STAT Week 8 Complete Solution

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Question Details: #3985
STAT Week 8 Complete Solution

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

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

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                                        _____              _____

• Posted by: Vikas
• Subjects: Math Environmental Law
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Solution Details: #3957
STAT Week 8 Complete Solution

Since observed F = 13.50 > 3.68, reject the null hypothesis. There...
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• Posted By: Vikas