What is A X B Interaction

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                      ∑X²=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 η² 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                      ∑X²=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                       ∑X²=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 η², 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.