1 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Learning Objectives: 1.Explain the difference between dependence and interdependence techniques. 2.Understand how to use factor analysis to simplify data analysis. 3.Demonstrate the usefulness of cluster analysis. 4.Understand when and how to use discriminant analysis. Other Multivariate Techniques Chapter 13

2 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Dependence vs. Interdependence Techniques Interdependence Techniques = instead of analyzing both sets of variables at the same time, we only examine one set. Thus, we do not compare independent and dependent variables. Dependence Techniques = variables are divided into independent and dependent sets for analysis purposes.

3 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Factor Analysis What is it? Why use it? ?

4 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Factor Analysis.... an interdependence technique that combines many variables into a few factors to simplify our understanding of the data.

5 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-1 Ratings of Fast Food Restaurants Respondent Taste Portion Freshness Friendly Courteous Competent Size # # # # # #

6 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-2 Factor Analysis of Selection Factors On Line

7 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, What can we do with factor analysis? 1.Identify the structure of the relationships among either variables or respondents. 2.Identify representative variables from a much larger set of variables for use in subsequent analysis. 3.Create an entirely new set of variables for use in subsequent analysis.

8 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Using Factor Analysis Extraction Methods Number of Factors Factor Loadings/Interpretation Using with Other Techniques

9 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Extraction Methods:  Variance Considerations. u Component Analysis u Common Factor  Rotation Approaches. u Orthogonal u Oblique

10 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-3 Types of Variance in Factor Analysis Error Variance Unique Variance Common Variance Common Factor Analysis Principal Components Analysis

11 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Component vs. Common? Two Criteria: 1. Objectives of the factor analysis. 2. Amount of prior knowledge about the variance in the variables.

12 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-4 Orthogonal and Oblique Rotation of Factors y98hojhkyuiyiuhbjk987897y98hojhkyuiyiuhbjk F 2 Oblique Rotation F 1 Oblique Rotation F 1 Orthogonal Rotation X4X4 X5X5 X6X6 X3X3 X2X2 X1X1 F 2 Unrotated F1F1 F 2 Orthogonal Rotation

13 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Comparison of Factor Analysis and Cluster Analysis Variables 123 Respondent A767 B676 C434 D343 Score Respondent A Respondent B Respondent C Respondent D

14 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Assumptions: Multicollinearity.  Measured by MSA (measure of sampling adequacy). Homogeneity of sample.

15 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Number of Factors? Latent Root Criterion Percentage of Variance

16 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Which Factor Loadings Are Significant? Customary Criteria = Practical Significance. Sample Size & Statistical Significance. Number of Factors and/or Variables.

17 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Guidelines for Identifying Significant Factor Loadings Based on Sample Size Factor LoadingSample Size Needed for Significance* * Significance is based on a.05 significance level, a power level of 80 percent, and standard errors assumed to be twice those of conventional correlation coefficients.

18 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-5 Example of Varimax-Rotated Principal Components Factor Matrix

19 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-7 Descriptive Statistics for Customer Survey VariablesMean X 1 – Excellent Food Quality5.53 X 2 – Attractive Interior4.70 X 3 – Generous Portions3.89 X 4 – Excellent Food Taste5.15 X 5 – Good Value for the Money4.33 X 6 – Friendly Employees3.66 Descriptive Statistics X 7 – Appears Clean and Neat 4.11 X 8 – Fun Place to Go 3.39 X 9 – Wide Variety of Menu Items 5.51 X 10 – Reasonable Prices 4.06 X 11 – Courteous Employees 2.40 X 12 – Competent Employees 2.19

20 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-8 Rotated Factor Solution for Customer Survey Perceptions Components (Factors) X 4 – Excellent Food Taste.912 X 9 – Wide Variety of Menu Items.901 X 4 – Excellent Food Quality.883 X 6 – Friendly Employees.892 X 11 – Courteous Employees.850 X 12 – Competent Employees.800 X 8 – Fun Place to Go.869 X 2 – Attractive Interior.854 X 7 – Appears Clean and Neat.751 X 3 – Generous Portions.896 X 5 – Good Value for Money.775 X 10 – Reasonable Prices.754

21 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit 13-8 Rotated Factor Solution for Customer Survey Perceptions Continued Component Rotation Sums of Squared Loadings % of VarianceCumulative % Total

22 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Interpreting the Factor Matrix Steps: 1.Examine the Factor Matrix of Loadings. 2.Identify the Highest Loading for Each Variable. 3.Assess Communalities of the Variables. 4.Label the Factors.

23 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Select Surrogate Variables? Select Surrogate Variables? Create Summated Scales? Create Summated Scales? Compute Factor Scores? Compute Factor Scores? Using Factor Analysis with Other Multivariate Techniques

24 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Cluster Analysis Overview What is it? Why use it?

25 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Cluster Analysis... an interdependence technique that groups objects (respondents, products, firms, variables, etc.) so that each object is similar to the other objects in the cluster and different from objects in all the other clusters.

26 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Low Frequency of Using Coupons High LowFrequency of Looking for Low Prices High Low Frequency of Looking for Low Prices High Exhibit 13-9 Three Clusters of Shopper Types

27 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, High High Low Low Low High Low High Scatter Diagram for Cluster Observations Level of Education Brand Loyalty

28 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, High High Low Low Low High Low High Scatter Diagram for Cluster Observations Scatter Diagram for Cluster Observations Level of Education Brand Loyalty

29 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, HighLow LowHigh Scatter Diagram for Cluster Observations Scatter Diagram for Cluster Observations Level of Education Brand Loyalty

30 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Between and Within Cluster Variation Within Cluster Variation Between Cluster Distances

31 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, “McDonald’s” “Wendy’s” “Burger King” Low Preference for Tasty Burgers High LowIncome High Low Income High Cluster Analysis

32 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Three Phases of Cluster Analysis: Phase One: Divide the total sample into smaller subgroups. Phase Two: Verify the subgroups identified are statistically different and theoretically meaningful. Phase Three: Profile the clusters in terms of demographics, psychographics, and other relevant characteristics.

33 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Questions to Answer in Phase One: 1. How do we measure the distances between the objects we are clustering? 2. What procedure will be used to group similar objects into clusters? 3. How many clusters will we derive?

34 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Research Design Considerations in Using Cluster Analysis: in Using Cluster Analysis: Detecting Outliers Similarity Measures Distance Standardizing the Data

35 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Go On-Line Nonhierarchical Hierarchical Cluster Grouping Approaches

36 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Hierarchical vs. Nonhierarchical Cluster Approaches Nonhierarchical = referred to a K-means clustering, these procedures do not involve the tree-like process, but instead select one or more cluster seeds and then objects within a prespecified distance from the cluster seeds are considered to be in a particular cluster. Hierarchical = develops a hierarchy or tree-like format using either a build-up or divisive approach.

37 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Divisive = starts with all objects as a single cluster and then takes away one object at a time until each object is a separate cluster. Build-up = also referred to as agglomerative, it starts with all the objects as separate clusters and combines them one at a time until there is a single cluster representing all the objects. Build-up vs. Divisive Approaches

38 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Dendogram of Hierarchical Clustering Exhibit Dendogram of Hierarchical Clustering Object Number Steps

39 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Phase Two – Cluster Analysis... involves verifying that the identified groups are in fact statistically different and theoretically meaningful.

40 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Phase Three – Cluster Analysis... examines the demographic and other characteristics of the objects in each cluster and attempts to explain why the objects were grouped in the manner they were.

41 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, HOW MANY CLUSTERS ? 1.Run cluster; examine similarity or distance measure for two, three, four, etc. clusters? 2.Select number of clusters based on “a priori” criteria, practical judgement, common sense, and/or theoretical foundations.

42 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Cluster Analysis Example Variables Used: X 6 – Friendly Employees X 11 – Courteous Employees X 12 – Competent Employees

43 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Error Coefficients for Cluster Solutions Error Coefficients Error Reduction Four Clusters = – 4 Clusters = Three Clusters= – 3 Clusters = Two Clusters = – 2 Clusters = One Cluster =

44 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Characteristics of Two-Group Cluster Solution VariablesGroupsNMeans X 6 – Friendly Employees Total X 11 – Courteous Employees Total X 12 – Competent Employees Total Descriptives

45 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Characteristics of Two- Group Cluster Solution Continued VariablesFSig. X 6 – Friendly EmployeesBetween Groups X 11 – Courteous EmployeesBetween Groups X 12 – Competent EmployeesBetween Groups ANOVA

46 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Demographic Profiles of Two Cluster Solution VariablesGroupsNMeans X 22 – Gender Total X 23 – Age Total X 24 – Income Total X 25 – Competitor Total Descriptives

47 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Demographic Profiles of Two Cluster Solution Continued VariablesFSig. X 22 – GenderBetween Groups X 23 – AgeBetween Groups X 24 – IncomeBetween Groups X 25 – CompetitorBetween Groups ANOVA

48 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Discriminant Analysis What is it? Why use it? ?

49 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Discriminant Analysis.... a dependence technique that is used to predict which group an individual (object) is likely to belong to using two or more metric independent variables. The single dependent variable is non-metric.

50 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, “McDonald’s” “Burger King” Less Important Food Taste More Important Less ImportantFun Place for Kids More Important Less Important Fun Place for Kids More Important Exhibit Two Dimensional Discriminant Analysis Plot of Restaurant Customers

51 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, What Can We Do With Discriminant Analysis? 1.Determine whether statistically significant differences exist between the average score profiles on a set of variables for two (or more) a priori defined groups. 2.Establish procedures for classifying statistical units (individuals or objects) into groups on the basis of their composite Z scores computed from a set of independent variables. 3.Determine which of the independent variables account the most for the differences in the average score profiles of the two or more groups.

52 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Scatter Diagram and Projection of Two-Group Discriminant Analysis

53 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Z = W 1 X 1 + W 2 X W n X n Potential Independent Variables: X 1 = income X 2 = education X 3 = family size X 4 = ? ? Each respondent has a variate value (Z). The Z value is a single composite Z score (linear combination) for each individual. It is computed from the entire set of independent variables so that it best achieves the statistical objective.

54 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Using Discriminant Analysis Computational Method. Statistical Significance. (Mahalanobis D 2 ) Predictive Accuracy. (Hit Ratio) Interpretation of Results.

55 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Computational Methods: 1. Simultaneous 2. Stepwise

56 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Predictive Accuracy: Group Centroids & Z Scores. Classification Matrices.  Cutting Score Determination.  Hit Ratio.  Costs of Misclassification.

57 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Discriminant Function Z Axis and Cutoff Scores

58 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Classification Matrix for Burger King and McDonald’s Customers Predicted Group Burger KingMcDonald’sTotal BK (80%) (20%) Actual Group McD (5%) (95%) Overall prediction accuracy (hit ratio) = 87.5% ( = 350 / 400 = 87.5% )

59 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Discriminant Analysis of Customer Surveys Test of Function(s)Wilks’ LambdaSig Classification Results * 79% of original grouped cases correctly classified Predicted Group Membership Total X 25 – CompetitorSamouel’sGino’s Original Group CountSamouel’s Gino’s %Samouel’s Gino’s

60 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Tests of Equality of Group Means VariablesFSig. X 1 – Excellent Food Quality X 4 – Excellent Food Taste X 6 – Friendly Employees X 9 – Wide Variety of Menu Items X 11 – Courteous Employees X 12 – Competent Employees

61 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Structure Matrix for Restaurant Perceptions Variables VariablesFunction 1 X 6 – Friendly Employees.843 X 12 – Competent Employees.791 X 11 – Courteous Employees.571 X 4 – Excellent Food Taste.267 X 1 – Excellent Food Quality.255 X 9 – Wide Variety of Menu Items.050 Correlations between discriminating variables and the discriminant function. Variables ordered by absolute size of correlation within function.

62 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Exhibit Means of Independent Variables for Restaurants Variables Mean Samouel’sGino’s X 1 – Excellent Food Quality* X 4 – Excellent Food Taste* X 6 – Friendly Employees* X 9 – Wide Variety of Menu Items X 11 – Courteous Employees* X 12 – Competent Employees* Function X 25 – Competitor 1 Samouel’s-.916 Gino’s.916 Functions at Group Centroids * Significant <.05 on a univariate basis.

63 Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, Other Multivariate Techniques Go On-Line Explore this website and identify its value for business researchers.