STATWeek 8 Complete Solution

Question: #3985

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                      III
                        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 MSwithin which would be the denominator of the F-ratio for an ANOVA.
Because the samples are all the same size, you should find that MSwithin 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

M=10

M=20

M=15


                                                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                                        _____              _____