# BTM8106 Week 3 Complete Solution

1. Jackson, even-numbered Chapter Exercises, pp. 308-310.

2) What is the difference between a randomized ANOVA and a repeated measures ANOVA? What does the term one-way mean with respect to ANOVA?

4) If a researcher decides to use multiple comparisons in a study with three conditions, what is the probability of a Type I error across these comparisons? Use the Bonferroni adjustment to determine the suggested alpha level.

6) When should post-hoc comparisons be performed?

8) Why is repeated measures ANOVA statistically more powerful than a randomized ANOVA?

10) In a study of the effects of stress on illness, a researcher taillied the number of colds people contracted during a 6-month period as a function of the amount of stress they reported during the same period. There were three stress levels: minimal, moderate, and high stress. The sums of squares appear in the following ANOVA summary table. The mean for each condition and the number of subjects per condition and the number of subjects per condition are also noted.

Source df SS MS f

Between groups 22.167

Within groups 14.750

Total 36.917

Stress level Mean N

minimal 3 4

moderate 4 4

maximum 6 4

A) Complete the ANOVA summary table

B) Is F obt significant at a=.05, or at a=.01

C) Perform post hoc comparisons if necessary.

D)What conclusions can be drawn from the F-ratio and the post hoc comparisons?

E) What is the effect size? What does it mean?

F) Graph the means.

12) A researcher conducted an experiment on the effects of a new “drug” on depression. The researcher had a control group that received nothing, a placebo group and an experimental group that received the “drug”. A depression inventory that provided a measure of depression on a 50-point scale was used (50 indicates that an individual is very high on the depression variable). The ANOVA summary table appears next, along with the mean depressing score for each condition.

source df ss ms f

between groups 1,202.313

within groups 2,118.00

total 3,320.313

drug condition mean n

control 36.26 15

placebo 33.33 15

drug 24.13 15

A. complete the ANOVA summary table

b. Is f obt significant at α= .05; at α= .01?

c. Perform post hoc comparisons if necessary

d. What conclusions can be drawn from the F ration and the post hoc comparisons?

e. What is the effect size , and what does this mean?

f. Graph the means

14) A researcher has been hired by a pizzeria to determine which type of crust customers prefer. The restaurant offers three types of crust: hand-tossed, thick, and thin. Following are the mean number of l-inch pieces of pizza eaten for each condition from 10 subjects who had the opportunity to eat as many pieces with each type of crust as they desired. The ANOVA summary table also follows

Source df ss MS F

Subject 2.75

Between 180.05

Error 21.65

Total 204.45

Crust type Mean n

Hand-tossed 2.73 10

Think 4.20 10

thin 8.50 10

a) Complete the ANOVA summary table.

b) Is Fobt significant at a = .05; at a = .01?

c) Perform post hoc comparisons if necessary.

d) What conclusions can be drawn from the F-ratio and the post hoc comparisons?

e) What is the effect size, and what does this mean?

f) Graph the means

2. What is an F-ratio? Define all the technical terms in your answer.

3. What is error variance and how is it calculated?

4. Why would anyone ever want more than two (2) levels of an independent variable?

5. If you were doing a study to see if a treatment causes a significant effect, what would it mean if within groups variance was higher than between groups variance? If between groups variance was higher than within groups variance? Explain your answer

6. What is the purpose of a post-hoc test with analysis of variance?

7. What is probabilistic equivalence? Why is it important?

2) What is the difference between a randomized ANOVA and a repeated measures ANOVA? What does the term one-way mean with respect to ANOVA?

4) If a researcher decides to use multiple comparisons in a study with three conditions, what is the probability of a Type I error across these comparisons? Use the Bonferroni adjustment to determine the suggested alpha level.

6) When should post-hoc comparisons be performed?

8) Why is repeated measures ANOVA statistically more powerful than a randomized ANOVA?

10) In a study of the effects of stress on illness, a researcher taillied the number of colds people contracted during a 6-month period as a function of the amount of stress they reported during the same period. There were three stress levels: minimal, moderate, and high stress. The sums of squares appear in the following ANOVA summary table. The mean for each condition and the number of subjects per condition and the number of subjects per condition are also noted.

Source df SS MS f

Between groups 22.167

Within groups 14.750

Total 36.917

Stress level Mean N

minimal 3 4

moderate 4 4

maximum 6 4

A) Complete the ANOVA summary table

B) Is F obt significant at a=.05, or at a=.01

C) Perform post hoc comparisons if necessary.

D)What conclusions can be drawn from the F-ratio and the post hoc comparisons?

E) What is the effect size? What does it mean?

F) Graph the means.

12) A researcher conducted an experiment on the effects of a new “drug” on depression. The researcher had a control group that received nothing, a placebo group and an experimental group that received the “drug”. A depression inventory that provided a measure of depression on a 50-point scale was used (50 indicates that an individual is very high on the depression variable). The ANOVA summary table appears next, along with the mean depressing score for each condition.

source df ss ms f

between groups 1,202.313

within groups 2,118.00

total 3,320.313

drug condition mean n

control 36.26 15

placebo 33.33 15

drug 24.13 15

A. complete the ANOVA summary table

b. Is f obt significant at α= .05; at α= .01?

c. Perform post hoc comparisons if necessary

d. What conclusions can be drawn from the F ration and the post hoc comparisons?

e. What is the effect size , and what does this mean?

f. Graph the means

14) A researcher has been hired by a pizzeria to determine which type of crust customers prefer. The restaurant offers three types of crust: hand-tossed, thick, and thin. Following are the mean number of l-inch pieces of pizza eaten for each condition from 10 subjects who had the opportunity to eat as many pieces with each type of crust as they desired. The ANOVA summary table also follows

Source df ss MS F

Subject 2.75

Between 180.05

Error 21.65

Total 204.45

Crust type Mean n

Hand-tossed 2.73 10

Think 4.20 10

thin 8.50 10

a) Complete the ANOVA summary table.

b) Is Fobt significant at a = .05; at a = .01?

c) Perform post hoc comparisons if necessary.

d) What conclusions can be drawn from the F-ratio and the post hoc comparisons?

e) What is the effect size, and what does this mean?

f) Graph the means

2. What is an F-ratio? Define all the technical terms in your answer.

3. What is error variance and how is it calculated?

4. Why would anyone ever want more than two (2) levels of an independent variable?

5. If you were doing a study to see if a treatment causes a significant effect, what would it mean if within groups variance was higher than between groups variance? If between groups variance was higher than within groups variance? Explain your answer

6. What is the purpose of a post-hoc test with analysis of variance?

7. What is probabilistic equivalence? Why is it important?

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