Bài giảng Business Research Methods - Chapter 17: Hypothesis Testing

Hypothesis TestingChapter 17Learning ObjectivesUnderstand . . . The nature and logic of hypothesis testing.A statistically significant differenceThe six-step hypothesis testing procedure.Learning 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 statisticsPull Quote“A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective.”Edward Teller, theoretical physicist,“father of the hydrogen bomb”(1908–2003)Hypothesis TestingDeductiveReasoningInductive ReasoningHypothesis Testing Finds Truth“One finds the truth by making a hypothesis and comparing the truth to the hypothesis.”David Douglass physicistUniversity of RochesterStatistical ProceduresDescriptive StatisticsInferential StatisticsHypothesis Testing and the Research ProcessWhen 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.Approaches to Hypothesis TestingClassical statistics Objective view of probability Established hypothesis is rejected or fails to be rejected Analysis based on sample dataBayesian statistics Extension of classical approach Analysis based on sample data Also considers established subjective probability estimatesStatistical SignificanceTypes of HypothesesNullH0:  = 50 mpgH0:  50 mpgAlternateHA:  = 50 mpgHA:  > 50 mpgHA:  < 50 mpgTwo-Tailed Test of SignificanceOne-Tailed Test of SignificanceDecision RuleTake no corrective action if the analysis shows that one cannot reject the null hypothesis.Statistical DecisionsProbability of Making a Type I ErrorCritical ValuesProbability of Making A Type I Error Factors Affecting Probability of Committing a  ErrorTrue value of parameterAlpha level selectedOne or two-tailed test usedSample standard deviationSample sizeProbability of Making A Type II ErrorStatistical Testing ProceduresObtain critical test valueInterpret the testStagesChoose statistical testState null hypothesisSelect level of significanceCompute difference valueTests of SignificanceNonparametricParametricAssumptions for Using Parametric TestsIndependent observationsNormal distributionEqual variancesInterval or ratio scalesProbability PlotProbability PlotProbability PlotAdvantages of Nonparametric TestsEasy to understand and useUsable with nominal dataAppropriate for ordinal dataAppropriate for non-normal population distributionsHow 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?Recommended 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 testWilcoxon matched-pairs test Median testMann-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 ANOVAQuestions 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?Parametric Testst-testZ-testOne-Sample t-Test ExampleNullHo: = 50 mpgStatistical testt-test Significance level.05, n=100Calculated value1.786Critical test value1.66 (from Appendix C, Exhibit C-2)One Sample Chi-Square Test ExampleLiving ArrangementIntend to JoinNumber InterviewedPercent(no. interviewed/200)ExpectedFrequencies(percent x 60)Dorm/fraternity16904527Apartment/rooming house, nearby13402012Apartment/rooming house, distant16402012Live at home15_____30_____15_____ 9_____Total6020010060One-Sample Chi-Square ExampleNullHo: 0 = EStatistical testOne-sample chi-squareSignificance level.05Calculated value9.89Critical test value7.82 (from Appendix C, Exhibit C-3)Two-Sample Parametric TestsTwo-Sample t-Test ExampleA GroupB GroupAverage hourly salesX1 = $1,500X2 = $1,300Standard deviations1 = 225s2 = 251Two-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)Two-Sample Nonparametric Tests: Chi-SquareOn-the-Job-AccidentCell DesignationCountExpected ValuesYesNoRow TotalSmokerHeavy Smoker1,112,8.241,247.7516Moderate2,197.732,267.2715Nonsmoker3,11318.033,22216.9735Column Total343266Two-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)SPSS Cross-Tabulation ProcedureTwo-Related-Samples TestsNonparametricParametricSales Data for Paired-Samples t-Test Company Sales Year 2SalesYear 1Difference DD2 GM GE Exxon IBM Ford AT&T Mobil DuPont Sears Amoco Total12693254574866566271096146361125022035099537942396612350549662789445951292300351734811132427499752077934274912771231923846 9392109263238193187ΣD = 35781 .1174432924127744594749441022720414971716 881721 4447881 6927424 1458476110156969ΣD = 157364693 .Paired-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)SPSS Output for Paired-Samples t-TestRelated Samples Nonparametric Tests: McNemar TestBeforeAfterDo Not FavorAfterFavorFavorABDo Not FavorCDRelated Samples Nonparametric Tests: McNemar TestBeforeAfterDo Not FavorAfterFavorFavorA=10B=90Do Not FavorC=60D=40k-Independent-Samples Tests: ANOVA Tests the null hypothesis that the means of three or more populations are equal. One-way: Uses a single-factor, fixed-effects model to compare the effects of a treatment or factor on a continuous dependent variable.ANOVA 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 hypotheticalANOVA 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)Post Hoc: Scheffe’s S Multiple Comparison ProcedureVersesDiffCrit. Diff.p ValueLufthansaMalaysia Airlines19,95011.400.0002Cathay Pacific33.95011.400.0001Malaysia AirlinesCathay Pacific14.00011.400.0122Multiple Comparison ProceduresTestComplexComparisonsPairwiseComparisonsEqualn’sOnlyUnequaln’sEqualVariancesAssumedUnequalVariancesNotAssumedFisher LSDXXXBonferroniXXXTukey HSDXXXTukey-KramerXXXGames-HowellXXXTamhane T2XXXScheffé SXXXXBrown-ForsytheXXXXNewman-KeulsXXDuncanXXDunnet’s T3XDunnet’s CXANOVA PlotsTwo-Way ANOVA Example________________________________Model Summary________________________Sourced.f.Sum of SquaresMean SquareF Valuep ValueAirline211644.0335822.01739.1780.0001Seat selection13182.8173182.81721.4180.0001Airline by seat selection2517.033258.5171.7400.1853Residual548024.700148.606Means 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 business1081.0009.6033.037All data are hypotheticalk-Related-Samples TestsMore than two levels in grouping factorObservations are matchedData are interval or ratioRepeated-Measures ANOVA Example__________________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 26061.48323.2082.996All 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 Pacific2079.80011.2652.519Key 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 plotKey TermsNull hypothesisObserved significance levelOne-sample testsOne-tailed testp valueParametric testsPower of the testPractical significanceRegion of acceptanceRegion of rejectionStatistical significancet distributionTrialst-testTwo-independent-samples testsKey TermsTwo-related-samples testsTwo-tailed testType I errorType II errorZ distributionZ testAdditional Discussion opportunitiesChapter 17Snapshot: Troy-BiltWhat elements in TV advertising build recall and consideration?Those who are market ready in category process TV ads differently than those who aren’t market ready.Test and control groups used.Test ads embedded in DIY House Crashers.Snapshot: Drug use in MoviesTop 200 rental movies during 2 years.Trained coders.Prevalence of use, frequency of use, percentage of characters using.Content analysis of drinking, smoking, illicit drugs, prescriptions and OLC drugs.Snapshot: A/B TestingDoes web page design alter click behavior?Test one or multiple factors. What hypothesis could drive A/B tests?Are we being tested whenever we visit a web page?PullQuote: Hypothesis Testing vs. TheoryDon’t confuse “hypothesis” and “theory.” The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.Martin H. Fischer professor emeritus. physiologyUniversity of CincinnatiPulsePoint: Research Revelation$28The amount, in billions, saved by North American companies by having employees use a company purchasing card.Hypothesis TestingChapter 17Photo AttributionsSlideSource9Courtesy of Abacus11Courtesy of Toyota53Francisco Cruz/Purestock/SuperStock61Purestock/age fotostock62Ingram Publishing63Jeffrey Coolidge/Photodisc/Getty Images