1. The following data summarize the results from an independent-measures study

comparing three treatment conditions.

Treatment

I II III

0 2 4 N=18

0 3 2 G=36

0 1 4 ∑X^{2}=114

3 3 3

0 2 4

0 1 4

M=0.5 M=2 M=3.5

T=3 T=12 T=21

SS=7.5 SS=4 SS=3.5

a. Use an ANOVA with α=.05 to determine whether there are any

significant differences among the three treatment means.

b. Calculate η^{2} to measure the effect size for this study.

2. The following data summarize the results from an independent-measures study

comparing three treatment conditions.

Treatment

I II II

4 1 0 N=12

6 4 2 G=36

3 5 0 ∑X^{2}=164

7 2 2

M=5 M=3 M=1

T=20 T=12 T=4

SS=10 SS=10 SS=4

a. Calculate the sample variances for each of the three samples.

b. Use an ANOVA with α=.05 to determine whether there are any significant differences among the three treatment means.

3. The following values are from an independent-measures study comparing three treatment conditions.

Treatment

I II III

n=10 n=10 n=10

SS=63 SS=66 SS=87

a. Compute the variance for each sample.

b. Compute MS_{within} which would be the denominator of the F-ratio for an ANOVA.

Because the samples are all the same size, you should find that MS_{within} is equal to the average of the three sample variances.

4. The following summary table presents the results from an ANOVA comparing four treatment conditions with n=12 participants in each condition. Complete all missing values. (*Hint*: Start with the *df** *column.)

Source SS df MS

Between Treatments _____ _____ _____ F = 2.50

Within Treatments 88 _____ _____

Total _____ _____

5. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriguez- Teijeiro, 2005). Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to the actual results. The numbers represent relative brain size for the individual birds in each sample.

Non-Migrating Short-Distance Migrants Long Distance Migrants

18 6 4 N=18

13 11 9 G=180

19 7 5 ∑X^{2}=2150

12 9 6

16 8 5

12 13 7

M=15 M=9 M=6

T=90 T=54 T=36

SS=48 SS=34 SS=16

a. Use an ANOVA with α=.05 to determine whether there are any significant mean differences among the three groups of birds.

b. Compute η^{2}, the percentage of variance explained by the group differences, for these data.

c. Write a sentence demonstrating how a research report would present the results of the hypothesis test and the measure of effect size.

d. Use the Tukey HSD posttest to determine which groups are significantly different.

6. A published report of a repeated-measures research study includes the following description of the statistical analysis. “The results show significant differences among the treatment conditions, F(2,20) = 5.00, p< .05.”

a. How many treatment conditions were compared in the study?

b. How many individuals participated in the study?

7. A recent study examined how applicants with a facial blemish such as a scar or birthmark fared in job interviews (Madera & Hebl, 2011). The results indicate that interviewers recalled less information and gave lower ratings to applicants with a blemish. In a similar study, participants conducted computer-simulated interviews with a series of applicants including one with a facial scar and one with a facial birthmark. The following data represent the ratings given to each applicant.

Applicant

Participant Scar Birthmark No Blemish Person Totals

A 1 1 4 P = 6

B 3 4 8 P = 15 N = 15

C 0 2 7 P = 9 G = 45

D 0 0 6 P = 6 ∑X^{2} = 231

E 1 3 5 P = 9

M=1 M=2 M=6

T=5 T=10 T=30

SS=6 SS=10 SS=10

a. Use a repeated-measures ANOVA with α=.05 to determine whether there are significant mean differences among the three conditions.

b. Compute η^{2}, the percentage of variance accounted for by the mean differences, to measure the size of the treatment effects.

c. Write a sentence demonstrating how a research report would present the results of the hypothesis test and the measure of effect size.

8. The following data are from an experiment comparing three different treatment conditions:

A B C

0 1 2 N=15

2 5 5 ∑X^{2}=354

1 2 6

5 4 9

2 8 8

T=10 T=20 T=30

SS=14 SS=30 SS=30

a. If the experiment uses an *independent-measures design*, can the researcher conclude that the treatments are significantly different? Test at the .05 level of significance.

b. If the experiment is done with a *repeated-measures design*, should the researcher conclude that the treatments are significantly different? Set alpha at .05 again.

9. The following summary table presents the results from a repeated-measures ANOVA comparing three treatment conditions with a sample of n=12 subjects. Fill in the missing values in the table. (*Hint*: Start with the *df* values.)

Source *SS* *df* *MS*

Between treatments _____ _____ 10 *F* = _____

Within treatments _____ _____

Between subjects _____ _____

Error 44 _____ _____

Total 106 _____

10. 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. Factor B

B1 B2

A1

Factor A

A2

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 main effect for factor B?

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

Extra Credit (+1)

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=11 participants in each treatment condition. Fill in the missing values. (*Hint*: Start with the *df* values.)

Source SS df MS

Between Treatments 124 ____

Factor A _____ _____ _____ F = 10

Factor B _____ _____ _____ F = _____

A X B Interaction 20 _____ _____ F = _____

Within Treatments _____ _____ 4

Total _____ _____

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