Chapter 5 Discriminant Analysis: Overview and Applications

1. Chapter 5 Discriminant Analysis: Overview and Applications

2. Discriminant Analysis • What is it? • A non-metric (categorical) dependent variable is predicted by several metric independent variables. • Why use it? • Examples: • Gender – Male vs. Female • Heavy Users vs. Light Users • Purchasers vs. Non-purchasers • Good Credit Risk vs. Poor Credit Risk • Member vs. Non-Member

3. Discriminant Analysis Dependent Variable (Z) = Credit Risk (Favorable vs. Unfavorable) Independent Variables: X1 = income X2 = education X3 = family size X4 = occupation X5 = ? ?

4. Discriminant Analysis LowIncome High “Wendy’s” “McDonald’s” “Burger King” Low Preference for Tasty Burgers High

5. Survey Results for the Evaluation* of a New Consumer Product Subject Number X1 Durability X2 Performance X3 Style Purchase Intention Group 1 Would purchase 1 8 9 6 2 6 7 5 3 10 6 3 4 9 4 4 5 4 8 2 Group Mean 7.4 6.8 4.0 Group 2 Would not purchase 6 5 4 7 7 3 7 2 8 4 5 5 9 2 4 3 10 2 2 2 Group Mean 3.2 4.4 3.8 Difference between group means 4.2 2.4 0.2 *Evaluations made on a 0 (very poor) to 10 (excellent) rating scale.

6. Univariate Representation of Discriminant Z Scores A B Z Discriminant Function A B Z Discriminant Function

7. Graphic Illustration of Two-Group Discriminant Analysis X2 A B A’ X1 B’ Discriminant Function Z

8. What Can We Do With Discriminant Analysis? • Determine if statistically significant differences exist between the two (or more) a priori defined groups. • Examine the predictive accuracy (hit ratio) of the discriminant function to see if it is acceptable (> 25% increase). • Identify the relative importance of each of the independent variables in predicting group membership.

9. Research Design Considerations in Using Discriminant Analysis • Selection of Independent and Dependent Variables. • Sample Size (total & per variable). • Sample Division.

10. Key Assumptions: • Multivariate normality of the independent variables. • Equal variance and covariance for the groups.

11. Other Assumptions: • Minimal multicollinearity among independent variables. • Group sample sizes relatively equal. • Linear relationships. • Elimination of outliers.

12. Decisions to Make When Using Discriminant Analysis • Computational Method? • Statistical Significance? (Mahalanobis D2 ) • Predictive Accuracy? • (Hit Ratio) • Interpretation of Results?

13. Computational Methods: Simultaneous Stepwise

14. Evaluating Predictive Accuracy: • Hit Ratio – Overall and Group. • Classification Matrices. • Cutting Score Determination. • Costs of Misclassification. • Benchmark for Hit Ratio? • Maximum Chance Criterion – based • on sample size of largest group. • Proportional Chance Criterion – adjusts for • unequal group sizes and uses the “average” • probability of classification. • Should be 25% higher than without • discriminant model.

15. Classification Matrix HATCO’s New Consumer Product Predicted Group Would Not Purchase Percent Correct Classification Actual Group Would Purchase Actual Total (1) 22 3 25 88% (2) 5 20 25 80% Predicted Total 27 23 50 Percent Correctly Classified (hit ratio) = 100 x [(22 + 20)/50] = 84%

16. Optimal Cutting Score with Equal Samples Sizes Group A Group B _ ZA _ ZB Classify as B (Purchaser) Classify as A (Nonpurchaser)

17. Optimal Cutting Score with Unequal Samples Sizes Unweighted Cutting Score Optimal Weighted Cutting Score Group B Group A _ ZA _ ZB

18. Hit Ratios: Samouel’s Organizational Commitment Two Clusters Calculated with equal group sizes assumed. Calculated with unequal group sizes assumed.

19. Samouel's Restaurant Description of Employee Survey Variables Variable DescriptionVariable Type Work Environment Measures X1 I am paid fairly for the work I do. Metric X2 I am doing the kind of work I want. Metric X3 My supervisor gives credit an praise for work well done. Metric X4 There is a lot of cooperation among the members of my work group. Metric X5 My job allows me to learn new skills. Metric X6 My supervisor recognizes my potential. Metric X7 My work gives me a sense of accomplishment. Metric X8 My immediate work group functions as a team. Metric X9 My pay reflects the effort I put into doing my work. Metric X10 My supervisor is friendly and helpful. Metric X11 The members of my work group have the skills and/or training to do their job well. Metric X12 The benefits I receive are reasonable. Metric Relationship Measures X13 Loyalty – I have a sense of loyalty to Samouel’s restaurant. Metric X14 Effort – I am willing to put in a great deal of effort beyond that expected to help Samouel’s restaurant to be successful. Metric X15 Proud – I am proud to tell others that I work for Samouel’s restaurant. Metric Classification Variables X16 Intention to Search Metric X17 Length of Time an Employee Nonmetric X18 Work Type = Part-Time vs. Full-Time Nonmetric X19 Gender Nonmetric X20 Age Nonmetric X21 Performance Metric

20. Description of Customer Survey Variables GINO'S Samouel's Restaurant VS. Variable DescriptionVariable Type Restaurant Perceptions X1 Excellent Food Quality Metric X2 Attractive Interior Metric X3 Generous Portions Metric X4 Excellent Food Taste Metric X5 Good Value for the Money Metric X6 Friendly Employees Metric X7 Appears Clean & Neat Metric X8 Fun Place to Go Metric X9 Wide Variety of menu Items Metric X10 Reasonable Prices Metric X11 Courteous Employees Metric X12 Competent Employees Metric Selection Factor Rankings X13 Food Quality Nonmetric X14 Atmosphere Nonmetric X15 Prices Nonmetric X16 Employees Nonmetric Relationship Variables X17 Satisfaction Metric X18 Likely to Return in Future Metric X19 Recommend to Friend Metric X20 Frequency of Patronage Nonmetric X21 Length of Time a Customer Nonmetric Classification Variables X22 Gender Nonmetric X23 Age Nonmetric X24 Income Nonmetric X25 Competitor Nonmetric X26 Which AD Viewed (#1, 2 or 3) Nonmetric X27 AD Rating Metric X28 Respondents that Viewed Ads Nonmetric

21. Discriminant Analysis Dialog Boxes: Customer Survey

22. Discriminant Analysis Dialog Boxes: Customer Survey

23. Discriminant Analysis Learning Checkpoint When should multiple discriminant analysis be used? What are the major considerations in the application of discriminant analysis? Which measures are used to assess the validity of the discriminant function? How should you identify variables that predict group membership well?