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

VAN YES Count% within VAN

% within FINANCE

% of Total

YES NO TotalFINANCE

315.0%

10.0%

3.0%

2733.8%

90.0%

27.0%

Count% within VAN

% within FINANCE

% of Total

Count% within VAN

% within FINANCE

% of Total

3030.0%

100.0%

30.0%

NO

Total

1785.0%

24.3%

17.0%

5366.3%

75.7%

53.0%

7070.0%

100.0%

70.0%

20100.0%

20.0%

20.0%

80100.0%

80.0%

80.0%

100100.0%

100.0%

100.0%

VAN*FINANCE Crosstabulation

Financing the Purchase by Van Ownership

FINANCE MOST RECENT AUTO PURCHASE?

SLIDE 21-4

OWN VAN? YES NO TOTAL

YES

NO

3(15%)

27(34%)

17(85%)

53(66%)

20(100%)

80(100%)

Total 30 70 100

Spearman Rank-Order Correlation:Distributor Performance Data

Distributor

SLIDE 21-5

Service Quality Ranking Xi

Overall Performance Ranking Yi

Ranking DifferenceDi = Xi = Yi

Difference Squared Di

2

123456789101112131415

621317411153912514810

84

122

1059

1316

143

157

11

-2+2+1-1-3-1+2+2+2+3-2+2-1+1-1

44119144494411115

i=1ΣDi

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 Ri

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

RANK ADVOCATED BY

Independent Samples T-test: Store Sales of Floor Wax (in Units)

SLIDE 21-7

Store Plastic Container

Metal Container12345678910

11121314151617181920

432360397408417380422406400408

____________________

__________________

365405396390404372378410383400

Paired Sample T-test:Store Sales of Sleeping Bags

SLIDE 21-8

Store Bright Colors Earth Colors

1

2

3

4

5

64

72

43

22

50

56

66

39

20

45

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

ANOVAa,b

SLIDE 21-10

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

Main Effects

Model

ResidualTotal

CURRAUTOCOMMIT

Sum of Squares df

Mean Square F Sig.

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 21-11

Satisfaction Level No (n) Yes (n) Total (n)

Lower

Higher

Total

3.2

4.3

3.7

(61)

(51)

(112)

3.6

5.0

4.3

(132)

(153)

(285)

3.4

4.8

4.1

(193)

(204)

(397)

Scatter Diagram: Sales vs. TV Spots

0

100

200

300

400

500

600

700

800

0 5 10 15 20

Sales-Y

ThousandsofDollars

TV Spots-X1 SLIDE 21-12

SPSS Output for the Correlation of Sales and TV Spots

Correlations

SLIDE 21-13

NUMSPOTS SALES

NUMSPOTS

SALES

NUMSPOTS

SALES

NUMSPOTS

SALES

Pearson

Correlation

Sig.

(2-tailed)

N

1.000

.880**

.

.000

40

40

.880**

1.000

.000

.

40

40

**.Correlation is significant at the 0.01 level (2-tailed).

Scatter Diagram: Sales vs. Number of Salespersons

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10

Sales-Y

ThousandsofDollars

Number of Salespersons-X2SLIDE 21-14

Does Number of Sales Reps Influence Sales?

SIMPLE REGRESSION ANALYSIS OUTPUT FROM SPSS

Model Summary

SLIDE 21-15

aPredictors: (Constant), NUMREPS

Model B Std. Error Beta1 80.141

66.24430.1415.732 .882

(Constant)NUMREPS

t2.659

11.557.011.000

Sig.

Unstandardized Coefficients

Standardized Coefficients

Model R R SquareAdjusted R Square

Std. Error of the Estimate1 .882a .778 .773 59.016

ANOVAb

aPredictors: (Constant), NUMREPS bDependent Variable: SALES

ModelSum of Squares df

Mean Square

1 RegressionResidualTotal

465161.13132349.55597510.67

13839

465161.13

3482.883

F Sig.133.556 .000a

Coefficientsa

Plot of Equation Relating Sales to Number of Sales Reps

SLIDE 21-16

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10

Sales-Y

ThousandsofDollars

Number of Sales Reps-X

Y = 80.1 + 66.2X

Scatter Diagram: Sales vs. Wholesaler Efficiency Index

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5

Sales-Y

ThousandsofDollars

Wholesaler Efficiency Index-X3 SLIDE 21-17

Computer Output: Multiple Regression Analysis

Coefficient of Multiple Determination

Coefficient of Multiple Correlation

Standard Error of EstimateVariable Regression Standard T- StandardizedStatus Coefficient Error Value Coefficient p-value

Constant 31.382TV Spots in 12.93

12.730 4.737

ANOVA

Regression

Residual

Total

526849.11

70661.57

597510.67

3

36

39

175616.37

1962.82

89.471

Sum ofSquares

Degrees of Freedom

MeanSquare

FRatio

.882

.939

44.304

Salespersons in 41.316

7.260 5.691Wholeeff in 11.48

67.670 1.497

.000

.000

.143

Sales

Dependent Variable

34.083

0.921.450

.550

.091

.363

.000p-value

SLIDE 21-18

Modifying Bivariate Relationships by Introducing a Third Variable

FINANCED CAR PURCHASE?

SLIDE 21-19

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 21-20

INCOME

Education of Household Head

High school or less

Some college

Less than $37,500

12%

40%

Total

30%

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