Bluman A.G. Elementary Statistics- A Step By Step Approach

688 Chapter 13 Nonparametric StatisticsMann-Whitney Test and CI: Army, MarinesN MedianArmy 12 18.500Marines 11 14.000Point estimate for ETA1-ETA2 is 6.00095.5 Percent CI for ETA1-ETA2 is (1.003, 9.998)W = 183.0Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0178The test is significant at 0.0177 (adjusted for ties)The P-value for the test is 0.0177. Reject the null hypothesis. There is a significant differencein the times it takes the recruits to complete the course.ExcelStep by StepThe Wilcoxon Mann-Whitney TestExcel does not have a procedure to conduct the Mann-Whitney rank sum test. However, youmay conduct this test by using the MegaStat Add-in available on your CD. If you have notinstalled this add-in, do so, following the instructions from the Chapter 1 Excel Step by Step.1. Enter the data from Example 13–4 into columns A and B of a new worksheet.2. From the toolbar, select Add-Ins, MegaStat>Nonparametric Tests>Wilcoxon-Mann/Whitney Test. Note: You may need to open MegaStat from the MegaStat.xls file onyour computer’s hard drive.3. Type A1:A12 in the box for Group 1.4. Type B1:B11 in the box for Group 2.5. Check the option labeled Correct for ties, and select the “not equal” Alternative.6. Click [OK].Wilcoxon Mann-Whitney Testn Sum of ranks12 183 Group 111 93 Group 223 276 Total144.00 Expected value16.23 Standard deviation2.37 z, corrected for ties0.0177 P-value (two-tailed)The P-value is 0.0177. Reject the null hypothesis.13–4 The Wilcoxon Signed-Rank TestObjective 4Test hypotheses, usingthe signed-rank test.When the samples are dependent, as they would be in a before-and-after test using thesame subjects, the Wilcoxon signed-rank test can be used in place of the t test for dependentsamples. Again, this test does not require the condition of normality. Table K is usedto find the critical values.The procedure for this test is shown in Example 13–5.Example 13–5Shoplifting IncidentsIn a large department store, the owner wishes to see whether the number ofshoplifting incidents per day will change if the number of uniformed securityofficers is doubled. A sample of 7 days before security is increased and 7 days after theincrease shows the number of shoplifting incidents.13–18