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

Chapter 18Measures of AssociationMcGraw-Hill/IrwinCopyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved. 18-*Learning 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.18-*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.18-*Invalid Assumptions“The invalid assumption that correlationimplies cause is probably among the twoor three most serious and common errorsof human reasoning.”Stephen Jay Gouldpaleontologist and science writer18-*PulsePoint: Research Revelation25The percent of students using a credit card for college costs due to convenience.18-*Measures 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 scores18-*Measures 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 data18-*Measures 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 measure18-*Researchers 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.18-*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?18-*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 Group18-*Scatterplots of Relationships18-*Scatterplots18-*Diagram of Common Variance18-*Interpretation of CorrelationsX causes YY causes XX and Y are activated by one or more other variablesX and Y influence each other reciprocally18-*Artifact Correlations18-*Interpretation of CoefficientsA coefficient is not remarkable simply because it is statistically significant! It must be practically meaningful.18-*Comparison of Bivariate Linear Correlation and Regression18-*Examples of Different Slopes18-*Concept ApplicationXAverage Temperature (Celsius)YPrice per Case (FF)122,000163,000204,000245,000Mean =18Mean = 3,50018-*Plot of Wine Price by Average Temperature18-*Distribution of Y for Observation of X18-*Wine Price Study Example18-*Least Squares Line: Wine Price Study18-*Plot of Standardized Residuals18-*Prediction and Confidence Bands18-*Testing 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 function18-*Components of Variation18-*F Ratio in Regression18-*Coefficient of Determination: r2Total proportion of variance in Y explained by XDesired r2: 80% or more18-*Chi-Square Based Measures18-*Proportional Reduction of Error Measures18-*Statistical Alternatives for Ordinal Measures18-*Calculation of Concordant (P), Discordant (Q), Tied (Tx,Ty), and Total Paired Observations: KeyDesign Example18-*KDL 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 .18-*Key TermsArtifact correlationsBivariate correlation analysisBivariate normal distributionChi-square-based measuresContingency coefficient CCramer’s VPhiCoefficient of determination (r2)ConcordantCorrelation matrixDiscordantError termGoodness of fitlambda18-*Key Terms LinearityMethod of least squaresOrdinal measuresGammaSomers’s dSpearman’s rhotau btau cPearson correlation coefficientPrediction and confidence bandsProportional reduction in error (PRE)Regression analysisRegression coefficients18-*Key Terms InterceptSlopeResidual ScatterplotSimple predictiontau