This document discusses the results of a study that used a 2x3 factorial MANOVA to analyze the effects of three different anxiety treatments (medication, psychotherapy, placebo) on worry and emotion scales, for both males and females. Key findings included: - The dependent variables were sufficiently correlated to justify MANOVA use. - The assumption of equal covariance matrices was not violated. - There was a significant multivariate interaction effect for emotion. - Follow-up tests should include separate one-way ANOVAs for males and females with treatment as the independent variable. - The LSD post hoc test was appropriate given equal variances. - There was a significant multivariate gender effect but it

1. College of Doctoral Studies
RES-845: Module 8 Problem Set
Solution
s
Factorial (2 x 3) MANOVA
1.
Is there a sufficient correlation between the dependent variables
to justify the use of MANOVA?
YES! THE DEPENDENT VARIABLES ARE BOTH
CONCEPTUALLY AND STATISTICALLY (r = .513)
RELATED.
2.
Was the assumption of Equality of Covariance Matrices
violated? Explain.
NO! RESULT OF THE BOX'S TEST OF EQUALITY OF
COVARIANCE MATRICES INDICATED NO VIOLATION (p =
.463).
3.
Is there a statistically significant multivariate interaction
effect?

2. YES!
Identify the dependent variable(s) of this interaction effect.
EMOTION ONLY
4.
What would be the proper follow-up tests for a statistically
significant interaction effect?
CONDUCT TWO SEPARATE ONE-WAY ANOVAs WITH
TREATMENT AS THE INDEPENDENT VARIABLE FOR
MALES AND FEMALES. IF THE ONE-WAY ANOVAs
REPORT A STATISTICALLY SIGNIFICANT OMNIBUS,
THEN PERFORM THE APPROPRIATE POST-HOC.
5.
Identify the proper post hoc analyses for any statistically
significant univariate effects. Explain your answer.
THE LSD IS ONE OF THE PROPER POST-HOCS BECAUSE
THE EQUAL VARIANCES ASSUMPTION IS NOT
VIOLATED.
6.
Is there a statistically significant multivariate gender effect on
the dependent variate?
YES! BUT BECAUSE THERE IS AN INTERACTION EFFECT,
THIS MAIN EFFECT IS OF LITTLE INTEREST.
7.
Why would a researcher conduct a MANOVA instead of several
ANOVAs?

3. THERE ARE AT LEAST TWO REASONS TO CONDUCT A
MANOVA INSTEAD OF A SERIES OF ANOVAs. (1)
MANOVA IS A MORE POWERFUL STATISTICAL
TECHNIQUE (I.E., IT IS BETTER ABLE TO DETECT
DIFFERENCES IF THEY REALLY EXIST), (2) MANOVA
CONTROLS FOR AN INFLATED TYPE I ERROR.
8.
Write a Results section for this research.
Correlations
General Linear Model
Box's Test of Equality of Covariance Matricesa
Multivariate Tests c
Levene's Test of Equality of Error Variances a
Tests of Between-Subjects Effects

4. General Linear Model
1. Treatment
2. Gender
3. Treatment * Gender
Univariate Analysis of Variance
Tests of Between-Subjects Effects
Estimated Marginal Means
1. Treatment
2. Gender
3. Treatment * Gender
Univariate Analysis of Variance for MALES
Tests of Between-Subjects Effects

5. Estimated Marginal Means
Treatment
Post Hoc Tests
Multiple Comparisons
Univariate Analysis of Variance for FEMALES
Tests of Between-Subjects Effects
Estimated Marginal Means
Treatment
Post Hoc Tests Treatment
Multiple Comparisons
Univariate Analysis of Variance for TREATMENT Main Effect
Tests of Between-Subjects Effects
Estimated Marginal Means
Treatment
Post Hoc Tests
Treatment

6. © 2012. Grand Canyon University. All Rights Reserved.
College of Doctoral Studies
RES-845: Module 8 Problem Set
Factorial (2 × 3) MANOVA
This study investigates the symptomatic improvement
(measured by indexes of both worry and general emotion) of
three different anxiety treatments for females and males. We are
therefore interested not only in gender differences and treatment
differences but also in whether or not gender moderates the
effectiveness of the treatments (i.e., whether gender
significantly interacts with treatment). To address these issues
we use a factorial MANOVA design.
Variables in study:
· Treatment: 1 = medication; 2 = psychotherapy; 3 = placebo
· Sex: 1 = male; 0 = female
· Worry scale
· Emotion scale
Using the SPSS data file for Module 8 (located in Topic
Materials), answer the following questions:
1. Is there a sufficient correlation between the dependent
variables to justify the use of MANOVA?

7. 2. Was the assumption of equality of covariance matrices
violated? Explain.
3. Is there a statistically significant multivariate interaction
effect? Identify the dependent variable(s) of this interaction
effect.
4. What would be the proper follow-up tests for a statistically
significant interaction effect?
5. Identify the proper post hoc analyses for any statistically
significant univariate effects. Explain your answer.
6. Is there a statistically significant multivariate gender effect
on the dependent variate?
7. Why would a researcher conduct a MANOVA instead of
several ANOVAs?
8. Write a results section for this research.
© 2012. Grand Canyon University. All Rights Reserved.