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Chapter 18

Chapter 18. Measures of Association. Learning Objectives. Understand . . . How correlation analysis may be applied to study relationships between two or more variables The uses, requirements, and interpretation of the product moment correlation coefficient.

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Chapter 18

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  1. Chapter 18 Measures of Association

  2. Learning Objectives Understand . . . • How correlation analysis may be applied to study relationships between two or more variables • The 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.

  3. Learning Objectives Understand . . . • 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.

  4. 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 Nast

  5. Measures of Association: Interval/Ratio Data

  6. Measures of Association: Ordinal Data

  7. Measures of Association: Nominal Data

  8. Researchers Search for Insights Burke, 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 gray…what the data really mean.

  9. Pearson’s Product Moment Correlation r Is there a relationship between X and Y? What is the magnitude of the relationship? What is the direction of the relationship?

  10. 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 insights Zyman Marketing Group

  11. Scatterplots of Relationships

  12. Scatterplots

  13. Plot of Forbes 500 Net Profits with Cash Flow

  14. Diagram of Common Variance

  15. Interpretation of Correlations X causes Y Y causes X X and Y are activated by one or more other variables X and Y influence each other reciprocally

  16. Artifact Correlations

  17. Interpretation of Coefficients A coefficient is not remarkable simply because it is statistically significant! It must be practically meaningful.

  18. Comparison of Bivariate Linear Correlation and Regression

  19. Examples of Different Slopes

  20. Concept Application

  21. Plot of Wine Price by Average Temperature

  22. Distribution of Y for Observation of X

  23. Wine Price Study Example

  24. Least Squares Line: Wine Price Study

  25. Plot of Standardized Residuals

  26. Prediction and Confidence Bands

  27. Testing Goodness of Fit Y is completely unrelated to X and no systematic pattern is evident There are constant values of Y for every value of X The data are related but represented by a nonlinear function

  28. Components of Variation

  29. F Ratio in Regression

  30. F Ratio in Regression

  31. Coefficient of Determination: r2 Total proportion of variance in Y explained by X Desired r2: 80% or more

  32. Chi-Square Based Measures

  33. Proportional Reduction of Error Measures

  34. Statistical Alternatives for Ordinal Measures

  35. Calculation of Concordant (P), Discordant (Q), Tied (Tx,Ty), and Total Paired Observations: KeyDesign Example

  36. KDL Data for Spearman’s Rho

  37. Key Terms • Artifact correlations • Bivariate correlation analysis • Bivariate normal distribution • Chi-square-based measures • Contingency coefficient C • Cramer’s V • Phi • Coefficient of determination (r2) • Concordant • Correlation matrix • Discordant • Error term • Goodness of fit • lambda

  38. Key Terms • Linearity • Method of least squares • Ordinal measures • Gamma • Somers’s d • Spearman’s rho • tau b • tau c • Pearson correlation coefficient • Prediction and confidence bands • Proportional reduction in error (PRE) • Regression analysis • Regression coefficients

  39. Key Terms • Intercept • Slope • Residual • Scatterplot • Simple prediction • tau

  40. Chapter 18 Additional Discussion opportunities

  41. Snapshot: Oscars Does 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?

  42. PicProfile: Constellation Wines Recession affected wine behavior. Positioning research using focus groups. Word sorts to reveal how Blackstone compared to other brands. ‘Masculine’ wasn’t threatening but a strength. Three ads by Amazon Advertising were tested; “Count on it” strongest.

  43. Snapshot: Environsell Does how you drive affect how you shop? Envirosell tracked shoppers’ behaviors. Observation studies. Brits and Aussies shop as they drive.

  44. 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.”

  45. Pull Quote “The invalid assumption that correlation implies cause is probably among the two or three most serious and common errors of human reasoning.” Stephen Jay Gould paleontologist and science writer

  46. PulsePoint: Research Revelation 25 The percent of students using a credit card for college costs due to convenience.

  47. Chapter 18 Measures of Association

  48. Photo Attributions

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