Chapter Outline
1) Overview
2) Relationship Among Techniques
3) One-Way Analysis of Variance
4) Statistics Associated with One-Way Analysis of Variance
5) Conducting One-Way Analysis of Variance
i. Identification of Dependent & Independent
Variables
ii. Decomposition of the Total Variation
iii. Measurement of Effects
iv. Significance Testing
6) Illustrative Applications of One-Way Analysis of Variance
7) Assumptions in Analysis of Variance
8) N-Way Analysis of Variance
9) Analysis of Covariance
10) Issues in Interpretation
i. Interactions
ii. Relative Importance of Factors
iii. Multiple Comparisons
11) Repeated Measures ANOVA
13) Multivariate Analysis of Variance
14) Internet and Computer Applications
15) Focus on Burke
16) Summary
17) Key Terms and Concepts
Relationship Among t Test, Analysis of
Variance, Analysis of Covariance, & Regression
t Test Binary One Independent Variable One-Way Analysis of Variance One Factor N-Way Analysis of Variance More Than One Factor Analysis of Variance Categorical: Factorial Analysis of Covariance Categorical and Interval Regression Interval One or More
[image:5.720.32.696.43.502.2]Independent Variables Metric Dependent Variable
Conducting One-Way ANOVA
Identify the Dependent and Independent Variables
Decompose the Total Variation
Measure the Effects
Test the Significance
[image:6.720.133.631.114.481.2]Interpret the Results
Independent Variable
X
Total
Categories
Sample
X1
X2
X3
…
Xc
Y1
Y1
Y1
Y1
Y1
Y2
Y2
Y2
Y2
Y2
:
:
:
:
Yn
Yn
Yn
Yn
YN
Y1
Y2
Y3
Yc
Y
Within
Category
Variation
=SSwithin
Between Category Variation = SS between
Total Variation =SS y
Category
Mean
Decomposition of the Total
Variation: One-Way ANOVA
Store Number Coupon Level In-Store Prom otion Sales Clientel Rating
1 1.00 1.00 10.00 9.00 2 1.00 1.00 9.00 10.00 3 1.00 1.00 10.00 8.00 4 1.00 1.00 8.00 4.00 5 1.00 1.00 9.00 6.00 6 1.00 2.00 8.00 8.00 7 1.00 2.00 8.00 4.00 8 1.00 2.00 7.00 10.00 9 1.00 2.00 9.00 6.00 10 1.00 2.00 6.00 9.00 11 1.00 3.00 5.00 8.00 12 1.00 3.00 7.00 9.00 13 1.00 3.00 6.00 6.00 14 1.00 3.00 4.00 10.00 15 1.00 3.00 5.00 4.00 16 2.00 1.00 8.00 10.00 17 2.00 1.00 9.00 6.00 18 2.00 1.00 7.00 8.00 19 2.00 1.00 7.00 4.00 20 2.00 1.00 6.00 9.00 21 2.00 2.00 4.00 6.00 22 2.00 2.00 5.00 8.00 23 2.00 2.00 5.00 10.00 24 2.00 2.00 6.00 4.00 25 2.00 2.00 4.00 9.00 26 2.00 3.00 2.00 4.00 27 2.00 3.00 3.00 6.00 28 2.00 3.00 2.00 10.00 29 2.00 3.00 1.00 9.00 30 2.00 3.00 2.00 8.00
Store Level of In-Store Promotion
Number High Medium Low
1 10 8 5
2 9 8 7
3 10 7 6
4 8 9 4
5 9 6 5
6 8 4 2
7 9 5 3
8 7 5 2
9 7 6 1
10 6 4 2
Column totals 83 62 37
Category means: 83/10 62/10 37/10
Y = 8.3 = 6.2 = 3.7
Grand mean:
Y = (83 + 62 + 37)/30 = 6.067
j
Cell means
Level of Count Mean
Promotion
High (1) 10 8.300
Medium (2) 10 6.200
Low (3) 10 3.700
TOTAL 30 6.067
Source of Sum of df Mean F ratio F prob.
Variation squares square
Between groups 106.067 2 53.033 17.944 0.000 (Promotion)
Within groups 79.800 27 2.956
(Error)
TOTAL 185.867 29 6.409
One-Way ANOVA:
Effect of In-store Promotion on Store Sales
Source of Sum of Mean Sig. of
Variation squares df square F F
Main Effects
Promotion 106.067 2 53.033 54.862 .000 .557 Coupon 53.333 1 53.333 55.172 .000 .280 Combined 159.400 3 53.133 54.966 .000
Two-way 3.267 2 1.633 1.690 .226 interaction
Model 162.667 5 32.533 33.655 .000 Residual (error) 23.200 24 0.967
TOTAL 185.867 29 6.409
2
[image:11.720.38.689.124.428.2]Two-Way Analysis of Variance
Cell Means
Promotion Coupon Count Mean
High Yes 5 9.200 High No 5 7.400 Medium Yes 5 7.600 Medium No 5 4.800 Low Yes 5 5.400 Low No 5 2.000
TOTAL 30
Factor Level Means
Promotion Coupon Count Mean
[image:12.720.20.686.92.504.2]Possible Interaction Effects
No Interaction
(Case 1)
Interaction
Ordinal
(Case 2)
Disordinal
Noncrossover
(Case 3)
Crossover
(Case 4)
[image:13.720.22.689.82.503.2]A Classification of Interaction Effects
Y
X
11
X
12
X
13
[image:14.720.26.678.37.525.2]Case 1: No Interaction
Patterns of Interaction
Figure 16.4X22
X21
X
11
X
12
X
13
X22
X21
Y
Case 2: Ordinal Interaction
Y
X
11
X
12
X
13
X22
X21
Case 3: Disordinal Interaction:
Noncrossover
Y
X
11
X
12
X
13
X22
X21
Sum of Mean Sig. Source of Variation Squares df Square F of F
Covariance
Clientele 0.838 1 0.838 0.862 .363 Main effects
Promotion 106.067 2 53.033 54.546 .000 Coupon 53.333 1 53.333 54.855 .000 Combined 159.400 3 53.133 54.649 .000 2-Way Interaction
Promotion* Coupon 3.267 2 1.633 1.680 .208
Model 163.505 6 27.251 28.028 .000
Residual (Error) 22.362 23 0.972
TOTAL 185.867 29 6.409 Covariate Raw Coefficient
Clientele -0.078
[image:15.720.4.701.75.498.2]Independent Variable
X
Subject
Categories
Total
No.
Sample
X1
X2
X3
…
Xc
1
Y11
Y12
Y13
Y1c
Y1
2
Y21
Y22
Y23
Y2c
Y2
:
:
:
:
n
Yn1
Yn2
Yn3
Ync
YN
Y1
Y2
Y3
Yc
Y
Between People Variation =SS between people
Total Variation =SSy
Within People Category Variation = SS within people
Category Mean
[image:16.720.8.704.48.454.2]Decomposition of the Total Variation:
Repeated Measures ANOVA
A study examined marketing professionals’ perceptions of the
commonality of unethical marketing research practices on a
cross-national basis. The sample of marketing professionals was drawn
from Australia, Canada, Great Britain, and the United States.
Respondents’ evaluations were analyzed using computer programs
for MANOVA and ANOVA. Country of respondent comprised the
predictor variable in the analysis, and 15 commonality evaluations
served as the criterion variables. The F-values from the ANOVA
analyses indicated that only two of the 15 commonality evaluations
achieved significance (p<.05 or better). Further, the MANOVA
F
value was not significant, implying the lack of overall differences in
commonality evaluations across respondents of the four countries.
Therefore, it was concluded that marketing professionals in the four
countries evince similar perceptions of the commonality of unethical
marketing research practices. The finding is not surprising, given
research evidence that organizations in the four countries reflect
similar corporate cultures.
The Commonality of Unethical Research
Practices Worldwide
In order to investigate differences between research ethics judgements in
men and women, the statistical techniques of MANOVA and ANOVA were
used. Respondents were asked to indicate their degree of approval with
regards to series of scenarios involving decisions of an ethical nature.
These evaluations served as the dependent variable in the analysis, while
sex of the respondent served as the independent variable. MANOVA was
used for multivariate analysis and its resultant F value was significant at
the p<0.001 level - indicating that there was an “overall” difference
between males and females in research ethics judgements. Univariate
analysis was conducted via ANOVA, and F values indicated that three
items were the greatest contributors to the overall gender difference in
ethical evaluations: the use of ultraviolet ink to precode a mail
questionnaire, the use of an ad that encourages consumer misuse of a
product, and unwillingness by researcher to offer data help to an inner city
advisory group.
“MAN” OVA Demonstrates that
Man is Different from Women
