Discriminant Analysis Chapter Outline 1 Overview 2 Basic

Discriminant Analysis

Chapter Outline 1) Overview 2) Basic Concept 3) Relation to Regression and ANOVA 4) Discriminant Analysis Model 5) Statistics Associated with Discriminant Analysis 6) Conducting Discriminant Analysis i. Formulation ii. Estimation iii. Determination of Significance iv. Interpretation v. Validation

7) Multiple Discriminant Analysis i. Formulation ii. Estimation iii. Determination of Significance iv. Interpretation v. Validation 8) Stepwise Discriminant Analysis 9) Internet and Computer Applications 10) Focus on Burke 11) Summary 12) Key Terms and Concepts 13) Acronyms

Similarities and Differences between ANOVA, Table 18. 1 Regression, and Discriminant Analysis ANOVA Similarities Number of dependent variables Number of independent variables Differences Nature of the dependent variable Nature of the independent variables REGRESSION DISCRIMINANT ANALYSIS One One Multiple Metric Categorical Metric

Fig. 18. 1 Conducting Discriminant Analysis Formulate the Problem Estimate the Discriminant Function Coefficients Determine the Significance of the Discriminant Function Interpret the Results Assess Validity of Discriminant Analysis

Information on Resort Visits: Analysis Sample Table 18. 2 No. Resort Visit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 1 Annual Family Income ($000) 50. 2 70. 3 62. 9 48. 5 52. 7 75. 0 46. 2 57. 0 64. 1 68. 1 73. 4 71. 9 56. 2 49. 3 62. 0 Attitude Importance Household Age of Toward Attached Size Head of Travel to Family Household Vacation 5 6 7 7 6 8 5 2 7 7 6 5 1 4 5 8 7 5 5 6 7 3 4 5 6 7 8 8 2 6 3 4 6 5 4 5 3 6 4 5 5 4 6 3 2 43 61 52 36 55 68 62 51 57 45 44 64 54 56 58 Amount Spent on Family Vacation M (2) H (3) L (1) H (3) M (2) H (3)

Table 18. 2 Contd. No. Resort Visit 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2 2 2 2 Annual Family Income ($000) 32. 1 36. 2 43. 2 50. 4 44. 1 38. 3 55. 0 46. 1 35. 0 37. 3 41. 8 57. 0 33. 4 37. 5 41. 3 Attitude Importance Household Age of Toward Attached Size Head of Travel to Family Household Vacation 5 4 2 5 6 6 1 3 6 2 5 8 6 3 3 4 3 5 2 6 6 2 5 4 7 1 3 8 2 3 3 2 2 4 3 2 2 3 5 4 3 2 2 3 2 58 55 57 37 42 45 57 51 64 54 56 36 50 48 42 Amount Spent on Family Vacation L (1) M (2) L (1) M (2) L (1)

Information on Resort Visits: Holdout Sample Table 18. 3 No. Resort Visit 1 2 3 4 5 6 7 8 9 10 11 12 1 1 1 2 2 2 Annual Family Income ($000) 50. 8 63. 6 54. 0 45. 0 68. 0 62. 1 35. 0 49. 6 39. 4 37. 0 54. 5 38. 2 Attitude Importance Household Age of Toward Attached Size Head of Travel to Family Household Vacation 4 7 6 5 4 5 6 2 7 4 7 4 6 6 3 3 5 6 3 2 3 7 4 3 6 3 4 5 3 3 45 55 58 60 46 56 54 39 44 51 37 49 Amount Spent on Family Vacation M (2) H (3) L (1) H (3) L (1) M (2) L (1)

Table 18. 4 Results of Two-Group Discriminant Analysis GROUP MEANS VISIT 1 2 Total INCOME TRAVEL VACATION HSIZE 60. 52000 41. 91333 51. 21667 5. 40000 4. 33333 4. 86667 AGE 5. 80000 4. 06667 4. 9333 4. 33333 2. 80000 3. 56667 53. 73333 50. 13333 51. 93333 1. 82052 2. 05171 2. 09981 1. 23443. 94112 1. 33089 8. 77062 8. 27101 8. 57395 HSIZE AGE Group Standard Deviations 1 2 Total 9. 83065 7. 55115 12. 79523 1. 91982 1. 95180 1. 97804 Pooled Within-Groups Correlation Matrix INCOME TRAVEL VACATION HSIZE AGE 1. 00000. 19745. 09148. 08887 -. 01431 1. 00000. 08434 -. 01681 -. 19709 1. 00000. 07046. 01742 1. 00000 -. 04301 1. 00000 Wilks' (U-statistic) and univariate F ratio with 1 and 28 degrees of freedom Variable INCOME TRAVEL VACATION HSIZE AGE Wilks'. 45310. 92479. 82377. 65672. 95441 F 33. 800 2. 277 5. 990 14. 640 1. 338 Significance. 0000. 1425. 0209. 0007. 2572 Contd.

Table 18. 4 Results of Two-Group Discriminant Analysis CANONICAL DISCRIMINANT FUNCTIONS Function Eigenvalue 1* 1. 7862 % of Cum Canonical After Wilks' Variance % Correlation Function Chi-square df Significance : 0. 3589 26. 130 5. 0001 100. 00. 8007 : * marks the 1 canonical discriminant functions remaining in the analysis. Standard Canonical Discriminant Function Coefficients FUNC 1 INCOME TRAVEL VACATION HSIZE AGE . 74301. 09611. 23329. 46911. 20922 Structure Matrix: Pooled within-groups correlations between discriminating variables & canonical discriminant functions (variables ordered by size of correlation within function) FUNC 1 INCOME HSIZE VACATION TRAVEL AGE . 82202. 54096. 34607. 21337. 16354 Contd.

Table 18. 4 Results of Two-Group Discriminant Analysis Unstandardized canonical discriminant function coefficients FUNC 1. 8476710 E-01. 4964455 E-01. 1202813. 4273893. 2454380 E-01 -7. 975476 INCOME TRAVEL VACATION HSIZE AGE (constant) Canonical discriminant functions evaluated at group means (group centroids) Group 1 2 FUNC 1 1. 29118 -1. 29118 Classification results for cases selected for use in analysis Actual Group Predicted Group Membership No. of Cases 1 2 Group 1 15 12 80. 0% 3 20. 0% Group 2 15 0. 0% 15 100. 0% Percent of grouped cases correctly classified: 90. 00% Contd.

Table 18. 4 Results of Two-Group Discriminant Analysis Classification Results for cases not selected for use in the analysis (holdout sample) Actual Group Predicted Group Membership No. of Cases 1 2 Group 1 6 4 66. 7% 2 33. 3% Group 2 6 0. 0% 6 100. 0% Percent of grouped cases correctly classified: 83. 33%.

Table 18. 5 Results of Three-Group Discriminant Analysis Group Means AMOUNT INCOME TRAVEL VACATION HSIZE 1 2 3 Total 38. 57000 50. 11000 64. 97000 51. 21667 4. 50000 4. 00000 6. 10000 4. 86667 AGE 4. 70000 4. 20000 5. 90000 4. 93333 3. 10000 3. 40000 4. 20000 3. 56667 50. 30000 49. 50000 56. 00000 51. 93333 1. 88856 2. 48551 1. 66333 2. 09981 1. 19722 1. 50555 1. 13529 1. 33089 8. 09732 9. 25263 7. 60117 8. 57395 Group Standard Deviations 1 2 3 Total 5. 29718 6. 00231 8. 61434 12. 79523 1. 71594 2. 35702 1. 19722 1. 97804 Pooled Within-Groups Correlation Matrix INCOME TRAVEL VACATION HSIZE AGE 1. 00000. 05120. 30681. 38050 -. 20939 1. 00000. 03588. 00474 -. 34022 1. 00000. 22080 -. 01326 1. 00000 -. 02512 AGE 1. 00000 Contd.

Table 18. 5 Results of Three-Group Discriminant Analysis Wilks' (U-statistic) and univariate F ratio with 2 and 27 degrees of freedom. Variable Wilks' Lambda INCOME. 26215 TRAVEL. 78790 VACATION. 88060 HSIZE. 87411 AGE. 88214 F Significance 38. 00 3. 634 1. 830 1. 944 1. 804 . 0000. 0400. 1797. 1626. 1840 CANONICAL DISCRIMINANT FUNCTIONS Function Eigenvalue 1* 3. 8190 2* . 2469 % of Cum Canonical After Wilks' Variance % Correlation Function Chi-square df Significance : 0. 1664 44. 831 10. 00 93. 93. 8902 : 1. 8020 5. 517 4. 24 6. 07 100. 00 . 4450 : * marks the two canonical discriminant functions remaining in the analysis. Standardized Canonical Discriminant Function Coefficients INCOME TRAVEL VACATION HSIZE AGE FUNC 1 1. 04740. 33991 -. 14198 -. 16317. 49474 FUNC 2 -. 42076. 76851. 53354. 12932. 52447 Contd.

Table 18. 5 Results of Three-Group Discriminant Analysis Structure Matrix: Pooled within-groups correlations between discriminating variables and canonical discriminant functions (variables ordered by size of correlation within function) INCOME HSIZE VACATION TRAVEL AGE FUNC 1. 85556*. 19319*. 21935. 14899. 16576 FUNC 2 -. 27833. 07749. 58829*. 45362*. 34079* Unstandardized canonical discriminant function coefficients FUNC 1 FUNC 2 INCOME. 1542658 -. 6197148 E-01 TRAVEL. 1867977. 4223430 VACATION -. 6952264 E-01. 2612652 HSIZE -. 1265334. 1002796 AGE. 5928055 E-01. 6284206 E-01 (constant) -11. 09442 -3. 791600 Canonical discriminant functions evaluated at group means (group centroids) Group FUNC 1 FUNC 2 1 -2. 04100. 41847 2 -. 40479 -. 65867 3 2. 44578. 24020 Contd.

Table 18. 5 Results of Three-Group Discriminant Analysis Classification Results: Actual Group Predicted Group Membership No. of Cases 1 2 3 Group 1 10 9 90. 0% 1 10. 0% Group 2 10 1 10. 0% 9 90. 0% Group 3 10 0 2. 0% 20. 0% Percent of grouped cases correctly classified: 86. 67% 8 80. 0% Classification results for cases not selected for use in the analysis Predicted Group Membership Actual Group No. of Cases 1 2 3 Group 1 4 3 75. 0% 1 25. 0% 0. 0% Group 2 4 0. 0% 3 75. 0% 1 25. 0% Group 3 4 1 0 25. 0% Percent of grouped cases correctly classified: 75. 00% 3 75. 0%

All-Groups Scattergram Fig. 18. 2 Across: Function 1 Down: Function 2 4. 0 1 1 1 23 *1 1 1 12 1 1 *2 2 1 2 0. 0 3 3* 3 3 3 -4. 0 * indicates a group centroid -6. 0 -4. 0 -2. 0 0. 0 2. 0 4. 0 6. 0

Territorial Map Fig. 18. 3 13 13 Across: Function 1 13 Down: Function 2 13 13 * Indicates a 13 group centroid 13 112233 *1 1 1 2 2 3 3 * 1 1 2 2* 223 233 1122 223 11122 233 11222 223 1122 233 11122 223 1122 11122 233 8. 0 4. 0 0. 0 -4. 0 -8. 0 -6. 0 -4. 0 -2. 0 0. 0 2. 0 4. 0 6. 0 8. 0

RIP 18. 1 Satisfactory Results Of Satisfaction Programs In Europe These days more and more computer companies are emphasizing customer service programs rather than their erstwhile emphasis on computer features and capabilities. Hewlett-Packard learned this lesson while doing business in Europe. Research conducted on the European market revealed that there was a difference in emphasis on service requirements across age segments. Focus groups revealed that customers above 40 years of age had a hard time with the technical aspects of the computer and greatly required the customer service programs. On the other hand, young customers appreciated the technical aspects of the product which added to their satisfaction. Further research in the form of a large single cross-sectional survey was done to uncover the factors leading to differences in the two segments.

RIP 18. 1 Contd. A two group discriminant analysis was conducted with satisfied and dissatisfied customers as the two groups and several independent variables such as technical information, ease of operation, variety and scope of customer service programs, etc. Results confirmed the fact that the variety and scope of customer satisfaction programs was indeed a strong differentiating factor. This was a crucial finding since HP could better handle dissatisfied customers by focusing more on customer services than technical details. Consequently, HP successfully started three programs on customer satisfaction - customer feedback, customer satisfaction surveys, and total quality control. This effort resulted in increased customer satisfaction.

RIP 18. 2 Discriminant Analysis Discriminates Ethical and Unethical Firms In order to identify the important variables that predict ethical and unethical behavior, discriminant analysis was used. Prior research suggested that the variables that impact ethical decisions are attitudes, leadership, the presence or absence of ethical codes of conduct, and the organization's size. To determine which of these variables are the best predictors of ethical behavior, 149 firms were surveyed and respondents indicated how their firms operate in 18 different ethical situations. Of these 18 situations, nine related to marketing activities. These activities included using misleading sales presentations, accepting gifts for preferential treatment, pricing below out-of-pocket expenses, etc. Based on these nine issues, the respondent firms were classified into two groups: never practice and practice unethical marketing.

RIP 18. 2 Contd. An examination of the variables that influenced classification indicated that attitudes and a company's size were the best predictors of ethical behavior. Smaller firms tend to demonstrate more ethical behavior on marketing issues.