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.

                                                            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       ∑X² = 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 η², 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                      ∑X²=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                                        _____              _____