Spent by Women 130 135 150 50 80 110 140 180

13. Assume that the distributions of amounts spent by the men and women are not normally distributed. At 0.05 significance level, is there a difference in the distributions of amounts spent by men and women?   Examples: