Nonparametric-Methods.pptx

CHAPTER 14:Nonparametric Methodsto accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 14-Learning ObjectivesDifferentiate between nonparametric and parametric hypothesis tests.Determine when a nonparametric test should be used instead of its parametric counterpart.Appropriately apply each of the nonparametric methods introduced.2002 The Wadsworth GroupChapter 14 Key TermsNonparametric testsWilcoxon signed rank test:One samplePaired samplesWilcoxon rank sum test,two independent samplesKruskal-Wallis Test,three or more independent samplesFriedman test,randomized block designSign Test,paired samplesRuns test for randomnessLilliefors test for normality 2002 The Wadsworth GroupNonparametric TestsAdvantages:Fewer assumptions about the populationShapeVarianceValid for small samplesDefined over a range of variables,nominal and ordinal scales includedCalculations simpleDisadvantages:Sample data used less efficientlyPower of nonparametric analysis lowerPlaces greater reliance on statistical tables if computer statistical package or spreadsheet not being used 2002 The Wadsworth GroupWilcoxon Signed Rank Test,One SampleRequirements:Variable-Continuous dataScale-Interval or ratio scale of measurementThe Research Question(H1):Test the value of a single population median,m,m0Critical Value/Decision Rule:W,Wilcoxon signed rank test 2002 The Wadsworth GroupAn ExampleProblem 14.8:According to the director of a county tourist bureau,there is a median of 10 hours of sunshine per day during the summer months.For a random sample of 20 days during the past three summers,the number of hours of sunshine has been recorded below.Use the 0.05 level in evaluating the directors claim.8 9 810 9 7 7 9 7 7 9 811 910 7 811 812 2002 The Wadsworth GroupAn Example,continuedhrs.di|di|hrs.di|di|822911 911822 82211+1110 00911 91110 00 733733 733822 91111+11 733822 73312+22There are:7 with rank 11,2,3,4,5,6,7average rank=46 with rank 28,9,10,11,12,13average rank=10.55 with rank 314,15,16,17,18average rank=16 2002 The Wadsworth GroupAn Example,continuedhrs.di|di|Rank R+R hrs.di|di|Rank R+R 8 2210.5-10.59114-4 9 114-482210.5-10.58 2210.5-10.511+1144-10 00-9114-49 114-410 00-7 3316-1673316-167 3316-1682210.5-10.59 114-411+1 144-7 3316-1682210.5-10.57 3316-1612+2 210.510.5-So,SR+=18.5,SR=152.5 2002 The Wadsworth GroupAn Example,continuedI.H0:m=10 hours H1:m 10 hoursII.Rejection Region:a=0.05,n=18 data values not equal to the hypothesized median of 10If SR+130,reject H0.III.Test Statistics:SR+=18.5 SR=152.5 2002 The Wadsworth GroupAn Example,concludedIV.Conclusion:Since the test statistic of SR+=18.5 falls below the critical value of W=41,we reject H0 with at least 95%confidence.V.Implications:There is enough evidence to dispute the directors claim that this county has a median of 10 days of sunshine per day during the summer months.2002 The Wadsworth GroupWilcoxon Signed Rank Test forComparing Paired SamplesRequirements:Variable-Continuous dataScale-Interval or ratio scale of measurementThe Research Question(H1):Test the difference in two population medians,paired samples,md,1.96 orz 1.96,reject H0.III.Test Statistic:z=2.59 2002 The Wadsworth GroupAn Example,concludedIV.Conclusion:Since the test statistic of z=2.59 falls below the critical bound of z=1.96,we reject H0 with at least 95%confidence.V.Implications:There is enough evidence to show that the sequence is not random.2002 The Wadsworth GroupLilliefors Test for NormalityRequirements:Scale-Interval or ratio scaleHypothesized distribution must be completely specified.The Research Question(H1):The sample was not drawn from a normal distribution.Critical Value/Decision Rule:D=max|Fi Ei|2002 The Wadsworth Group