Data Analysis: Analyzing Multiple Variables Simultaneously Chapter 21

Multivariate Techniques Categorical Variables  Cross tab analysis Pearson  2 test of independence Cramer’s V  Independent Samples Z-test for Proportions  Spearman Rank-Order Correlation Coefficient  Kendall’s Coefficient of Concordance SLIDE 21-1

Multivariate Techniques Categorical and Continuous Variables (note: continuous variable must be the dependent variable in relationship)  Independent samples t-test for means  Paired sample t-test for means  Analysis of variance (ANOVA) Continuous Measures  Pearson product-moment correlation coefficient  Simple regression  Multiple regression SLIDE 21-2

Financing the Purchase by Van Ownership: SPSS Output Always calculate percentages in the direction of the causal variable. SLIDE 21-3 VANYES Count % within VAN % within FINANCE % of Total YESNO Total FINANCE % 10.0% 3.0% % 90.0% 27.0% Count % within VAN % within FINANCE % of Total Count % within VAN % within FINANCE % of Total % 100.0% 30.0% NO Total % 24.3% 17.0% % 75.7% 53.0% % 100.0% 70.0% % 20.0% % 80.0% % 100.0% VAN*FINANCE Crosstabulation

Financing the Purchase by Van Ownership FINANCE MOST RECENT AUTO PURCHASE? SLIDE 21-4 OWN VAN?YESNOTOTAL YES NO 3 (15%) 27 (34%) 17 (85%) 53 (66%) 20 (100%) 80 (100%) Total

Spearman Rank-Order Correlation: Distributor Performance Data Distributor SLIDE 21-5 Service Quality Ranking X i Overall Performance Ranking Y i Ranking Difference D i = X i = Y i Difference Squared D i i =1 Σ D i 2 =52

Kendall’s Coefficient of Concordance: Branch Manager Rankings SLIDE 21-6 Branch Manager Vice President of Marketing General Sales Manager Marketing Research Department Sum of Ranks R i ABCDEFGHIJABCDEFGHIJ RANK ADVOCATED BY

Independent Samples T-test: Store Sales of Floor Wax (in Units) SLIDE 21-7 StorePlastic ContainerMetal Container __

Paired Sample T-test: Store Sales of Sleeping Bags SLIDE 21-8 StoreBright ColorsEarth Colors

Analysis of Variance (ANOVA) A statistical technique used with a continuous dependent variable and one or more categorical independent variables. Advantages of ANOVA vs. Multiple T-tests  More efficient  Decreases likelihood of type I error  Considers joint effect of multiple independent variables SLIDE 21-9

Two-Way Consumer Commitment Study Question: Do both (a) level of satisfaction, and (b) whether a car owner drives a car purchased from a dealership influence consumer commitment to that dealership? MEAN COMMITMENT SCORES FOR FOUR TREATMENTS ANOVA a,b SLIDE Main Effects Model Residual Total CURRAUTOCOMMIT Sum of Squares df Mean Square FSig. Unique Method a.COMMIT by CURRAUTO b.All effects entered simultaneously

SPSS ANOVA Table for Two-Way Consumer Commitment Study Currently Drive Car from Dealership? SLIDE Satisfaction Level No(n)Yes(n)Total(n) Lower Higher Total (61) (51) (112) (132) (153) (285) (193) (204) (397)

Scatter Diagram: Sales vs. TV Spots Sales-Y Thousands of Dollars TV Spots-X 1 SLIDE 21-12

SPSS Output for the Correlation of Sales and TV Spots Correlations SLIDE NUMSPOTS SALES NUMSPOTS SALES NUMSPOTS SALES NUMSPOTS SALES Pearson Correlation Sig. (2-tailed) N ** ** **.Correlation is significant at the 0.01 level (2-tailed).

Scatter Diagram: Sales vs. Number of Salespersons Sales-Y Thousands of Dollars Number of Salespersons-X 2 SLIDE 21-14

Does Number of Sales Reps Influence Sales? SIMPLE REGRESSION ANALYSIS OUTPUT FROM SPSS Model Summary SLIDE a Predictors: (Constant), NUMREPS Model B Std. Error Beta (Constant) NUMREPS t Sig. Unstandardized Coefficients Standardized Coefficients ModelRR Square Adjusted R Square Std. Error of the Estimate a ANOVA b a Predictors: (Constant), NUMREPS b Dependent Variable: SALES Model Sum of Squares df Mean Square 1Regression Residual Total FSig a Coefficients a

Plot of Equation Relating Sales to Number of Sales Reps SLIDE Sales-Y Thousands of Dollars Number of Sales Reps-X Y = X

Scatter Diagram: Sales vs. Wholesaler Efficiency Index Sales-Y Thousands of Dollars Wholesaler Efficiency Index-X 3 SLIDE 21-17

Computer Output: Multiple Regression Analysis Coefficient of Multiple Determination Coefficient of Multiple Correlation Standard Error of Estimate Variable Regression Standard T- Standardized Status Coefficient Error Value Coefficient p-value Constant TV Spots in ANOVA Regression Residual Total Sum of Squares Degrees of Freedom Mean Square F Ratio Salespersons in Wholeeff in Sales Dependent Variable p-value SLIDE 21-18

Modifying Bivariate Relationships by Introducing a Third Variable FINANCED CAR PURCHASE? SLIDE Education of Household Head High school or less Some college Yes 24 (30%) 6 (30%) No 56 (70%) 14 (70%) Total 80 (100%) 20 (100%) Financed Car Purchase by Education of Household Head

More than $37,500 58% 27% Modifying Bivariate Relationships by Introducing a Third Variable SLIDE INCOME Education of Household Head High school or less Some college Less than $37,500 12% 40% Total 30% Financed Car Purchase by Education of Household Head and Income

The Importance of Theory in Marketing Research Many variables are correlated with other variables, especially in cross-sectional research where a respondent provides values for many (or all) variables Much of this correlation is spurious correlation Apparent relationships among variables can change with the introduction of other variables to the analysis As a result, marketing research projects (and the interpretation of their results) must be driven by theory, not simply by the data In addition, the development of knowledge depends upon multiple research projects, not just a single study SLIDE 21-21