# Describe their methodology 3 what adjustment has to

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Describe their methodology ? 3) What adjustment has to be made for ties in Kruskal-Wallies H test ? 15.6. SUMMARY The Mann-whitney U test and the Kruskal-Wallis test are called rank sum test because the test depends on the ranks of the sample observations. Ties often occur when ranking the data to perform a Mann-Whitney U test or a Kruskal-Wallis test, whenever you encounter such ties, remember that each tied value gets an average rank. Kruskal-Wallis method is the magnitude of observations is compared with every other observation by considering the ranks. 15. 7. TERMINAL EXERCISES 1) Summaries assumption of Mann-Whitney U test. 2) Give uses of Kruskal- Wallis test. 3) Give one important difference between sign test and rank test. Choose the correct answers: 1) Mann-Whitney test statistic U depends on the fact test. a. How many times Y’s precede X’s b. How many times X’s precede Y’s c. Both (a) and (b) d. None of (a) and (b) 2) If 1 n and 2 n in Mann-Whitney test are large, the variable U is distributed with mean a. 1 2 2 n n b. 1 2 2 n n c. 1 2 2 n n d. 1 2 n n 3) Kruskal Wallis analysis of data is meant for a. One way classification b. Two way classification c. Non-classified data d. None of the above 4) The statistic H under the Kruskal Wallies test is approximately distributed as a. Student-t b. Snede cor’s F c. Chi-square d. Normal deviate Z

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130 15.8. SUPPLEMENTARY MATERIALS 1) 2) 3) 4) 15.9. ASSIGNMENTS 1) Two quality control departments independently collected 25 articles from each production run and tested, them for quality. The numbers of defectives per production run were as follows Department A : 6 3 1 3 0 5 2 7 3 5 6 2 Department B : 8 3 4 3 5 3 1 5 7 6 Test the hypothesis that the two quality control departments have drawn the samples from the same population using the Mann-Whitney U test. 2) A particular consumer product sold in department stores is often purchased on impulse. Three different stores were tried for this product over a 26 week period and weekly sales in units for each store is given as follows. Store 1 : 26, 13, 27, 18, 24, 34, 40, 25, 28 Store 2 : 28, 31, 15, 33, 36, 42, 44, 18 Store 3 : 21, 12, 23, 25, 17, 19, 28, 30, 22 Using the Kruskal-Wallis test, evaluate the hypothesis that there is no difference in distribution of sales at the three different stores. 3) Samples have been taken from two branches of a chain of stores. The samples relate to the daily turn over of both the branches. Is there any difference in turnover between the two branches Branch 1: 23500 25500 35500 19500 24400 24000 23600 25900 26000 Branch 2 : 24000 19800 22000 21500 24500 4) An accounting firm wants to find out whether the current ratio for three companies is same. Random samples of eight firms in industry A, six firms in industry B, and six firms in industry C are available. The current ratios are as follows Company A Company B Company C 1.38 1.55 1.90 2.00 1.22 2.11 1.98 1.61 2.33 2.50 2.79 3.01 1.99 2.45 1.06 1.37 1.09 1.65 1.44 1.11 Conduct the test at 0.05 level of significance, and state your conclusion.
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• Spring '12
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