Bài giảng Business Research Methods - Chapter 17: Hypothesis Testing

Learning Objectives Understand . . . The nature and logic of hypothesis testing. A statistically significant difference The six-step hypothesis testing procedure.

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Chapter 17Hypothesis TestingMcGraw-Hill/IrwinCopyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved. Learning ObjectivesUnderstand . . . The nature and logic of hypothesis testing.A statistically significant differenceThe six-step hypothesis testing procedure.2Learning ObjectivesUnderstand . . .The differences between parametric and nonparametric tests and when to use each.The factors that influence the selection of an appropriate test of statistical significance.How to interpret the various test statistics3Hypothesis Testing vs. Theory“Don’t confuse “hypothesis” and “theory.”The former is a possible explanation; thelatter, the correct one. The establishmentof theory is the very purpose of science.”Martin H. Fischer professor emeritus. physiologyUniversity of Cincinnati4PulsePoint: Research Revelation$28The amount, in billions, saved by North American companies by having employees use a company purchasing card.5Hypothesis TestingDeductiveReasoningInductive Reasoning6Hypothesis Testing Finds Truth“One finds the truth by making a hypothesis and comparing the truth to the hypothesis.”David Douglass physicistUniversity of Rochester7Statistical ProceduresDescriptive StatisticsInferential Statistics8Hypothesis Testing and the Research Process9When Data Present a Clear PictureAs Abacus states in this ad, when researchers ‘sift through the chaos’ and ‘find what matters’ they experience the “ah ha!” moment.10Approaches to Hypothesis TestingClassical statisticsObjective view of probabilityEstablished hypothesis is rejected or fails to be rejectedAnalysis based on sample dataBayesian statisticsExtension of classical approachAnalysis based on sample dataAlso considers established subjective probability estimates11Statistical Significance12Types of HypothesesNullH0:  = 50 mpgH0:  50 mpgAlternateHA:  = 50 mpgHA:  > 50 mpgHA:  < 50 mpg13Two-Tailed Test of Significance14One-Tailed Test of Significance15Decision RuleTake no corrective action if the analysis shows that one cannot reject the null hypothesis.16Statistical Decisions17Probability of Making a Type I Error18Critical Values19Exhibit 17-4 Probability of Making A Type I Error 20Factors Affecting Probability of Committing a  ErrorTrue value of parameterAlpha level selectedOne or two-tailed test usedSample standard deviationSample size21Probability of Making A Type II Error22Statistical Testing ProceduresObtain critical test valueInterpret the testStagesChoose statistical testState null hypothesisSelect level of significanceCompute difference value23Tests of SignificanceNonparametricParametric24Assumptions for Using Parametric TestsIndependent observationsNormal distributionEqual variancesInterval or ratio scales25Probability Plot26Probability Plot27Probability Plot28Advantages of Nonparametric TestsEasy to understand and useUsable with nominal dataAppropriate for ordinal dataAppropriate for non-normal population distributions29How to Select a TestHow many samples are involved?If two or more samples:are the individual cases independent or related?Is the measurement scale nominal, ordinal, interval, or ratio?30Recommended Statistical TechniquesTwo-Sample Tests ____________________________________________k-Sample Tests ____________________________________________Measurement ScaleOne-Sample CaseRelated SamplesIndependent SamplesRelated SamplesIndependent SamplesNominal Binomial x2 one-sample test McNemar Fisher exact test x2 two-samples test Cochran Q x2 for k samplesOrdinal Kolmogorov-Smirnov one-sample test Runs test Sign test Wilcoxon matched-pairs test Median test Mann-Whitney UKolmogorov-SmirnovWald-Wolfowitz Friedman two-way ANOVA Median extensionKruskal-Wallis one-way ANOVAInterval and Ratio t-test Z test t-test for paired samples t-test Z test Repeated-measures ANOVA One-way ANOVA n-way ANOVA31Questions Answered by One-Sample TestsIs there a difference between observed frequencies and the frequencies we would expect?Is there a difference between observed and expected proportions?Is there a significant difference between some measures of central tendency and the population parameter?32Parametric Testst-testZ-test33One-Sample t-Test ExampleNullHo: = 50 mpgStatistical testt-test Significance level.05, n=100Calculated value1.786Critical test value1.66 (from Appendix C, Exhibit C-2)34One Sample Chi-Square Test ExampleLiving ArrangementIntend to JoinNumber InterviewedPercent (no. interviewed/200)Expected Frequencies (percent x 60)Dorm/fraternity16904527Apartment/rooming house, nearby13402012Apartment/rooming house, distant16402012Live at home15 _____30 _____15 _____ 9 _____Total602001006035One-Sample Chi-Square ExampleNullHo: 0 = EStatistical testOne-sample chi-squareSignificance level.05Calculated value9.89Critical test value7.82 (from Appendix C, Exhibit C-3)36Two-Sample Parametric Tests37Two-Sample t-Test ExampleA GroupB GroupAverage hourly salesX1 = $1,500X2 = $1,300Standard deviations1 = 225s2 = 25138Two-Sample t-Test ExampleNullHo: A sales = B salesStatistical testt-testSignificance level.05 (one-tailed)Calculated value1.97, d.f. = 20Critical test value1.725 (from Appendix C, Exhibit C-2)39Two-Sample Nonparametric Tests: Chi-SquareOn-the-Job-AccidentCell Designation Count Expected ValuesYesNoRow TotalSmokerHeavy Smoker1,112,8.241,247.7516Moderate2,197.732,267.2715Nonsmoker3,11318.033,22216.9735Column Total34326640Two-Sample Chi-Square ExampleNullThere is no difference in distribution channel for age categories.Statistical testChi-squareSignificance level.05Calculated value6.86, d.f. = 2Critical test value5.99 (from Appendix C, Exhibit C-3)41SPSS Cross-Tabulation Procedure42Two-Related-Samples TestsNonparametricParametric43Sales Data for Paired-Samples t-Test Company Sales Year 2Sales Year 1Difference DD2 GM GE Exxon IBM Ford AT&T Mobil DuPont Sears Amoco Total12693254574866566271096146361125022035099537942396612350549662789445951292300351734811132427499752077934274912771231923846 9392109263238193187ΣD = 35781 .1174432924127744594749441022720414971716 881721 4447881 6927424 1458476110156969ΣD = 157364693 .44Paired-Samples t-Test ExampleNullYear 1 sales = Year 2 salesStatistical testPaired sample t-testSignificance level.01Calculated value6.28, d.f. = 9Critical test value3.25 (from Appendix C, Exhibit C-2)45SPSS Output for Paired-Samples t-Test46Related Samples Nonparametric Tests: McNemar TestBeforeAfterDo Not FavorAfterFavorFavorABDo Not FavorCD47Related Samples Nonparametric Tests: McNemar TestBeforeAfterDo Not FavorAfterFavorFavorA=10B=90Do Not FavorC=60D=4048k-Independent-Samples Tests: ANOVATests the null hypothesis that the means of three or more populations are equalOne-way: Uses a single-factor, fixed-effects model to compare the effects of a treatment or factor on a continuous dependent variable49ANOVA Example__________________________________________Model Summary_________________________________________Sourced.f.Sum of SquaresMean SquareF Valuep ValueModel (airline)211644.0335822.01728.3040.0001Residual (error)5711724.550205.694 Total5923368.583_______________________Means Table________________________CountMeanStd. Dev.Std. ErrorLufthansa2038.95014.0063.132Malaysia Airlines2058.90015.0893.374Cathay Pacific2072.90013.9023.108All data are hypothetical50ANOVA Example ContinuedNullA1 = A2 = A3Statistical testANOVA and F ratioSignificance level.05Calculated value28.304, d.f. = 2, 57Critical test value3.16 (from Appendix C, Exhibit C-9)51Post Hoc: Scheffe’s S Multiple Comparison ProcedureVersesDiffCrit. Diff.p ValueLufthansaMalaysia Airlines19,95011.400.0002Cathay Pacific33.95011.400.0001Malaysia AirlinesCathay Pacific14.00011.400.012252Multiple Comparison ProceduresTestComplex ComparisonsPairwise ComparisonsEqual n’s OnlyUnequal n’sEqual Variances AssumedUnequal Variances Not AssumedFisher LSDXXXBonferroniXXXTukey HSDXXXTukey-KramerXXXGames-HowellXXXTamhane T2XXXScheffé SXXXXBrown-ForsytheXXXXNewman-KeulsXXDuncanXXDunnet’s T3XDunnet’s CX53ANOVA PlotsLufthansa Business Class Lounge54Two-Way ANOVA Example_______________________________________Model Summary___________________________Sourced.f.Sum of SquaresMean SquareF Valuep ValueAirline211644.0335822.01739.1780.0001Seat selection13182.8173182.81721.4180.0001Airline by seat selection2517.033258.5171.7400.1853Residual548024.700148.606All data are hypotheticalMeans Table Effect: Airline by Seat SelectionCountMeanStd. Dev.Std. ErrorLufthansa economy1035.60012.1403.839Lufthansa business1042.30015.5504.917Malaysia Airlines economy1048.50012.5013.953Malaysia Airlines business1069.3009.1662.898Cathay Pacific economy1064.80013.0374.123Cathay Pacific business1081.0009.6033.03755k-Related-Samples TestsMore than two levels in grouping factorObservations are matchedData are interval or ratio56Repeated-Measures ANOVA ExampleAll data are hypothetical.___________________________________Means Table by Airline _________________________________________________________________________CountMeanStd. Dev.Std. ErrorRating 1, Lufthansa2038.95014.0063.132Rating 1, Malaysia Airlines2058.90015.0893.374Rating 1, Cathay Pacific2072.90013.9023.108Rating 2, Lufthansa2032.4008.2681.849Rating 2, Malaysia Airlines2072.25010.5722.364Rating 2, Cathay Pacific2079.80011.2652.519__________________________________________________________Model Summary_________________________________________________________Sourced.f.Sum of SquaresMean SquareF Valuep ValueAirline23552735.5017763.77567.1990.0001Subject (group)5715067.650264.345Ratings1625.633625.63314.3180.0004Ratings by air.......22061.7171030.85823.5920.0001Ratings by subj.....572490.65043.696______________________________________Means Table Effect: Ratings_________________________________________________________________CountMeanStd. Dev.Std. ErrorRating 16056.91719.9022.569Rating 26061.48323.2082.99657Key Termsa priori contrastsAlternative hypothesisAnalysis of variance (ANOVABayesian statisticsChi-square testClassical statisticsCritical valueF ratioInferential statisticsK-independent-samples testsK-related-samples testsLevel of significanceMean squareMultiple comparison tests (range tests)Nonparametric testsNormal probability plot58Key TermsNull hypothesisObserved significance levelOne-sample testsOne-tailed testp valueParametric testsPower of the testPractical significanceRegion of acceptanceRegion of rejectionStatistical significancet distributionTrialst-testTwo-independent-samples tests59Key TermsTwo-related-samples testsTwo-tailed testType I errorType II errorZ distributionZ test60
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