I want you to answer this one also with your original words I will also include the answers but please use your original thoughts thank you. I have included the data set and the questions with the answers, but remember it must be your original words. I have included 3 sets of answers for you to look through, but please remember use your original words thank you
psy870.r.module6.spssdatafile.sav.zip
psy870.r.module6problemset_11_21_2013_1.docx
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College of Doctoral Studies
PSY 870: Module 6 Problem Set
Factorial (2 × 3) MANOVA
This study investigates whether there are differences in the outcomes of three different
treatments for anxiety. The treatment conditions that are compared are treatment with
medication, treatment with psychotherapy, and placebo (inactive pills). In addition, we want to
see if gender of the client moderates the effects of the treatment. Every participant had been
diagnosed with similar types and severity of anxiety disorders when they entered the study. Each
participant was randomly assigned only to one of the three treatment conditions. After 12-weeks
of treatment (or placebo), all participants completed two questionnaires to measure worry and
general emotion. The higher the scores on these measures, the higher the anxiety level of the
participant.
Directions:
The factorial MANOVA will combine what you have learned previously about
1. Post hoc tests when you have more than two groups on an IV (one-way ANOVA),
2. Main effects and interactions (factorial ANOVA), and
3. Working with multivariate analyses of multiple DVs (one-way MANOVA).
Using the SPSS data file for Module 6 (located in Topic Materials), answer the following
questions:
1. What are the independent variables in this study? What are the dependent variables?
2. Why is a factorial MANOVA appropriate to use for this research design?
3. Did you find any errors that the researcher made when setting up the SPSS data file (don’t
forget to check the variable view)? If so, what did you find? How did you correct it?
HINT:
Yes, there are coding errors for Measures.
4. Perform Initial Data Screening. What did you find regarding missing values, univariate
outliers, multivariate outliers, normality?
HINT:
Revisit instructions from last module’s readings on how to compute Mahalanobis
distance and then analyze for multivariate outliers.
5. Perform a factorial MANOVA on the data. Before interpreting the multivariate results of
the MANOVA, check outcomes that test other assumptions for this statistic: equality of
covariance matrices (see Box’s Test) and sufficient correlation among the DVs (see
Bartlett’s Test of Sphericity). Also check the results of the Levene’s Test of Equality of
Error Variances to evaluate that assumption for the univariate ANOVAs that are run and
show in the Tests of Between-Subjects Effects output. What have you found about
whether the data meet these additional assumptions for the MANOVA and follow-up
ANOVAs? Explain.
HINTS:
Once in the Options box, remember to check box for “Residual SSCP matrix”
to get results for the Bartlett’s test.
Also, remember to ask for post hoc tests for Treatment because there are more
than two conditions. Profile plots also help with visualizing interactions.
6. What are the outcomes of the multivariate tests (main effects and interaction)? Report
either the Pillai’s Trace or Wilks’s Lambda for each result, as well as the associated Fvalue and its statistical significance. Use the following format for notation to report each
result: Pillai’s Trace OR Wilks’ lambda = ____; F(df, df) = ____, p = ____.
HINTS:
Use Pillai’s trace if there are problems with heterogeneity of variancecovariance matrices for the DVs. Otherwise, Wilks’ lambda is fine.
Eta squared cannot be calculated from the information provided in the
multivariate tests results.
7. Given the results of the multivariate tests, would you now move on to interpret the results
of the Tests of Between-Subjects Tests? If yes, what are the results and what do they
mean? (Report each of the results using the format of F(df, df) = _____, p = _____ , 2 =
_____.)
8. Because one IV has more than two conditions, you would need to do post hoc tests if the
overall F-value was statistically significant. If so, what results did you find?
9. If you had a significant interaction effect, what follow-up tests do you need to perform to
understand how gender moderates the effects of treatment? What are the results?
10. Citing the results of your statistical analyses, what is the conclusion you can draw (and
support) regarding research question that was posed in this research (see problem
statement)?
© 2013. Grand Canyon University. All Rights Reserved.
HINT: Use the sample results write-up in the textbook to see what you should
report and how to say it. Just substitute the correct language and values for the
analyses you have done for this problem.
© 2013. Grand Canyon University. All Rights Reserved.
Factorial (2 × 3) MANOVA
This study investigates whether there are differences in the outcomes of three different treatments for
anxiety. The treatment conditions that are compared are treatment with medication, treatment with
psychotherapy, and placebo (inactive pills). In addition, we want to see if gender of the client moderates
the effects of the treatment. Every participant had been diagnosed with similar types and severity of
anxiety disorders when they entered the study. Each participant was randomly assigned only to one of
the three treatment conditions. After 12-weeks of treatment (or placebo), all participants completed
two questionnaires to measure worry and general emotion. The higher the scores on these measures,
the higher the anxiety level of the participant.
Directions:
The factorial MANOVA will combine what you have learned previously about
1. Post hoc tests when you have more than two groups on an IV (one-way ANOVA),
2. Main effects and interactions (factorial ANOVA), and
3. Working with multivariate analyses of multiple DVs (one-way MANOVA).
Using the SPSS data file for Module 6 (located in Topic Materials), answer the following questions:
1. What are the independent variables in this study? What are the dependent variables?
Independent variables: TREATMENT, GENDER
Dependent variables:
EMOTION, WORRY
2. Why is a factorial MANOVA appropriate to use for this research design?
There are two reasons why MANOVA is better for this research design:
(1) MANOVA is a more powerful statistical technique because it is better able to detect differences
when such difference do exist, when compared to a series of ANOVAS.
(2) MANOVA provides a way to control inflated type I error.
3. Did you find any errors that the researcher made when setting up the SPSS data file (don’t forget to
check the variable view)? If so, what did you find? How did you correct it?
HINT: Yes, there are coding errors for Measures.
Treatment and Gender variables should be nominal, not ordinal.
The Emotion and Worry variables are not labeled.
4. Perform Initial Data Screening. What did you find regarding missing values, univariate outliers,
multivariate outliers, normality?
HINT: Revisit instructions from last module’s readings on how to compute Mahalanobis distance and
then analyze for multivariate outliers.
MISING VALUES: There are no missing values.
Univariate Statistics
N
Mean
Std. Deviation
No. of Extremesa
Missing
Count
Percent
Low
High
Treatment
100
2.00
.829
0
.0
0
0
Gender
100
.50
.503
0
.0
0
0
Emotion
100
27.64
13.977
0
.0
0
0
Worry
100
34.88
8.985
0
.0
1
0
a.
Number of cases outside the range (Q1 – 1.5*IQR, Q3 + 1.5*IQR).
OUTLIERS. From the box plot, there is one outlier for WORRY. Observation No. 96, value = 8.
Residuals Statisticsa
Minimum Maximum Mean
Std. Deviation N
Predicted Value
-.44
1.19
.50
.432
100
Std. Predicted Value
-2.168
1.591
.000
1.000
100
Standard Error of
Predicted Value
.028
.092
.051
.011
100
Adjusted Predicted Value -.46
1.20
.50
.433
100
Residual
-.673
.504
.000
.257
100
Std. Residual
-2.582
1.934
.000
.985
100
Stud. Residual
-2.619
1.975
-.001
1.005
100
Deleted Residual
-.692
.526
.000
.268
100
Stud. Deleted Residual
-2.703
2.006
-.002
1.016
100
Mahal. Distance
.116
11.387
2.970
1.859
100
Cook’s Distance
.000
.132
.011
.018
100
Centered Leverage Value .001
.115
.030
.019
100
a. Dependent Variable: Gender
Outlier Statisticsa
Case Number
Statistic
1
96
11.387
2
39
8.173
3
71
7.761
4
7
7.586
5
57
7.431
6
3
6.373
7
1
6.049
8
22
5.564
9
95
5.400
10
68
5.382
outlier
Mahal. Distance
a. Dependent Variable: Gender
Tests of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Emotion
.095
100
.028
.969
100
.017
Worry
.085
100
.069
.986
100
.366
a. Lilliefors Significance Correction
EMOTION is not normal,
p = 0.028 < 0.05
WORRY is normal,
p = 0.069 > 0.05
5. Perform a factorial MANOVA on the data. Before interpreting the multivariate results of the
MANOVA, check outcomes that test other assumptions for this statistic: equality of covariance matrices
(see Box’s Test) and sufficient correlation among the DVs (see Bartlett’s Test of Sphericity). Also check
the results of the Levene’s Test of Equality of Error Variances to evaluate that assumption for the
univariate ANOVAs that are run and show in the Tests of Between-Subjects Effects output. What have
you found about whether the data meet these additional assumptions for the MANOVA and follow-up
ANOVAs? Explain.
HINTS:
• Once in the Options box, remember to check box for “Residual SSCP matrix” to get results for the
Bartlett’s test.
• Also, remember to ask for post hoc tests for Treatment because there are more than two conditions.
Profile plots also help with visualizing interactions.
Equality of covariance matrices (Box’s Test)
Box’s Test of Equality of Covariance Matricesa
Box’s M
12.642
F
.983
df1
12
df2
7143.492
Sig.
.463
Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal
across groups.
a. Design: Intercept + Treatment + Gender + Treatment * Gender
Sufficient correlation among the DVs (Bartlett’s Test of Sphericity)
Bartlett’s Test of Sphericitya
Likelihood Ratio
.000
Approx. Chi-Square
51.982
df
2
Sig.
.000
Tests the null hypothesis that the residual covariance matrix is proportional to an identity matrix.
Levene’s Test of Equality of Error Variances
Levene’s Test of Equality of Error Variancesa
F
df1
df2
Sig.
Emotion
1.733
5
94
.135
Worry
1.383
5
94
.238
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + Treatment + Gender + Treatment * Gender
Based on the foregoing output, the data meets these additional assumptions for the MANOVA and
follow-up ANOVAs. Significance levels are > 0.05. for equality of variances, and correlation among DV.
6. What are the outcomes of the multivariate tests (main effects and interaction)? Report either the
Pillai’s Trace or Wilks’s Lambda for each result, as well as the associated F-value and its statistical
significance. Use the following format for notation to report each result: Pillai’s Trace OR Wilks’ lambda
= ____; F(df, df) = ____, p = ____.
HINTS:
• Use Pillai’s trace if there are problems with heterogeneity of variance-covariance matrices for the DVs.
Otherwise, Wilks’ lambda is fine.
• Eta squared cannot be calculated from the information provided in the multivariate tests results.
The outcomes are:
Pillai’s trace for Treatment:
Pillai’s Trace OR Wilks’ lambda = 0.39 ; F(df, df) = 9.263, p = 0.000
Pillai’s Trace
.329
9.263
4.000
188.000
.000
93.000
.000
Pillai’s Trace for Gender:
Pillai’s Trace OR Wilks’ lambda = 0.523 ; F(df, df) = 50.919, p = 0.000
Pillai’s Trace
.523
50.919b
2.000
7. Given the results of the multivariate tests, would you now move on to interpret the results of the
Tests of Between-Subjects Tests? If yes, what are the results and what do they mean? (Report each of
the results using the format of F(df, df) = _____, p = _____ , 2 = _____.)
The results of Test of Between Subjects Test are:
Tests of Between-Subjects Effects
Source
Dependent
Variable
Type III Sum df
of Squares
Mean Square F
Sig.
Partial Eta
Squared
Emotion
12652.320a
5
2530.464
35.562
.000
.654
Worry
3911.493b
5
782.299
18.020
.000
.489
Emotion
34815.635
1
34815.635
489.285
.000
.839
Worry
51685.732
1
51685.732
1190.545 .000
.927
Emotion
1786.729
2
893.364
12.555
.000
.211
Worry
1951.834
2
975.917
22.480
.000
.324
Emotion
5538.603
1
5538.603
77.837
.000
.453
Worry
114.424
1
114.424
2.636
.108
.027
Emotion
806.236
2
403.118
5.665
.005
.108
Worry
208.084
2
104.042
2.397
.097
.049
Emotion
6688.673
94
71.156
Worry
4080.870
94
43.414
Emotion
95711.199
100
Worry
129621.437
100
Emotion
19340.992
99
Worry
7992.364
99
Corrected Model
Intercept
Treatment
Gender
Treatment *
Gender
Error
Total
Corrected Total
a. R Squared = .654 (Adjusted R Squared = .636)
b. R Squared = .489 (Adjusted R Squared = .462)
The results are: Gender has no significant effect. Treatment has significant effect.
8. Because one IV has more than two conditions, you would need to do post hoc tests if the overall Fvalue was statistically significant. If so, what results did you find?
Post Hoc Tests
Treatment Multiple Comparisons:
Meds v. Placebo & Psychotherapy v. Meds are significant.
Tukey HSD
Dependent
Variable
(I) Treatment (J) Treatment
Mean
Std. Error Sig.
Difference (IJ)
95% Confidence Interval
Lower Bound Upper Bound
Psychotherapy -12.71*
2.078
.000
-17.66
-7.76
Placebo
2.68
2.046
.393
-2.19
7.55
Meds
12.71*
2.078
.000
7.76
17.66
Placebo
15.39*
2.078
.000
10.44
20.34
Meds
-2.68
2.046
.393
-7.55
2.19
Psychotherapy -15.39*
2.078
.000
-20.34
-10.44
Psychotherapy -12.62*
1.623
.000
-16.48
-8.75
Placebo
-12.28*
1.598
.000
-16.08
-8.47
Meds
12.62*
1.623
.000
8.75
16.48
Placebo
.34
1.623
.976
-3.52
4.21
Meds
12.28*
1.598
.000
8.47
16.08
1.623
.976
-4.21
3.52
Meds
Emotion
Psychotherapy
Placebo
Meds
Worry
Psychotherapy
Placebo
Psychotherapy -.34
Based on observed means.
The error term is Mean Square(Error) = 43.414.
*. The mean difference is significant at the .05 level.
9. If you had a significant interaction effect, what follow-up tests do you need to perform to understand
how gender moderates the effects of treatment? What are the results?
We would follow up with post hoc tests for Gender.
The result is: Gender has insignificant role in the prognosis of the patients.
10. Citing the results of your statistical analyses, what is the conclusion you can draw (and support)
regarding research question that was posed in this research (see problem statement)?
Conclusion is that Meds have a significant role in reducing the anxiety of the patients. The next best
treatment is Psychotherapy.
Two-Way Factorial MANOVA Using SPSS: Output
General Linear Model
Notes
Output Created
Comments
Input
01-JUL-2014 08:11:10
Data
Active Dataset
Filter
Weight
Split File
N of Rows in
Working Data File
Definition of
Missing
Missing Value Handling
Cases Used
Syntax
Resources
Processor Time
Elapsed Time
Between-Subjects Factors
Value Label
1
Meds
Treatment 2
Psychotherapy
3
Placebo
0
Females
Gender
1
Males
N
34
32
34
50
50
DataSet1
100
User-defined missing values are
treated as missing.
Statistics are based on all cases
with valid data for all variables in
the model.
GLM Emotion Worry BY Treatment Gender
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/POSTHOC=Treatment(TUKEY)
/PRINT=DESCRIPTIVE ETASQ RSSCP
HOMOGENEITY
/PLOT=RESIDUALS
/CRITERIA=ALPHA(.05)
/DESIGN= Treatment Gender
Treatment*Gender.
00:00:01.73
00:00:01.13
Descriptive Statistics
Treatment
Females
Males
Total
Females
Psychotherapy Males
Total
Females
Placebo
Males
Total
Females
Total
Males
Total
Females
Meds
Males
Total
Females
Psychotherapy Males
Total
Females
Placebo
Males
Total
Females
Total
Males
Total
Meds
Emotion
Worry
Gender
Mean
14.03
27.70
24.48
17.07
46.33
37.19
20.31
45.59
21.80
18.66
36.61
27.64
26.61
26.68
26.66
33.85
41.75
39.28
38.83
40.66
38.94
35.88
33.87
34.88
Std.
Deviation
8.499
9.863
11.120
6.709
8.730
15.958
7.498
1.653
9.453
7.743
13.048
13.977
8.305
7.379
7.475
6.330
7.260
7.823
4.973
1.691
4.849
7.309
10.374
8.985
N
8
26
34
10
22
32
32
2
34
50
50
100
8
26
34
10
22
32
32
2
34
50
50
100
Box’s Test of Equality of Covariance Matricesa
Box’s M 12.642
F
.983
df1
12
df2
7143.492
Sig.
.463
Tests the null hypothesis that the observed covariance matrices of the
dependent variables are equal across groups.
a. Design: Intercept + Treatment + Gender + Treatment * Gender
Bartlett’s Test of Sphericitya
Likelihood Ratio
.000
Approx. Chi-Square 51.982
df
2
Sig.
.000
Tests the null hypothesis that the residual covariance matrix is proportional
to an identity matrix.
a. Design: Intercept + Treatment + Gender + Treatment * Gender
Multivariate Testsa
Effect
Value
F
Hypothesis df Error df
Sig.
Partial Eta
Squared
.927
589.144b
2.000
93.000
.000
.927
Wilks’ Lambda
.073
589.144b
2.000
93.000
.000
.927
Hotelling’s Trace
12.670
589.144b
2.000
93.000
.000
.927
12.670
589.144b
2.000
93.000
.000
.927
.329
.671
.490
.490
9.263
10.270b
11.276
23.016c
4.000
4.000
4.000
2.000
188.000
186.000
184.000
94.000
.000
.000
.000
.000
.165
.181
.197
.329
.523
.477
1.095
1.095
50.919b
50.919b
50.919b
50.919b
2.000
2.000
2.000
2.000
93.000
93.000
93.000
93.000
.000
.000
.000
.000
.523
.523
.523
.523
Pillai’s Trace
.118
2.953
4.000
188.000
.021
.059
Wilks’ Lambda
.883
2.988b
4.000
186.000
.020
.060
Hotelling’s Trace
.131
3.021
4.000
184.000
.019
.062
.121
5.669c
2.000
94.000
.005
.108
Pillai’s Trace
Intercept
Treatment
Roy’s Largest Root
Pillai’s Trace
Wilks’ Lambda
Hotelling’s Trace
Roy’s Largest Root
Gender
Pillai’s Trace
Wilks’ Lambda
Hotelling’s Trace
Roy’s Largest Root
Treatment *
Gender
Roy’s Largest Root
a. Design: Intercept + Treatment + Gender + Treatment * Gender
b. Exact statistic
c. The statistic is an upper bound on F that yields a lower bound on the
significance level.
Levene’s Test of Equality of Error Variancesa
F
df1
df2
Sig.
Emotion
1.733
5
94
.135
Worry
1.383
5
94
.238
Tests the null hypothesis that the error variance of the dependent variable
is equal across groups.
a. Design: Intercept + Treatment + Gender + Treatment * Gender
Tests of Between-Subjects Effects
Source
Corrected
Model
Intercept
Treatment
Gender
Treatment *
Gender
Error
Total
Corrected
Total
Dependent
Variable
Type III
Sum of
Squares
Emotion
Mean
Square
F
Sig.
Partial
Eta
Squared
12652.320a 5
2530.464
35.562
.000
.654
Worry
3911.493b
5
782.299
18.020
.000
.489
Emotion
34815.635
1
34815.635 489.285 .000
.839
51685.732
1
.927
Emotion
1786.729
2
51685.732 1190.54 .000
5
893.364
12.555 .000
Worry
1951.834
2
975.917
22.480
.000
.324
Emotion
5538.603
1
5538.603
77.837
.000
.453
Worry
114.424
1
114.424
2.636
.108
.027
Emotion
806.236
2
403.118
5.665
.005
.108
Worry
208.084
2
104.042
2.397
.097
.049
Emotion
6688.673
94
71.156
Worry
4080.870
94
43.414
Emotion
95711.199
100
Worry
129621.437 100
Emotion
19340.992
99
7992.364
99
Worry
Worry
df
a. R Squared = .654 (Adjusted R Squared = .636)
b. R Squared = .489 (Adjusted R Squared = .462)
Residual SSCP Matrix
Emotion
Worry
Emotion
Covariance
Worry
Emotion
Correlation
Worry
Based on Type III Sum of Squares
Sum-of-Squares and
Cross-Products
Emotion
6688.673
3273.441
71.156
34.824
1.000
.627
Worry
3273.441
4080.870
34.824
43.414
.627
1.000
.211
Post Hoc Tests
Treatment
Multiple Comparisons
Tukey HSD
Dependent
(I)
Variable
Treatment
(J)
Treatment
Mean
Std.
Difference Error
(I-J)
Sig.
Psychother -12.71*
2.078
.000
apy
Meds
2.68
2.046
.393
Placebo
*
12.71
2.078
.000
PsychotheraMeds
Emotion
py
15.39*
2.078
.000
Placebo
-2.68
2.046
.393
Meds
Placebo
Psychother -15.39*
2.078
.000
apy
Psychother -12.62*
1.623
.000
apy
Meds
-12.28*
1.598
.000
Placebo
*
12.62
1.623
.000
PsychotheraMeds
Worry
py
.34
1.623
.976
Plac …
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