chapter16.ppt 430KB Aug 17 2002 01:15:44 AM

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Analysis of Variance and

Covariance

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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

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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

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13) Multivariate Analysis of Variance

14) Internet and Computer Applications

15) Focus on Burke

16) Summary

17) Key Terms and Concepts

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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

Independent Variables Metric Dependent Variable

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Conducting One-Way ANOVA

Identify the Dependent and Independent Variables

Decompose the Total Variation

Measure the Effects

Test the Significance

Interpret the Results

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Independent Variable

X

Total

Sample

X1

X2

X3

…

Xc

Y1

Y2

:

Yn

YN

Y1

Y2

Y3

Yc

Y

Within

Variation

=SSwithin

Between Category Variation = SS between

Total Variation =SS y

Mean

Decomposition of the Total

Variation: One-Way ANOVA

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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

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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

Effect of In-Store Promotion on Sales

Table 16.3

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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

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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

Two-Way Analysis of Variance

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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

High 10 8.300 Medium 10 6.200 Low 10 3.700 Yes 15 7.400 No 15 4.733 Grand Mean 30 6.067

Table 16.5 Contd.

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Possible Interaction Effects

No Interaction

(Case 1)

Interaction

Ordinal

(Case 2)

Disordinal

Noncrossover

(Case 3)

Crossover

(Case 4)

A Classification of Interaction Effects

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Y

X

₁₁

X

₁₂

X

₁₃

Case 1: No Interaction

Patterns of Interaction

Figure 16.4

X22

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

Case 3: Disordinal Interaction:

Noncrossover

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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

Analysis of Covariance

Table 16.6

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Independent Variable

X

Subject

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

Decomposition of the Total Variation:

Repeated Measures ANOVA

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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

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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

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Possible Interaction Effects

No Interaction

(Case 1) Interaction

Ordinal

(Case 2) Disordinal

Noncrossover (Case 3)

Crossover (Case 4)

A Classification of Interaction Effects

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X ₁₁ X₁₂ X₁₃

Case 1: No Interaction

Patterns of Interaction

Figure 16.4

X22 X21

X₁₁ X₁₂ X₁₃ X22

X21 Y

Case 2: Ordinal Interaction

X₁₁ X₁₂ X₁₃

X22 X21

Case 3: Disordinal Interaction: Noncrossover

X₁₁ X₁₂ X₁₃

X22 X21

Case 3: Disordinal Interaction: Noncrossover

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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

Analysis of Covariance

Table 16.6

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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

Decomposition of the Total Variation:

Repeated Measures ANOVA

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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

(6)

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

RIP 16.2