Malhotra 18 tif (Discriminant) PDF

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Chapter 18 Discriminant Analysis True/False Questions 1. Discriminant functions are linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups). (True, easy, page 534) 2. When the criterion variable has two categories, the technique is referred to as multiple discriminant analysis. (False, moderate, page 534) 3. In two-group discriminant analysis it is possible to derive only one discriminant function. (True, moderate, page 534) 4. In the discriminant analysis model, the coefficients, or weights ( b), are estimated so that the groups differ as much as possible on the values of the discriminant function. This occurs when the ratio of between-group sum of squares to within-group sum of squares for the discriminant scores is at a maximum. (True, moderate, page 535) 5. The first step in discriminant analysis is to estimate the discriminant function coefficients. (False, easy, page 536) 6. If attitude towards the brand is measured on a seven-point scale from unfavorable to favorable, it could be categorized as unfavorable (1, 2, 3), neutral (4), or favorable (5, 6, 7). (True, moderate, page 536) 7. The direct method is an approach to discriminant analysis that involves estimating the discriminant function so that all the predictors are included simultaneously. (True, easy, page 539) 8. In discriminant analysis, rejecting the null hypothesis means there is significant discrimination between groups. (True, moderate, page 541) 9. In discriminant analysis, the value of the coefficient for a particular predictor depends on the other predictors included in the discriminant function. (True, moderate, page 542)

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10. In discriminant analysis, there is no multicollinearity in the predictor variables. Therefore, there is no ambiguous measure of the relative importance of the predictors in discriminating between groups. (False, moderate, page 542) 11. With the leave-one-out cross-validation option in SPSS, the discriminant model is reestimated as many times as there are respondents in the sample. (True, easy, page 543) 12. The results obtained from a classification matrix based on the analysis sample are invariably better than leave-one-out classification or the classification obtained on the holdout sample. (True, difficult, page 544) 13. The hit ratio is the number of variables found to be significant by the discriminant analysis. (False, easy, page 544) 14. The hit ratio is the percentage of cases correctly classified by the discriminant analysis. (True, easy, page 544) 15. In multiple discriminant analysis, with G groups and k predictors, it is possible to estimate up to the smaller of G-1 or k discriminant functions. (True, moderate, page 548) 16. To test the null hypothesis of equal group centroids, both the functions must be considered individually. (False, easy, page 548) 17. The Mahalanobis procedure is based on minimalizing a generalized measure of the distance between the two closest groups. (False, moderate, page 552) 18. Discriminant analysis is available in EXCEL. (False, moderate, page 553)

Multiple Choice Questions 19. An examination of differences across groups lies at the heart of the basic concept of _____. a. regression analysis b. discriminant analysis c. conjoint analysis d. factor analysis (b, moderate, page 534) 242

20. In discriminant analysis, the criterion or dependent variable is _____ and the predictor or independent variables are _____ in nature. a. interval; categorical b. ordinal; interval c. categorical; interval d. ordinal; categorical (c, easy, page 534) 21. The linear combinations of independent variables developed by discriminant analysis that will best discriminate between the categories of the dependent variable are _____. a. discriminant functions b. discriminant scores c. characteristic profiles d. classification matrix (a, difficult, page 534) 22. Which of the following statements is not an objective of discriminant analysis? a. examination of whether significant differences exist among the groups, in terms of the criterion variables b. determination of which predictor variables contribute to most of the intergroup differences c. classification of cases to one of the groups based on the values of the predictor variables d. evaluation of the accuracy of classification (a, difficult, page 534) 23. Discriminant analysis can be used to answer questions such as: a. How much of the variation in sales can be explained by advertising expenditures, prices, and level of distribution? b. In terms of demographic characteristics, how do customers who exhibit store loyalty differ from those who do not? c. What are the distinguishing characteristics of consumers who respond to direct mail solicitations? d. Both b and c are correct. (d, easy, page 534) 24. D is the _____ in the model D=b0+ b1 X1+ b2 X2+ b3X3+…+ bkXk. a. discriminant score b. disordinal interaction c. difference variable d. discriminant coefficients or weights (a, easy, page 535)

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25. The unstandardized coefficients are multiplied by the values of the variables. These products are summed and added to the constant term to obtain the _____. a. discriminant function coefficients b. classification matrix c. discriminant scores d. canonical correlation (c, moderate, page 536) 26. The assumptions in discriminant analysis are that each of the groups is a sample from a _____ population and all of the populations have the same _____. a. multivariate normal; standard deviation b. multivariate normal; covariance matrix c. multivariate normal; standard error d. multivariate normal; variance (b, difficult, page 536) 27. Which of the following is not one of the steps involved in the “formulating the problem” step in discriminant analysis? a. convert the dependent variable into categories b. divide the sample into an analysis and validation samples c. estimate the discriminant function coefficients d. repeatedly conduct the validation of the discriminant function (c, moderate, pages 536-537) 28. If you are using the direct method or stepwise discriminant analysis, you are at the _____ step of conducting discriminant analysis. a. formulate the problem b. estimate the discriminant function coefficients c. assess the validity of the discriminant analysis d. determine the size of the discriminant function (b, moderate, page 539) 29. What does it mean if the discriminant function is estimated and the square of the canonical correlation is .64? a. 64% of the variance in the dependent variable is explained by the model. b. The null hypothesis is not rejected. Therefore, there is no significant discrimination between groups. c. 64% of the explained variance is accounted for. d. b and c are correct (a, difficult, page 539)

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30. In discriminant analysis, we can obtain some idea of the relative importance of the variables by _____. a. examining the absolute magnitude of the standardized discriminant function coefficients b. examining the structure correlations, or canonical loadings or discriminant loadings c. examining the unstandardized discriminant function coefficients d. all of the above (d, moderate, page 542) 31. If you are using the leave-out option of SPSS, you are at the _____ step of discriminant analysis. a. estimate the discriminant coefficients b. determine the significance of the discriminant function c. interpret the results d. assess validity of discriminant analysis (d, easy, page 543) 32. The _____ is used for estimating the _____; the _____ is used for developing the ____. a. analysis sample; discriminant function; validation sample; classification matrix b. validation sample; discriminant function; analysis sample; classification matrix c. classification matrix; discriminant function; validation sample; analysis sample d. none of the above (a, difficult, page 544) 33. If there are 10 groups and 8 predictors, how many discriminant functions can be estimated? a. 10 b. 9 c. 8 d. 7 (c, difficult, page 548) 34. In multiple discriminant analysis, the interpretation of results is aided by an

examination of all of the following except: a. the standardized discriminant function coefficients b. the correlation coefficients c. the structure correlations d. certain plots (b, moderate, page 548)

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35. A _____ is a tool for assessing discriminant analysis results that plots the group membership of each case on a graph. a. characteristic profile b. scattergram c. territorial map d. pie chart (c, moderate, page 548) 36. Which of the following statements is true about stepwise discriminant analysis? a. The predictors are entered sequentially based on their ability to discriminate between groups. b. The predictor with the highest F ratio is the first to be selected for inclusion in the discriminant function, it if meets certain significance and tolerance criteria. c. Each predictor selected is tested for retention based on its association with the other predictors selected. d. All of the above statements are true. (d, moderate, page 552) 37. Discriminant analysis can be conducted via all of the following except: a. SPSS b. EXCEL c. MINITAB d. SAS (b, moderate, page 553)

Essay Questions 38. Discuss the similarities and differences among ANOVA, regression, and discriminant analysis. Answer All three procedures involve a single criterion or dependent variable and multiple predictor or independent variables. However, the nature of these variables differ. In analysis of variance and regression analysis, the dependent variable is metric or interval scaled (amount of life insurance purchased in dollars), whereas in discriminant analysis it is categorical (amount of life insurance purchased classified as high, medium, or low). The independent variables are categorical in the case of analysis of variance (age and income are each classified as high, medium, or low) but metric in the case of regression and discriminant analysis (age in years and income in dollars, i.e., both measured on a ratio scale). Two-group discriminant analysis, in which the dependent variable has only two categories, is closely related to multiple regression analysis. In this case, multiple regression, in which the dependent variable is coded as a 0 or 1 dummy variable, results in partial regression coefficients that are proportional to discriminant function coefficients. (moderate, page, 535) 246

39. What are the steps involved in conducting discriminant analysis (Figure 18.1)? Answer The steps involved in conducting discriminant analysis are shown in Figure 18.1 as: 1. Formulate the problem. 2. Estimate the discriminant function coefficients. 3. Determine the significance of the discriminant function. 4. Interpret the results. 5. Assess the validity of the discriminant analysis. (moderate, page 537)

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