Grand Canyon University PSY-380 Topic Six Homework Assignment

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This document presents a comprehensive solution to a PSY-380 Topic Six homework assignment, focusing on the application of Analysis of Variance (ANOVA) techniques. The assignment covers a wide range of concepts, including calculating degrees of freedom, interpreting F-tests, determining critical values, and making decisions based on significance levels. It includes problems involving one-way ANOVA, post hoc tests (Tukey's HSD), and the computation of effect sizes like omega-squared. The solutions demonstrate how to complete F-tables, identify significant factors, and differentiate between within-subjects and between-subjects designs. The assignment also explores the concepts of partial eta-squared and partial omega-squared, providing a thorough understanding of ANOVA principles and their practical application in psychological research scenarios, such as examining job satisfaction, memory recall, and classroom interventions. This homework covers various statistical concepts that are core to understanding and applying ANOVA in psychological research and data analysis.
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PSY-380, section LS02/03/20, Spring 2020
Topic Six Homework (Homework)
INSTRUCTOR
Lindsey Scholta
Grand Canyon University, AZ
Current Score
QUESTION
POINTS
TOTAL SCORE
183/183 100.0%
MON, MAR 16, 2020
12:29 PM GMT+5:30
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A researcher conducts a one-way ANOVA in which one independent variable has three levels. How many different groups are in this
study?
3 groups
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Are post hoc tests necessary following a significant ANOVA testing one independent variable with two levels Explain.
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State the degrees of freedom error in each of the following tests.
(a) A consultant measures job satisfaction in a sample of 13 supervisors, 13 managers, and 13 executives at a local firm.
36
(b) A researcher tests how nervous public speakers get in front of a small, medium, or large audience. Twelve participants are
randomly assigned to each group.
33
(c) A high school counselor has 10 students in each of five classes rate how much they like their teacher.
45
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(k = 2)?
Yes. When a variable has only two levels, then those two levels must be checked to determine if they are significantly different
following a significant ANOVA. A post hoc test is necessary.
No. When a variable has only two levels, then those two levels must be significantly different following a significant ANOVA.
There are no multiple comparisons to make, so a post hoc test is not necessary.
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What is the decision at a 0.05 level of significance for each of the following tests? Hint: Find the critical value for each test; then
make a decision. (Round your critical values to two decimal places.)
Part (a)
Part (b)
Part (c)
Part (d)
You may need to use the appropriate table in Appendix C to answer this question.
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F(3, 25) = 3.07
Fcrit = 2.99
Retain the null hypothesis.
Reject the null hypothesis.
F(5, 20) = 2.52
Fcrit = 2.71
Retain the null hypothesis.
Reject the null hypothesis.
F(4, 37) = 2.68
Fcrit = 2.63
Retain the null hypothesis.
Reject the null hypothesis.
F(2, 13) = 3.73
Fcrit = 3.80
Retain the null hypothesis.
Reject the null hypothesis.
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A researcher measures job satisfaction among married, single, and divorced employees to determine whether marital status can
influence job satisfaction. Based on the following description in APA format, state the value for k, N, and n.
A one-way analysis of variance showed that job satisfaction did not vary by marital status,
k = 3
N = 30
n = 10
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The following is an incomplete F-table summarizing the results of a study of the variance of life satisfaction scores among unemployed,
retired, part-time, and full-time employees.
Source of Variation SS df MS F
Between groups 16
Within groups (error) 36
Total 136
(a) Complete the F-table. (Round your values for mean squares and F to two decimal places.)
Source of Variation SS df MS F
Between groups 48 3 16 6.56
Within groups (error) 88 36 2.44
Total 136 39
(b) Compute omega-squared (Round your answer to two decimal places.)
ω2 = 0.29
(c) Is the decision to retain or reject the null hypothesis? (Assume alpha equal to 0.05.)
You may need to use the appropriate table in Appendix C to answer this question.
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F(2, 27) = 1.38, p > 0.05.
(ω2).
Retain the null hypothesis.
Reject the null hypothesis.
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Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of
memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as
possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer
recall. The number of letters correctly recalled is given in the table.
Delay Before Recall
0 0.5 1
5 10 4
7 6 4
10 3 6
11 8 2
9 5 3
6 4 5
(a) Complete the F-table. (Round your values for MS and F to two decimal places.)
Source of Variation SS df MS F
Between groups 48 2 24 5
Within groups (error) 72 15 4.8
Total 120 17
(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two
decimal places.)
The critical value is 3.29 for each pairwise comparison.
Which of the comparisons had significant differences? (Select all that apply.)
You may need to use the appropriate table in Appendix C to answer this question.
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Recall following no delay was significantly different from recall following a one second delay.
Recall following no delay was significantly different from recall following a half second delay.
Recall following a half second delay was significantly different from recall following a one second delay.
The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a
significant difference.
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An educator wants to evaluate four different methods aimed at reducing the time children spend "off task" in the classroom. To test
these methods, she implements one method in each of four similar classrooms and records the time spent off task (in minutes) in each
classroom. The results are given in the table.
Classroom Method
A B C D
3 1 0 2
1 4 6 3
5 2 3 2
2 5 3 4
1 0 0 3
0 1 5 2
2 3 4 5
4 4 5 4
4 0 4 4
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of
Variation SS df MS F
Between
groups 8.31 3 2.77 0.93
Within
groups (error) 95.33 32 2.98
Total 103.64 35
(b) Is it necessary to compute a post hoc test? Explain. (Assume alpha equal to 0.05.)
You may need to use the appropriate table in Appendix C to answer this question.
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Yes, post hoc analyses are appropriate because the ANOVA is significant.
No, post hoc analyses are not appropriate because the ANOVA is not significant.
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Drakou, Kambitsis, Charachousou, and Tzetzis (2006) tested differences in life satisfaction among sport coaches. They tested differences
by gender, age, marital status, and education. The results of each F-test in the following table are similar to the way in which the data
were given in their article.
Independent
Variables
Life Satisfaction
M SD F p
Gender 0.68 0.409
Men 3.99 0.51
Women 3.94 0.49
Age 3.04 0.029
20s 3.85 0.42
30s 4.03 0.52
40s 3.97 0.57
50s 4.02 0.50
Marital status 12.46 0.000
Single 3.85 0.48
Married 4.10 0.50
Divorced 4.00 0.35
Education 0.82 0.536
High school 3.92 0.48
Postsecondary 3.85 0.54
University degree 4.00 0.51
Masters 4.00 0.59
(a) Which factors were significant at a 0.05 level of significance? (Select all that apply.)
(b) State the number of levels for each factor.
gender 2 levels
age 4 levels
marital status 3 levels
education 4 levels
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age
gender
education
marital status
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Using a rating scale, Tekinarslan (2008) measured computer anxiety among university students who use the computer very often, often,
sometimes, and seldom. Below are the results of the one-way ANOVA.
Source of Variation SS df MS F
Between groups 1,959.79 3 653.26 21.16*
Within groups (error) 3,148.61 102 30.86
Total 5,108.41 105
(a) What are the values for N and k?
N = 106
k = 4
(b) Was the sample size, n, equal in each group? Explain.
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Which source of error is included in the F-table for the one-way within-subjects ANOVA but not for the one-way between-subjects
ANOVA?
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Yes, the sample size in each group was equal because such equality is necessary for one-way ANOVA.
Yes, the sample size in each group was equal because the total sample size can be equally divided into the correct
number of groups.
No, the sample size in each group was not equal because such inequality is necessary for one-way ANOVA.
No, the sample size in each group was not equal because the total sample size can not be equally divided into the
correct number of groups.
within-groups variation
within-persons variation
between-persons variation
between-groups variation
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Which measure (partial eta-squared or partial omega-squared) is the less conservative estimate of proportion of variance?
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State whether the following situations describe a between-subjects design or a within-subjects design.
Part (a)
Part (b)
Part (c)
Part (d)
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partial eta-squared ( ηp2)
partial omega-squared ( ωp2)
A sport psychologist compares mental functioning in a sample of athletes in four different sports.
between-subjects design
within-subjects design
A biopsychologist tests the time course for the release of a neurohormone before, during, and following a task thought to cause its
release.
between-subjects design
within-subjects design
A college professor compares the average class grade for students in each of three sections of a statistics course.
between-subjects design
within-subjects design
A behavioral psychologist allows a sample of children to play with four toys of various colors and has them rate how much they
like playing with each toy. The psychologist compares mean ratings for each toy.
between-subjects design
within-subjects design
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Given the following information for the one-way within-subjects ANOVA, state the number of participants observed in each group.
(a)
15 participants
(b)
13 participants
(c)
6 participants
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A researcher records the following data for each of three groups.
Group A Group B Group C
11 11 13
11 14 2
4 12 11
6 5 8
13 3 11
What is the value of the F-statistic? (Round your answer to two decimal places.)
F = 0
Explain your answer.
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dfBP = 14
k = 4, n = 13
dfBG = 5, df E = 25
F is the indicated value because the groups means are different. There is substantial variability between
groups.
F is the indicated value because the group means are the same. There is substantial variability between
groups.
F is the indicated value because the group means are the same. There is no variability between groups.
F is the indicated value because the group means are different. There is no variability between groups.
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A child psychologist treats four children who are afraid of snakes with a behavioral modification procedure called systematic
desensitization. In this procedure, children were slowly introduced to a snake over four treatment sessions. Children rated how fearful
they are of the snake before the first session (baseline) and following each treatment session. Higher ratings indicated greater fear. The
hypothetical data are listed in the table.
Sessions
Baseline 1 2 3 4
7 7 5 4 3
7 6 6 4 4
6 6 7 7 3
7 7 5 4 3
(a) Complete the F-table. (Round your value for F to two decimal places.)
Source of
Variation SS df MS Fobt
Between
groups 32.8 4 8.2 9.11
Between
persons 1.2 3 0.4
Within
groups (error) 10.8 12 0.9
Total 44.8 19
(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05.)
You may need to use the appropriate table in Appendix C to answer this question.
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Ratings of fear significantly decreased from baseline to Session 4.
Ratings of fear significantly decreased from Session 1 to Session 4. Ratings of fear also significantly decreased from
Session 2 to Session 4.
Ratings of fear significantly decreased from baseline to Session 3. Ratings of fear also significantly decreased from
baseline to Session 4.
None of the pairwise comparisons are significant.
Ratings of fear significantly decreased from baseline to Session 3. Ratings of fear also significantly decreased from
Session 1 to Session 4.
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A study investigated the effects of physical fatigue on the performance of professional tennis players. Researchers measured the number
of unforced errors committed by a random sample of 12 professional tennis players during the first three sets of a match. They
hypothesized that increased fatigue would be associated with a greater number of errors. The following is an F-table for this hypothetical
study using the one-way within-subjects ANOVA.
Source of Variation SS df MS Fobt
Between groups 13
Between persons 5
Within groups (error) 55
Total
(a) Complete the F-table.
Source of
Variation SS df MS Fobt
Between
groups 26 2 13 5.2
Between
persons 55 11 5
Within
groups (error) 55 22 2.5
Total 136 35
Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)
(b) Estimate effect size using partial omega-squared: ωP2. (Round your answer to two decimal places.)
ωP2 = 0.25
You may need to use the appropriate table in Appendix C to answer this question.
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Retain the null hypothesis.
Reject the null hypothesis.
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Air traffic controllers perform the vital function of regulating the traffic of passenger planes. Frequently, air traffic controllers work long
hours with little sleep. Researchers wanted to test their ability to make basic decisions as they become increasingly sleep deprived. To
test their abilities, a sample of 6 air traffic controllers is selected and given a decision-making skills test following 12-hour, 24-hour, and
48-hour sleep deprivation. Higher scores indicate better decision-making skills. The table lists the hypothetical results of this study.
Sleep Deprivation
12 Hours 24 Hours 48 Hours
22 17 16
18 22 21
33 22 22
26 20 13
23 15 15
21 20 15
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of
Variation SS df MS Fobt
Between
groups 144.78 2 72.39 6.39
Between
persons 126.94 5 25.39
Within
groups (error) 113.22 10 11.32
Total 384.94 17
(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that
apply.)
You may need to use the appropriate table in Appendix C to answer this question.
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There are no significant differences between any of the groups.
There is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions.
There is a significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.
There is a significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.
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Researchers in mental health fields are often interested in evaluating the effectiveness of using food images to enhance positive mood.
Adapting a typical design from such studies, suppose we have participants rate their mood change on a standard self-report affect scale
after viewing images of "comfort" foods, fruits/vegetables (F/V), and random non-food images (used as a control group). The results are
given in the table at right for this hypothetical study.
Images
Control F/V Comfort
Foods
0 0 3
0 1 2
1 2 4
3 3 5
0 1 0
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of
Variation SS df MS Fobt
Between
groups 10.53 2 5.27 7.71
Between
persons 21.33 4 5.33
Within
groups (error) 5.47 8 0.68
Total 37.33 14
(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that
apply.)
You may need to use the appropriate table in Appendix C to answer this question.
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There were no significant differences between any of the groups.
Participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood
change after viewing control images.
Participants rated a significantly larger mood change after viewing images of fruits/vegetables compared with the
mood change after viewing control images.
Participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood
change after viewing images of fruits/vegetables.
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Wilfley and colleagues (2008) tested whether the antiobesity drug sibutramine would be an effective treatment for people with binge
eating disorder. They measured the frequency of binge eating every 2 weeks for 24 weeks during treatment. The following table lists a
portion of the data similar to results reported by the authors for the frequency of binge eating over the first 8 weeks of the drug
treatment.
Frequency of Binge Eating
Baseline Week 2 Week 4 Week 6 Week 8
4 1 0 0 1
6 4 2 0 0
3 0 1 1 0
1 1 0 1 1
2 2 1 1 1
5 1 2 2 2
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of
Variation SS df MS Fobt
Between
groups 30.8 4 7.7 6.31
Between
persons 12.27 5 2.45
Within
groups (error) 24.4 20 1.22
Total 67.47 29
Make a decision to retain or reject the null hypothesis. (Assume experimentwise alpha equal to 0.05.)
(b) Use the Bonferroni procedure to make the post hoc test. In which week do we first see significant differences compared to
baseline?
Week 2 is the first week where significant differences from baseline are evident.
Week 4 is the first week where significant differences from baseline are evident.
Week 6 is the first week where significant differences from baseline are evident.
Week 8 is the first week where significant differences from baseline are evident.
None of the weeks are significantly different from the baseline.
You may need to use the appropriate table in Appendix C to answer this question.
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Retain the null hypothesis.
Reject the null hypothesis.
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When looking at a graph of an A × B interaction, describe the pattern that indicates that the interaction is possibly significant.
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State whether each of the following is an example of a between-subjects, mixed, or within-subjects two-way ANOVA design.
(a) An industrial organizational psychologist measures the GPA among men and women graduate students (Factor A: gender)
with low, medium, or high leadership potential (Factor B: leadership potential).
(b) A psychologist administers a small, medium, or large dose of a drug to a sample of mice (Factor A: drug dose) and measures
reward-seeking behavior across three experimental trials (Factor B: trials).
(c) A behavioral psychologist asks the same group of participants to rate the effectiveness of each of three marketing
commercials (Factor A: commercials) for each of two products (Factor B: products).
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The two lines are parallel, meaning they would never touch or cross.
The two lines are not parallel, meaning that they they touch or cross.
between-subjects design
mixed design
within-subjects design
between-subjects design
mixed design
within-subjects design
between-subjects design
mixed design
within-subjects design
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An educator evaluates the effects of small, medium, and large class sizes on academic performance among male and female students.
Identify each factor and the levels of each factor in this example. (Select all that apply.)
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gender (two levels: male, female)
academic performance (three levels: above average, average, below average)
class size (two levels: small, large)
class size (three levels: small, medium, large)
gender (three levels: male, female, trans)
academic performance (two levels: passing, failing)
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State the decision to retain or reject the null hypothesis for each of the following F-tests at a 0.05 level of significance.
(a)
(b)
(c)
(d)
You may need to use the appropriate table in Appendix C to answer this question.
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If the value of the mean square for Factor A increases, will the value of the test statistic of Factor A increase or decrease?
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F(2, 32) = 3.06
Retain the null hypothesis.
Reject the null hypothesis.
F(4, 27) = 3.12
Retain the null hypothesis.
Reject the null hypothesis.
F(1, 120) = 4.09
Retain the null hypothesis.
Reject the null hypothesis.
F(2, 60) = 3.08
Retain the null hypothesis.
Reject the null hypothesis.
increase
decrease
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For each of the following, state whether for a main effect, the A × B interaction, or both.
(a) Cell means are equal.
(b) Row totals are equal.
(c) Column totals are equal.
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F = 0
F = 0 for a main effect.
F = 0 for the A × B interaction.
F = 0 for a main effect and the A × B interaction.
F = 0 for a main effect.
F = 0 for the A × B interaction.
F = 0 for a main effect and the A × B interaction.
F = 0 for a main effect.
F = 0 for the A × B interaction.
F = 0 for a main effect and the A × B interaction.
26. PRIVITERASTATS3 14.E.019.3/3 points Previous Answers My Notes
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Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is
phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of
patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the
times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor
mood) to 9 (improved mood). The hypothetical results are given in the following table.
Light Intensity
Low Medium High
Time of
Day
Morning 5 5 7
5 6 8
4 4 6
7 7 9
5 9 5
6 8 8
Night 5 6 9
8 8 7
6 7 6
7 5 8
4 9 6
3 8 6
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your
answers to two decimal places. Assume experimentwise alpha equal to 0.05.)
Source of
Variation SS df MS F
Time of day 0.44 1 0.44 0.19
Intensity 19.39 2 9.69 4.15
Time of
day ×
Intensity
1.06 2 0.53 0.23
Error 70 30 2.33
Total 90.89 35
State the decision for the main effect of the time of day.
State the decision for the main effect of intensity.
State the decision for the interaction effect.
Retain the null hypothesis.
Reject the null hypothesis.
Retain the null hypothesis.
Reject the null hypothesis.
27. PRIVITERASTATS3 14.E.023.22/22 points Previous Answers My Notes
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(b) Compute Tukey's HSD to analyze the significant main effect.
The critical value is 1.54 for each pairwise comparison.
Summarize the results for this test using APA format.
Score: 1 out of 1
Comment:
You may need to use the appropriate table in Appendix C to answer this question.
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The two-way ANOVA showed that the main effect of intensity is
significant, F(2,30)=4.15,p<0.05.The main effect of time is
insignificant, F(1,30)=0.19, p>0.05.Moreover, the interaction
effect between intensity and time is also not
significant,F(2,30)=0.23,p<0.05.Post-hoc test proved that the
pair of means of intensity(low,high) differs significantly
Retain the null hypothesis.
Reject the null hypothesis.
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In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short,
long) and by type of technology (static, dynamic, interactive). Higher ratings indicated greater effectiveness.
Source of Variation SS df MS F
Length 5
Technology
Length × Technology 148
Error 570 114
Total 863
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Assume
experimentwise alpha equal to 0.05.)
Source of
Variation SS df MS F
Length 5 1 5 1
Technology 140 2 70 14
Length ×
Technology 148 2 74 14.8
Error 570 114 5
Total 863 119
State the decision for the main effect of length.
State the decision for the main effect of technology.
State the decision for the interaction effect.
(b) Based on the results you obtained, what is the next step?
Retain the null hypothesis.
Reject the null hypothesis.
Retain the null hypothesis.
Reject the null hypothesis.
Retain the null hypothesis.
Reject the null hypothesis.
Compute pairwise comparisons for the technology factor.
Compute pairwise comparisons for the length factor.
No further analysis is needed, because none of the effects are significant.
Compute simple main effect tests for the significant interaction.
28. PRIVITERASTATS3 14.E.025.16/16 points Previous Answers My Notes
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3/3/2020 Topic Six Homework - PSY-380, section LS02/03/20, Spring 2020 | WebAssign
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You may need to use the appropriate table in Appendix C to answer this question.
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Cheng and Lam (2007) noted that some people think of themselves independently of others (independent self-construal), whereas
others think of themselves as being part of a larger group (interdependent self-construal). Also, people tend to evaluate themselves as
being more positive when they compare themselves to others perceived to be below them (downward comparison), and they evaluate
themselves as being less positive when they compare themselves to others perceived to be above them (upward comparison). To test
whether there is a relationship between these two factors, the researchers computed a two-way between-subjects ANOVA. Participants
rated their self-perception on a scale from 1 (negative) to 7 (positive). The following table describes the cell means at each level of the
two factors.
Comparison
Standard
Self-Construal
Independent Interdependent
Upward 4.17 4.62
Downward 4.61 4.44
(a) Graph the cell means.
(b) Is a possible interaction evident? Explain.
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Yes, an interaction is possible because the lines are not parallel.
No, an interaction is not possible because the lines are parallel.
29. PRIVITERASTATS3 14.E.031.2/2 points Previous Answers My Notes
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Erkal, Copur, Dogan, and Safak (2007) studied how gender and gender roles influence the time parents spend with their children. In
their study, they asked a sample of parents to report the amount of time they make accessible for their children. Women reported
spending an average of 9.48 hours per week; men reported spending an average of 8.01 hours per week. The F-table summarizes the
results of their study.
Source of Variation SS df MS F
Gender 191.93 1 191.93 9.34
Gender Roles 11.90 3 3.97 0.19
Gender × Gender Roles 87.61 3 29.20 1.42
Error 12,163.98 592 20.55
Total 12,455.42 599
(a) Is a significant main effect or interaction evident in this study and, if so, for which factor?
Yes, this study found a significant main effect of gender.
Yes, this study found a significant main effect of gender roles.
Yes, this study found a significant main effect of gender and a significant main effect of gender roles.
No, this study found no significant main effect.
(b) Referring to the group means given for gender, state the conclusion for this study.
Mothers and fathers spend approximately the same amount of time with their children, independent of gender roles.
Fathers spend significantly more time with their children than mothers, independent of gender roles.
The amount of time that a mother and father spend with their children depends on gender roles.
Mothers spend significantly more time with their children than fathers, independent of gender roles.
You may need to use the appropriate table Appendix C to answer this question.
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