©The McGraw-Hill Companies, Inc., 2001Irwin/McGraw-Hill Donald Cooper Pamela Schindler Chapter 18 Business Research Methods

©The McGraw-Hill Companies, Inc., 2001Irwin/McGraw-Hill Chapter 18 Measures of Association

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Bivariate Correlation vs. Nonparametric Measures of Association äParametric correlation requires two continuous variables measured on an interval or ratio scale äThe coefficient does not distinguish between independent and dependent variables Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Bivariate Correlation Analysis Pearson correlation coefficient är symbolized the coefficient's estimate of linear association based on sampling data äCorrelation coefficients reveal the magnitude and direction of relationships äCoefficient’s sign (+ or -) signifies the direction of the relationship äAssumptions of r Linearity Bivariate normal distribution Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Bivariate Correlation Analysis Scatterplots äProvide a means for visual inspection of data äthe direction of a relationship äthe shape of a relationship äthe magnitude of a relationship (with practice) Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Interpretation of Coefficients äRelationship does not imply causation äStatistical significance does not imply a relationship is practically meaningful Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Interpretation of Coefficients äSuggests alternate explanations for correlation results äX causes Y... or äY causes X... or äX & Y are activated by one or more other variables... or äX & Y influence each other reciprocally Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Interpretation of Coefficients äArtifact Correlations äGoodness of fit F test Coefficient of determination Correlation matrix äused to display coefficients for more than two variables Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Bivariate Linear Regression äUsed to make simple and multiple predictions Regression coefficients Slope Intercept Error term Method of least squares Slide 18 -7

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Slide Interpreting Linear Regression Residuals äwhat remains after the line is fit or (Y i -Y i ) Prediction and confidence bands ^

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Interpreting Linear Regression Goodness of fit äZero slope äY completely unrelated to X and no systematic pattern is evident äconstant values of Y for every value of X ädata are related, but represented by a nonlinear function Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Nonparametric Measures of Association äMeasures for nominal data äWhen there is no relationship at all, coefficient is 0 äWhen there is complete dependency, the coefficient displays unity or 1 Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Nonparametric Measures of Association Chi-square based measure äPhi Cramer’s V Contingency coefficient of C Proportional reduction in error (PRE) äLambda äTau Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Characteristics of Ordinal Data Concordant- subject who ranks higher on one variable also ranks higher on the other variable Discordant- subject who ranks higher on one variable ranks lower on the other variable Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Measures for Ordinal Data äNo assumption of bivariate normal distribution äMost based on concordant/discordant pairs äValues range from +1.0 to -1.0 Slide

 The McGraw-Hill Companies, Inc., 2001 Irwin/McGraw-Hill Click to edit Master title style Measures for Ordinal Data Tests Gamma Somer’s d Spearman’s rho Kendall’s tau b Kendall’s tau c Slide