data analysis: analyzing multiple variables simultaneously chapter 21
TRANSCRIPT
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