2. The structure of a two-factor study can be presented as a matrix with the levels of one factor

determining the rows and the levels of the second factor determining the columns. With this structure in mind, describe the mean differences that are evaluated by each of the three hypothesis tests that make up a two-factor ANOVA.

4. For the data inthe following matrix:

5. The following matrix presents the results from an independent-measures, two-factor study with

a sample of n = 10 participants in each treatment condition. Note that one treatment mean is missing.

No Treatment

Treatment

Male

M=5 M _=3

Overall M = 4

Female

M = 9 M =13

Overall M =11

overall M =7

overall M = 8

a. Which two means are compared to describe the treatment main effect?

b. Which two means are compared to describe the gender main effect?

c. Is there an interaction between gender and treatment? Explain your answer.

6. The following matrix presents the results of a two factor study with n = 10 scores in

each of the six treatment conditions. Note that one of the treatment means is missing.

Factor

B

B1 B2 B3

A1 M =10 M =20 M = 40

Factor A

A2 M =20 M =30

a. What value for the missing mean would result in no main effect for factor A?

b. What value for the missing mean would result in no interaction?

8. A researcher conducts an independent-measures, two-factor study using a separate sample of n

= 15 participants in each treatment condition. The results are evaluated using an ANOVA and the researcher reports

an F-ratio with df =1, 84 for factor A, and an F-ratio with df = 2, 84 for factor B.

a. How many levels of factor A were used in the study?

b. How many levels of factor B were used in the study?

c. What are the df values for the F-ratio evaluating the interaction?

10. The following results are from an independent-measures,two-factor study with n = 5

participants in each treatment condition.

Factor

B

B1 B2

T =40 T =10

M =4

M = 1

SS _=50

SS =30

T =50 T =20

M = 5

M = 2

SS =60

SS =40

N =40

G =120

X2 =640

Factor

A

A1

A2

a. Use a two-factor

ANOVA with sd=.05 to evaluate the main effects and the

interaction.

b. Test the simple

main effects using sd= .05 to evaluate the mean difference

between treatment

A1 and A2 for each level of

factor B.

12. Most sports injuries are immediate and obvious, like a broken leg. However, some can be

more subtle, like the neurological damage that may occur when soccer players repeatedly head a soccer ball. To examine long-term effects of repeated heading, Downs and Abwender (2002) examined two different age groups of soccer players and swimmers. The dependent variable was performance on a conceptual thinking task. Following are hypothetical data, similar to the research results.

a. Use a two-factor ANOVA with = .05 to evaluate the main effects and interaction.

b. Calculate the effects size (n2) for the main effects and the interaction.

c. Briefly describe the outcome of the study.

Factor

B:

Age

College

Older

n _ 20

n _ 20

M _ 9

M _ 4

T _ 180

T _ 80

SS _ 380

SS _ 390

n _ 20

n _ 20

M _ 9

M _ 8

T _ 180

T _ 160

SS _ 350

SS _ 400

X2 _ 6360

14. The following

table summarizes the results from a two-factor study with 2 levels of factor A

and 3 levels

of factor B using a

separate sample of n = 8 participants in each treatment condition. Fill

in the missing values. (Hint: Start with the df values.)

Source

SS df MS

Between treatments 60

Factor A 5 F _

Factor B F_

A _ B

Interaction

25 F _

Within treatments 2.5

Total

a. Use a two-factor

ANOVA with = .05 to evaluate the mean differences.

b. Briefly explain

how temperature and pouring influence the bubbles in champagne according to

this pattern of results.

16. The Preview

section for this chapter described a two factor study examining performance

under two audience

conditions (factor B) for

high and low self-esteem participants (factor A). The following summary

table presents possible results from the analysis of that study.

Assuming that the study used a

separate sample of n = 15 participants in each treatment condition (each

cell), fill in the missing values in the table.

(Hint: Start with the df

values.)

Source

SS df MS

Between treatments 67

Audience F =

Self-esteem 29 F =

Interaction F = 5.50

Within treatments 4

Total

18. The following

data are from a two-factor study examining the effects of two treatment

conditions on males and females.

a. Use an ANOVA with

= .05 for all

tests to evaluate the significance of the main effects and the interaction.

b. Compute n2

to

measure the size of the effect for each main effect and the interaction.

Treatments

I

II

3 2

8 8

9 7

Tmale = 48

4 7

M =6

M = 6

T =24

T = 24 N =16

SS =26

SS =22 G =96

0 12

X2 = 806

0 6

2 9

6 13

M = 2

M = 10 Tfemale = 48

T =8

T =40

SS =24

SS =30

TI = 32 TII = 64

20. Mathematics word

problems can be particularly difficult, especially for primary-grade children.

A recent study investigated a combination of techniques for teaching students

to master these problems (Fuchs,Fuchs, Craddock, Hollenbeck, Hamlett, &

Schatschneider, 2008). The study investigated the effectiveness of small-group

tutoring and the

effectiveness of a classroom

instruction technique known as “hot math.” The hot-math program teaches

students to recognize types or categories of problems so that they can

generalize skills from one problem to another. The following data are similar

to the results obtained in the study. The dependent variable is a math test

score for each student after 16 weeks in the study.

Traditional

Instruction

No Tutoring

With Tutoring

3

9

6

4

2

5

2

8

4

4

7

6

Hot-Math Instruction

7

8

7

12

2

9

6

13

8

9

6

9

a. Use a two-factor

ANOVA with = .05 to evaluate the significance of

the main effects and the

interaction.

b. Calculate the _2

values

to measure the effect size for the two main effects.

c. Describe the

pattern of results. (Is tutoring significantly better than no tutoring? Is

traditional classroom instruction significantly different from hot math? Does

the effect of tutoring depend on the type of classroom instruction?)

22. In Chapter 11, we

described a research study in which the color red appeared to increase men’s

attraction to women (Elliot & Niesta, 2008). The same researchers have

published other results showing that red also increases women’s attraction to

men but does not appear to affect judgments of same sex individuals (Elliot, et

al., 2010). Combining these results into one study produces a two-factor design

in which men judge photographs of both women and men, which are

shown on both red and white backgrounds.

The dependent variable is a rating of attractiveness for the person shown in

the photograph. The study uses a separate group of participants for each

condition. The following table presents data similar to the results from

previous research.

a.

Use a two-factor ANOVA with = .05 to evaluate

the main effects and the interaction.

Person Shown in Photograph

WhiteFemale Male

n

= 10 n = 10

M

= 4.5 M = 4.4

SS

=6 SS = 7

RedFemale Male

n

=10 n =10

M

=7.5 M =4.6

` SS

= 9 SS = 8

b.

Describe the effect of background color on judgments

of males and females.