The results of a two-way ANOVA using the accompanying data and hypothesis tests

ID: 3072905 • Letter: T

Question

The results of a two-way ANOVA using the accompanying data and hypothesis tests for interaction between Factor A and Factor B and for each factor are provided below. Using these data and results, determine which means are different using = 0.01when warranted.

Factor A

FactorB

Level 1

Level 2

Level 3

Level 1

1010

1212

3232

1010

1919

3030

Level 2

2828

3030

1111

2020

3838

1616

2020

3939

Level 3

3535

4040

4242

3131

2929

4141

2121

4040

3232

Are the means for Factor A, Level 1 and Factor A, Level 2 significantly different?

A.Yes

B. No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor A, Level 1 and Factor A, Level 3 significantly different?

A.Yes

B. No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor A, Level 2 and Factor A, Level 3 significantly different?

A.Yes

B.No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor B, Level 1 and Factor B, Level 2 significantly different?

A.Yes

B.No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor B, Level 1 and Factor B, Level 3 significantly different?

A.No

B.Yes

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor B, Level 2 and Factor B, Level 3 significantly different?

A.No

B.Yes

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Factor A

FactorB

Level 1

Level 2

Level 3

Level 1

1010

1212

3232

1010

1919

3030

Level 2

2828

3030

1111

2020

3838

1616

2020

3939

Level 3

3535

4040

4242

3131

2929

4141

2121

4040

3232

Explanation / Answer

Answer:

MINITAB used.

General Linear Model: Data versus A, B

Method

Factor coding

(-1, 0, +1)

Factor Information

Factor

Type

Levels

Values

Fixed

A1, A2, A3

Fixed

B1, B2, B3

Analysis of Variance

Source

Adj SS

Adj MS

F-Value

P-Value

11325157

5662578

9.66

0.001

21976136

10988068

18.75

0.000

A*B

1484102

371026

0.63

0.645

Error

10548520

586029

Total

45333915

Model Summary

R-sq

R-sq(adj)

R-sq(pred)

765.525

76.73%

66.39%

47.65%

Comparisons for Data

Tukey Pairwise Comparisons: A

Grouping Information Using the Tukey Method and 99% Confidence

Mean

Grouping

3299.33

2366.44

1721.67

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference
of A Levels

Difference
of Means

SE of
Difference

Simultaneous
99% CI

T-Value

Adjusted
P-Value

A2 - A1

645

361

(-555, 1844)

1.79

0.202

A3 - A1

1578

361

(378, 2777)

4.37

0.001

A3 - A2

933

361

(-266, 2132)

2.59

0.047

Individual confidence level = 99.62%

Tukey Pairwise Comparisons: B

Grouping Information Using the Tukey Method and 99% Confidence

Mean

Grouping

3490.11

2603.56

1293.78

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference
of B Levels

Difference
of Means

SE of
Difference

Simultaneous
99% CI

T-Value

Adjusted
P-Value

B2 - B1

1310

361

(110, 2509)

3.63

0.005

B3 - B1

2196

361

(997, 3396)

6.09

0.000

B3 - B2

887

361

(-313, 2086)

2.46

0.060

Individual confidence level = 99.62%

Are the means for Factor A, Level 1 and Factor A, Level 2 significantly different?

A.Yes

Answer: B. No ( p value 0.202 which is > 0.01 level)

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor A, Level 1 and Factor A, Level 3 significantly different?

Answer: A.Yes ( p value 0.001 which is < 0.01 level)

B. No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor A, Level 2 and Factor A, Level 3 significantly different?

A.Yes

Answer: B.No( p value 0.047 which is > 0.01 level)

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor B, Level 1 and Factor B, Level 2 significantly different?

Answer A.Yes ( p value 0.005 which is < 0.01 level)

B.No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor B, Level 1 and Factor B, Level 3 significantly different?

A.No

Answer B.Yes( p value 0.000 which is < 0.01 level)

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor B, Level 2 and Factor B, Level 3 significantly different?

Answer:A.No( p value 0.060 which is > 0.01 level)

B.Yes

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Factor coding

(-1, 0, +1)

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The results of a two-way ANOVA using the accompanying data and hypothesis tests

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