Bài giảng Business Research Methods - Chapter 18: Measures of Association

Measures of AssociationChapter 18Learning ObjectivesUnderstand . . .How correlation analysis may be applied to study relationships between two or more variablesThe uses, requirements, and interpretation of the product moment correlation coefficient.How predictions are made with regression analysis using the method of least squares to minimize errors in drawing a line of best fit.Learning ObjectivesUnderstand . . .How to test regression models for linearity and whether the equation is effective in fitting the data.Nonparametric measures of association and the alternatives they offer when key assumptions and requirements for parametric techniques cannot be met.Pull Quote“Consumer behavior with digital editions of magazines is very much like their behavior with print editions of magazines, and very much unlike their behavior with websites. Readers typically swipe through tablet editions from front to back, for example, the same way they work their way through print editions. They browse—taking in ads as they go—instead of jumping directly to specific articles the way web surfers do.” Scott McDonald, senior vice-president for research and insights,Conde NastMeasures of Association: Interval/Ratio DataPearson correlation coefficientFor continuous linearly related variablesCorrelation ratio (eta)For nonlinear data or relating a main effect to a continuous dependent variableBiserialOne continuous and one dichotomous variable with an underlying normal distributionPartial correlationThree variables; relating two with the third’s effect taken outMultiple correlationThree variables; relating one variable with two othersBivariate linear regressionPredicting one variable from another’s scoresMeasures of Association: Ordinal DataGammaBased on concordant-discordant pairs; proportional reduction in error (PRE) interpretationKendall’s tau bP-Q based; adjustment for tied ranksKendall’s tau cP-Q based; adjustment for table dimensionsSomers’s dP-Q based; asymmetrical extension of gammaSpearman’s rhoProduct moment correlation for ranked dataMeasures of Association: Nominal DataPhiChi-square based for 2*2 tablesCramer’s VCS based; adjustment when one table dimension >2Contingency coefficient CCS based; flexible data and distribution assumptionsLambdaPRE based interpretationGoodman & Kruskal’s tauPRE based with table marginals emphasisUncertainty coefficientUseful for multidimensional tablesKappaAgreement measureResearchers Search for InsightsBurke, one of the world’s leading research companies, claims researchers add the most value to a project when they look beyond the raw numbers to the shades of graywhat the data really mean.Pearson’s Product Moment Correlation rIs there a relationship between X and Y?What is the magnitude of the relationship?What is the direction of the relationship?Connections and Disconnections“To truly understand consumers’ motives and actions, you must determine relationships between what they think and feel and what they actually do.”David Singleton, vp of insightsZyman Marketing GroupScatterplots of RelationshipsScatterplotsPlot of Forbes 500 Net Profits with Cash FlowDiagram of Common VarianceInterpretation of CorrelationsX causes YY causes XX and Y are activated by one or more other variablesX and Y influence each other reciprocallyArtifact CorrelationsInterpretation of CoefficientsA coefficient is not remarkable simply because it is statistically significant! It must be practically meaningful.Comparison of Bivariate Linear Correlation and RegressionExamples of Different SlopesConcept ApplicationXAverage Temperature (Celsius)YPrice per Case (FF)122,000163,000204,000245,000Mean =18Mean = 3,500Plot of Wine Price by Average TemperatureDistribution of Y for Observation of XWine Price Study ExampleLeast Squares Line: Wine Price StudyPlot of Standardized ResidualsPrediction and Confidence BandsTesting Goodness of FitY is completely unrelated to X and no systematic pattern is evidentThere are constant values ofY for every value of XThe data are related but represented by a nonlinear functionComponents of VariationF Ratio in RegressionF Ratio in RegressionCoefficient of Determination: r2Total proportion of variance in Y explained by XDesired r2: 80% or moreChi-Square Based MeasuresProportional Reduction of Error MeasuresStatistical Alternatives for Ordinal MeasuresCalculation of Concordant (P), Discordant (Q), Tied (Tx,Ty), and Total Paired Observations: KeyDesign ExampleKDL Data for Spearman’s Rho_______ _____ Rank By_____ _____ _____ApplicantPanel xPsychologist ydd2123456789103.510.06.52.01.09.03.56.58.05.06.05.08.01.53.07.01.59.010.04.0-2.55.0-1.5.05-22.02.0-2.5-21.06.2525.002.520.254.004.004.006.254.00_1.00_57.00 .Key TermsArtifact correlationsBivariate correlation analysisBivariate normal distributionChi-square-based measuresContingency coefficient CCramer’s VPhiCoefficient of determination (r2)ConcordantCorrelation matrixDiscordantError termGoodness of fitlambda18-37Key Terms LinearityMethod of least squaresOrdinal measuresGammaSomers’s dSpearman’s rhotau btau cPearson correlation coefficientPrediction and confidence bandsProportional reduction in error (PRE)Regression analysisRegression coefficients18-38Key Terms InterceptSlopeResidual ScatterplotSimple predictiontau18-39Additional Discussion opportunitiesChapter 18Snapshot: OscarsDoes the Oscar have any measurable effect on movie viewership?Brief online survey via OmniPulse.Event hype only a small influence.Do women respond differently than men?PicProfile: Constellation WinesRecession affected wine behavior.Word sorts to reveal how Blackstone compared to other brands.‘Masculine’ wasn’t threatening but a strength.Positioning research using focus groups.Three ads by Amazon Advertising were tested; “Count on it” strongest.Snapshot: EnvironsellDoes how you drive affect how you shop?Observation studies. Brits and Aussies shop as they drive.Envirosell tracked shoppers’ behaviors.Snapshot: Advanced Statistics“A risk score model was embedded in the daily transactions processing system to automatically determine how much cash each member can withdraw from an ATM or receive when making deposits.”Pull Quote“The invalid assumption that correlationimplies cause is probably among the twoor three most serious and common errorsof human reasoning.”Stephen Jay Gouldpaleontologist and science writerPulsePoint: Research Revelation25The percent of students using a credit card for college costs due to convenience.Measures of AssociationChapter 18Photo AttributionsSlideSource8Courtesy of Burke Research Inc.41©Image Source, all rights reserved42Purestock/SuperStock43Purestock/SuperStock44Comstock Images/Getty Images