Week 5 ANOVA Exercises
Research Question: Is there a difference in the overall satisfaction of women based on the number of
housing problems (no problems, 1 problem, 2 or more problems)?
Using Polit2SetA dataset, run an ANOVA using Overall Satisfaction, Material Well-Being (satovrl) as the
dependent variable and Housing Problems (hprobgrp) (this is the last variable in the dataset) as the
Independent Variable.
Follow these steps when using SPSS:
1. Open Polit2SetA dataset.
2. Click Analyze then click Compare Means, then One-way ANOVA.
3. Move the Dependent Variable (Overall Satisfaction “satovrl”) in the box labelled Dependent List
by clicking the arrow button. The dependent variable is a continuous variable.
4. Move the Independent Variable (Housing Problems “Hprobgrp”) into the box labelled Factor. The
hprobgrp is a categorical variable coded as (1= no hoursing problem, 2=one housing problem,
3=two or more housing problems).
5. Click the Options button (right side of box) and click on Descriptives and Homogeneity of
Variance and then click continue.
6. Click on Post Hoc (right side of box). Click on Tukey and then click continue.
7. Click OK.
8. Check your answers against SPSS output provided.
9. Do not submit the SPSS tables/output as answers to the questions.
Assignment: Through analysis of the data and use of the questions below, answer the questions on your
findings from this ANOVA test. Answers should be short and do not need to be written as a sentence. No
ciattion or APA is required.
1.
2.
3.
4.
What is the total sample size?
How many women were in each of the different hprobgrp groups?
What are the mean and standrad deviation (SD) overall satisfaction scores for each group?
Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are
equal variances assumed or not assumed?)
5. What is the value of the F-statistic, number of degrees of freedom and the p-value?
6. Is there a significant difference in the overall satisfaction level of women in each of the hprobgrp
groups?
7. Interpret the post hoc test. When interpreting the post hoc test indicate the mean and standard
deviation for each group and indicate which group was signifantly higher or lower from the other.
If there is no difference between two groups indicate that as well.
Week 5 t Test Exercises SPSS Output
Independent t test
Group Statistics
Currently employed?
CES-D Score
N
Mean
Std. Deviation
Std. Error Mean
No
524
20.8965
12.46425
.54450
Yes
436
15.8239
10.13655
.48545
dimension1
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
95% Confidence
Interval of the
Sig. (2-
CES-D
Equal variances
Score
assumed
Equal variances not
assumed
F
Sig.
t
23.615
.000
6.825
df
tailed)
Mean
Std. Error
Difference Difference
Difference
Lower
Upper
958
.000
5.07264
.74326
3.61404
6.53124
6.954 957.514
.000
5.07264
.72949
3.64107
6.50421
Dependent t test
Paired Samples Statistics
Mean
Pair 1
N
Std. Deviation
Std. Error Mean
CES-D Score
18.5516
157
11.87462
.94770
CESD Score, Wave 1
17.8344
157
11.49908
.91773
Paired Samples Correlations
N
Pair 1
CES-D Score & CESD
Correlation
157
Sig.
.412
.000
Score, Wave 1
Paired Samples Test
Paired Differences
95% Confidence Interval of
Mean
Pair 1 CES-D Score –
CESD Score, Wave 1
.71718
Std.
Std. Error
Deviation
Mean
12.67921
1.01191
the Difference
Lower
-1.28164
Upper
2.71599
Sig. (2t
.709
df
156
tailed)
.480
Independent t test with 3 outcome variables
Group Statistics
Educational attainment
CES-D Score
N
Mean
Std. Deviation
Std. Error Mean
No high school diploma
453
20.1408
11.49986
.54031
Diploma or GED
475
17.5931
11.72389
.53793
SF12: Physical Health
No high school diploma
421
44.03546
10.781420
.525454
Component Score,
Diploma or GED
440
46.27713
10.597265
.505205
SF12: Mental Health
No high school diploma
421
45.70217
10.693544
.521171
Component Score,
Diploma or GED
440
47.48328
10.895127
.519405
standardized
standardized
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
95% Confidence
Interval of the
F
CES-D Score
Equal variances
.228
Sig.
.633
t
df
Sig. (2-
Mean
Std. Error
tailed)
Difference
Difference
Difference
Lower
Upper
3.340
926
.001
2.54776
.76278
1.05078
4.04474
3.342
925.265
.001
2.54776
.76243
1.05146
4.04406
-3.076
859
.002
-2.241671
.728649 -3.671812
-.811529
-3.075
855.772
.002
-2.241671
.728927 -3.672364
-.810977
-2.420
859
.016
-1.781113
.736103 -3.225884
-.336341
-2.421
858.441
.016
-1.781113
.735800 -3.225290
-.336936
assumed
Equal variances
not assumed
SF12: Physical
Equal variances
Health
assumed
Component
Equal variances
Score,
not assumed
1.106
.293
standardized
SF12: Mental
Equal variances
Health
assumed
Component
Equal variances
Score,
not assumed
standardized
.174
.677
Week 5 Independent t Test Exercises
Answer the questions below for Part I II and III. Make sure to create the table if asked and do
not submit SPSS output as your answer. If you have any questions, please email your instructor.
Don’t forget to save the document as instructed in the assignment submission directs. You do
not have to submit a title page or reference list for this assignment. No citations are required
for your submission.
Part I
The hypothesis being tested is: Women who are working will have a lower level of depression as
compared to women who are not working.
Using Polit2SetC SPSS dataset, which contains a number of mental health variables, determine if the
above hypothesis is true.
Follow these steps when using SPSS:
1.
2.
3.
4.
Open Polit2SetC dataset.
Click Analyze then click Compare Means, then Independent Sample T-test.
Move the Dependent Variable (CES_D Score “cesd”) in the area labelled Test Variable.
Move the Independent Variable (Currently Employed “worknow”) into the area labelled
Grouping Variable. The worknow variable is coded as (0= those women who do not work and 1=
those women who are working). Click on Define Groups in group 1 box type 0 and in group 2
box type 1. Click Continue.
5. Click continue and then click OK.
6. Check your answers to the Week 5 t Test Excercises SPSS Output.
Assignment: Through analysis of the data answer the questions below with your findings from this t-test.
1.
2.
3.
4.
How many women were employed versus not employed in the sample?
What is the total sample size?
What are the mean and standard deviation for the CES-D scores for each group?
Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are
equal variances assumed or not assumed?) Why?
5. What is the value of the t-statistic, number of degrees of freedom and the p-value?
6. Does the data support the hypothesis? Why or why not?
Part II
Hypothesis: Women who reported depression scores in wave 1 and wave 2 of the study did not have a
significant difference in their level of depression.
Using Polit2SetC SPSS dataset, determine if the above hypothesis is true.
Follow these steps when using SPSS:
1. Open Polit2SetC dataset.
2. Click Analyze then click Compare Means, then Paired Samples T-test.
3. First click on CES-D Score (cesd) and move it into the box labelled Paired Variables (in the
rectangle for Pair 1 of Variable 1 and then click on CESD Score, Wave 1 (cesdwav1) and move it
into the Paired Variables box (in the rectangle next to CES-D Score, pair 1, variable 2).
4. Click continue and then click OK.
5. Check your answers to the Week 5 t Test Excercises SPSS Output
Assignment: Through analysis of the data and answer the questions below for the findings from this ttest.
1.
2.
3.
4.
5.
What is the total sample size?
What are the mean and the standard deviation of the CES-D scores at wave 1 and wave 2?
What is the mean difference between the two time periods?
What is the value of the t-statistic, number of degrees of freedom and the p-value(sig)?
Does the data support the hypothesis? Why or why not?
Part III
Using Polit2SetC dataset, run independent groups t-tests for three outcomes. The outcome variables are
CES-D Score (cesd), SF12: Physical Health Component Score, standardized (sf12phys) and SF12: Mental
Health Component Score, standardized (sf12ment).
Follow these steps when using SPSS:
1. Open Polit2SetC dataset.
2. Click Analyze then click Compare Means, then Independent Sample T-test.
3. Move the Dependent Variables (CES_D Score “cesd”, SF12: Physical Health Component Score,
standardized (sf12phys), and SF12: Mental Health Component Score, standardized (sf12ment) )
in the area labelled Test Variable.
4. Move the Independent Variable (Educational Attainment “educatn”) into the area labelled
Grouping Variable. The educatn variable is coded as (1= no high school credential and
2=diploma or GED). Click on Define Groups in group 1 box type 1 and in group 2 box type 2.
Click Continue.
5. Click continue and then click OK.
6. Check your answers to the Week 5 t Test Excercises SPSS Output
Assignment: Create a table to present your results, use the table 6.3 in Chapter 6 in your book as a
model. Write one or two paragraphs explaining and summarizing your results. Do not submit the SPSS
output that is provided.
Week 5 ANOVA Exercises SPSS Output
Descriptives
Overall satisfaction, material well-being
95% Confidence Interval for
Mean
N
Mean
Std. Deviation Std. Error
Lower Bound
Upper Bound
Minimum
Maximum
No Housing Problem
367
12.71
2.353
.123
12.47
12.95
4
16
One Housing Problem
264
11.97
2.588
.159
11.66
12.28
4
16
Two or More Housing
304
10.57
2.594
.149
10.28
10.86
4
16
935
11.80
2.658
.087
11.63
11.97
4
16
Problems
Total
Test of Homogeneity of Variances
Overall satisfaction, material well-being
Levene Statistic
df1
2.109
df2
2
Sig.
932
.122
ANOVA
Overall satisfaction, material well-being
Sum of Squares
Between Groups
df
Mean Square
771.072
2
385.536
Within Groups
5826.111
932
6.251
Total
6597.183
934
F
Sig.
61.674
.000
Multiple Comparisons
Overall satisfaction, material well-being
Tukey HSD
(I) Housing Problems
(J) Housing Problems
95% Confidence Interval
Mean
Difference (I-J)
No Housing Problem
One Housing Problem
Two or More Housing
Std. Error
Sig.
Lower Bound
Upper Bound
.739*
.202
.001
.27
1.21
*
2.139
.194
.000
1.68
2.59
-.739*
.202
.001
-1.21
-.27
*
1.401
.210
.000
.91
1.89
-2.139*
.194
.000
-2.59
-1.68
*
.210
.000
-1.89
-.91
Problems
One Housing Problem
No Housing Problem
Two or More Housing
Problems
Two or More Housing
Problems
No Housing Problem
One Housing Problem
*. The mean difference is significant at the 0.05 level.
-1.401
Week 5 ANOVA Exercises
Research Question: Is there a difference in the overall satisfaction of women based on the
number of housing problems (no problems, 1 problem, 2 or more problems)?
Using Polit2SetA dataset, run an ANOVA using Overall Satisfaction, Material Well-Being
(satovrl) as the dependent variable and Housing Problems (hprobgrp) (this is the last variable in
the dataset) as the Independent Variable.
Follow these steps when using SPSS:
1. Open Polit2SetA dataset.
2. Click Analyze then click Compare Means, then One-way ANOVA.
3. Move the Dependent Variable (Overall Satisfaction “satovrl”) in the box labelled
Dependent List by clicking the arrow button. The dependent variable is a continuous
variable.
4. Move the Independent Variable (Housing Problems “Hprobgrp”) into the box labelled
Factor. The hprobgrp is a categorical variable coded as (1= no hoursing problem, 2=one
housing problem, 3=two or more housing problems).
5. Click the Options button (right side of box) and click on Descriptives and Homogeneity
of Variance and then click continue.
6. Click on Post Hoc (right side of box). Click on Tukey and then click continue.
7. Click OK.
8. Check your answers against SPSS output provided.
9. Do not submit the SPSS tables/output as answers to the questions.
Assignment: Through analysis of the data and use of the questions below, answer the questions
on your findings from this ANOVA test. Answers should be short and do not need to be written
as a sentence. No ciattion or APA is required.
1. What is the total sample size?
2. How many women were in each of the different hprobgrp groups?
3. What are the mean and standrad deviation (SD) overall satisfaction scores for each
group?
4. Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met?
Are equal variances assumed or not assumed?)
5. What is the value of the F-statistic, number of degrees of freedom and the p-value?
6. Is there a significant difference in the overall satisfaction level of women in each of the
hprobgrp groups?
7. Interpret the post hoc test. When interpreting the post hoc test indicate the mean and
standard deviation for each group and indicate which group was signifantly higher or
lower from the other. If there is no difference between two groups indicate that as well.
Answer 1: What is the total sample size?
We are considering a data of 935 individuals and take a sample of size is 935.
Answer 2: How many women were in each of the different hprobgrp groups?
From 935 sample size, 367, 264 and 304 respectively fall in the groups of no Housing
Problem, One Housing Problem and Two or More Housing Problems.
Answer 3: What are the mean (SD) overall satisfaction scores for each group?
The above result shows that the mean (sd), by the overall satisfaction scores are mean 12.71 sd
2.353, mean 11.97 sd 2.588 and mean 10.57 sd 2.594 respectively for the groups No Housing
Problem, One Housing Problem and Two or More Housing Problems. The overall mean
satisfaction scores is 11.80 while sd satisfaction scores is 2.658.
Answer 4: Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance
met? Are equal variances assumed or not assumed?)
We use Levene’s test is used to test whether the variances of the groups are same or
significantly different. The null hypothesis is that the variances are not significantly different.
The obtained output indicated that the test statistic is 2.109 with associated p-value of 0.122. As
the p-value is larger than the significance level of 0.05. Hence the null hypothesis was not
rejected as the variances are not significantly different across the groups thus the assumption of
homogeneity of variance are met.
Answer 5: What is the value of the F-statistic, number of degrees of freedom and the p-value?
The result shows that the test statistic is 61.974 with associated p-value 0.000.
Answer 6: Is there a significant difference in the overall satisfaction level of women in each of
the hprobgrp groups?
As the p-value is lower compared to the significance level 0.05, thus null hypothesis may not be
rejected. Therefore, the result above result to the assumption that, the variances are not
significantly distinct across the groups. In addition, the homogeneity assumption of variance is
met. By the ANOVA test, we see that F-statistic value is 61.674 with df of between groups, 2
and that of within groups 932 .Similarly, the related p-value is 0.000. We clearly see that the Ftest p-value is lower compared to the significance level of 0.05 thereby we reject the null
hypothesis. In addition, we finalize that there is a major difference in the whole satisfaction level
of women in every of the hprobgrp groups.
Answer 7: Interpret the post hoc test. When interpreting the post hoc test indicate the mean and
standard deviation for each group and indicate which group was signifantly higher or lower from
the other. If there is no difference between two groups indicate that as well.
The post hoc analysis is utilized for the analysis. As there is major group’s differences,
we have to recognize the specific group that varies. The output display that p-values of the post
hoc test for every pair is much smaller compared to the significance level of 0.05. Therefore,
every group means are significantly distinct. Therefore, every group has significantly dissimilar
mean. The descriptive statistics shows that the group of No Housing Problem has the higher
mean. In addition, the group with Two or More Housing Problems has lower mean.
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