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Data Analysis: Analyzing Multiple Variables Simultaneously

Discover advanced statistical methods for analyzing categorical and continuous variables simultaneously, including chi-square test, regression, ANOVA, and more. Interpret SPSS outputs to draw meaningful insights and make data-driven decisions.

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Data Analysis: Analyzing Multiple Variables Simultaneously

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  1. Data Analysis: Analyzing Multiple Variables Simultaneously Chapter 21

  2. SLIDE 21-1 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

  3. SLIDE 21-2 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

  4. SLIDE 21-3 Financing the Purchase by Van Ownership: SPSS Output VAN*FINANCE Crosstabulation FINANCE Total YES NO VAN YES 20100.0% 20.0% 20.0% 1785.0% 24.3% 17.0% Count% within VAN % within FINANCE % of Total 315.0% 10.0% 3.0% 80100.0% 80.0% 80.0% 5366.3% 75.7% 53.0% Count% within VAN % within FINANCE % of Total 2733.8% 90.0% 27.0% NO Total 100100.0% 100.0% 100.0% 7070.0% 100.0% 70.0% Count% within VAN % within FINANCE % of Total 3030.0% 100.0% 30.0% Always calculate percentages in the direction of the causal variable.

  5. SLIDE 21-4 Financing the Purchase by Van Ownership FINANCE MOST RECENT AUTO PURCHASE? OWN VAN? YES NO TOTAL 3(15%) 17(85%) 20(100%) YES 27(34%) 53(66%) 80(100%) NO Total 30 70 100

  6. 15 i=1 Σ Di2=52 SLIDE 21-5 Spearman Rank-Order Correlation:Distributor Performance Data Service Quality Ranking Xi Overall Performance Ranking Yi Ranking DifferenceDi = Xi = Yi Difference Squared Di2 Distributor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 2 13 1 7 4 11 15 3 9 12 5 14 8 10 8 4 12 2 10 5 9 13 1 6 14 3 15 7 11 -2 +2 +1 -1 -3 -1 +2 +2 +2 +3 -2 +2 -1 +1 -1 4 4 1 1 9 1 4 4 4 9 4 4 1 1 1

  7. SLIDE 21-6 Kendall’s Coefficient of Concordance: Branch Manager Rankings RANK ADVOCATED BY Branch Manager Vice President of Marketing Marketing Research Department Sum of Ranks Ri General Sales Manager A B C D E F G H I J 4 3 9 10 2 1 6 8 5 7 4 2 10 9 3 1 5 7 6 8 5 2 10 9 3 1 4 7 6 8 13 7 29 28 8 3 15 22 17 23

  8. SLIDE 21-7 Independent Samples T-test: Store Sales of Floor Wax (in Units) Store Plastic Container Metal Container 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 432 360 397 408 417 380 422 406 400 408 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 365 405 396 390 404 372 378 410 383 400

  9. SLIDE 21-8 Paired Sample T-test:Store Sales of Sleeping Bags Store Bright Colors Earth Colors 1 2 3 4 5 64 72 43 22 50 56 66 39 20 45

  10. SLIDE 21-9 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

  11. SLIDE 21-10 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 ANOVAa,b Unique Method Sum of Squares Mean Square df F Sig. COMMIT CURRAUTO Main Effects Model ResidualTotal 30.981 30.981 1147.219 1178.200 1 1 395 396 30.981 30.981 2.904 2.975 10.667 10.667 .001 .001 • COMMIT by CURRAUTO • All effects entered simultaneously

  12. SLIDE 21-11 SPSS ANOVA Table for Two-Way Consumer Commitment Study Currently Drive Car from Dealership? Satisfaction Level No (n) Yes (n) Total (n) 3.4 4.8 4.1 (193) (204) (397) 3.6 5.0 4.3 (132) (153) (285) Lower Higher Total 3.2 4.3 3.7 (61) (51) (112)

  13. SLIDE 21-12 Scatter Diagram: Sales vs. TV Spots 800 700 Sales-Y 600 500 400 Thousands of Dollars 300 200 100 0 0 5 10 15 20 TV Spots-X1

  14. SLIDE 21-13 SPSS Output for the Correlation of Sales and TV Spots Correlations SALES NUMSPOTS Pearson Correlation Sig. (2-tailed)N NUMSPOTS SALES NUMSPOTS SALESNUMSPOTS SALES 1.000 .880** . .00040 40 .880** 1.000 .000 .40 40 **.Correlation is significant at the 0.01 level (2-tailed).

  15. SLIDE 21-14 Scatter Diagram: Sales vs. Number of Salespersons Sales-Y Thousands of Dollars Number of Salespersons-X2

  16. Adjusted R Square Std. Error of the Estimate Model R R Square 1 .882a .778 .773 59.016 Sum of Squares Mean Square Model df F Sig. 1 RegressionResidualTotal 465161.13132349.55597510.67 13839 465161.133482.883 133.556 .000a SLIDE 21-15 Does Number of Sales Reps Influence Sales? SIMPLE REGRESSION ANALYSIS OUTPUT FROM SPSS Model Summary aPredictors: (Constant), NUMREPS ANOVAb aPredictors: (Constant), NUMREPS bDependent Variable: SALES Coefficientsa Unstandardized Coefficients Standardized Coefficients Model t Sig. B Beta Std. Error (Constant)NUMREPS 80.14166.244 2.65911.557 .011.000 30.1415.732 1 .882

  17. SLIDE 21-16 Plot of Equation Relating Sales to Number of Sales Reps Y = 80.1 + 66.2X Sales-Y Thousands of Dollars Number of Sales Reps-X

  18. SLIDE 21-17 Scatter Diagram: Sales vs. Wholesaler Efficiency Index Sales-Y Thousands of Dollars Wholesaler Efficiency Index-X3

  19. .450 .550 .091 SLIDE 21-18 Computer Output: Multiple Regression Analysis Sales Dependent Variable Coefficient of Multiple Determination Coefficient of Multiple Correlation Standard Error of Estimate .882 .939 44.304 Variable Regression Standard T- Standardized Status Coefficient Error Value Coefficient p-value Constant 31.382 34.083 0.921 .363 TV Spots in 12.931 2.730 4.737 .000 Salespersons in 41.316 7.260 5.691 .000 Wholeeff in 11.486 7.670 1.497 .143 ANOVA p-value Sum of Squares Degrees of Freedom F Ratio Mean Square .000 Regression Residual Total 526849.11 70661.57 597510.67 3 36 39 89.471 175616.37 1962.82

  20. SLIDE 21-19 Modifying Bivariate Relationships by Introducing a Third Variable Financed Car Purchase by Education of Household Head FINANCED CAR PURCHASE? 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%)

  21. SLIDE 21-20 Modifying Bivariate Relationships by Introducing a Third Variable Financed Car Purchase by Education of Household Head and Income INCOME Education of Household Head High school or less Some college Less than $37,500 12% 40% More than $37,500 58% 27% Total 30% 30%

  22. SLIDE 21-21 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

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