By Hui Bian
Office for Faculty Excellence
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 K-group between-subjects MANOVA with SPSS
 Factorial between-subjects MANOVA with SPSS
 How to interpret SPSS outputs
 How to report results
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 We use 2009 Youth Risk Behavior Surveillance
System (YRBSS, CDC) as an example.
 YRBSS monitors priority health-risk behaviors and
the prevalence of obesity and asthma among youth
and young adults.
 The target population is high school students
 Multiple health behaviors include drinking,
smoking, exercise, eating habits, etc.
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 MANOVA
 We focus on K-group between subjects design.
 Assess the effects of one independent variable (K-
group) on two or more dependent variables
simultaneously.
 Dependent variables are correlated and share a
common conceptual meaning.
 MANOVA uses Pillai’s trace, Wilks’lambda,
Hotelling’s trace, and Roy’s largest root criterion
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 Why use MANOVA
 Single dependent measure seldom captures completely a
phenomenon being studied.
 MANOVA provides some control over the overall alpha
level or type I error. Multiple univariate t tests or
ANOVA can inflate the operational alpha level.
 MANOVA considers dependent variable
intercorrelations.
 MANOVA helps indentify dependent variables that
produce the most group separation or distinction.
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 When NOT use MANOVA
 If the dependent variables are not correlated.
 If the dependent variables are highly correlated. It
will produce the risk of a multicollinearity
condition.
 Use subscales together with the total scores of the scale
as dependent variables
 The dependent variable is computed from one or more
of the others.
 Using baseline and posttest scores would create linear
dependence.
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 Assumptions
 Independence: the participants that compose the levels
of an independent variable must be independent of
each other.
 Homogeneity of covariance matrices
 Box’s M test from SPSS is used to assess equivalence of
covariance matrices.
 Homogeneity of variance
 When the sample size is fairly equal across the group,
violation of homogeneity produces minor consequences.
 The group sizes are approximately equal (largest/smallest 1.5).
 Multivariate normality
 Check univariate normality for each dependent variable.
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 Example:
 Research design: four-group between-subjects design
 Research question: whether grade levels affect high
school students’ sedentary behaviors.
 One independent variable: Grade with 4 levels: 9th, 10th, 11th,
and 12th grade (Q3r).
 Two dependent variables: sedentary behaviors: Q80 (physical
activity) and Q81: (How many hours watch TV).
 Higher score of Q80 = More days of physically active.
 Higher score of Q81 = More hours on watching TV.
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 Initial data screening
 Stem-and-Leaf Plots: use the original data values to
display the distribution's shape.
 Normal Q-Q Plots: the straight line in the plot
represents expected values when the data are
normally distributed.
 Box Plots: is used to identify outliers.
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 Select Analyze
Descriptive Statistics
Explore
 Move Q80 and Q81
 Move Q3r
 Click Plots
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 Stem-and-Leaf Plots (Q80 for 9th grade)
Leaves
Stem
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 Stem-and-Leaf Plots (Q81 for 9th grade)
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 Normal Q-Q Plots: the straight line in the plot represents
expected values when the data are normally distributed.
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 Box Plots
Kurtosis
75th
percentile
Median
25th
percentile
Minimum
value
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 Normality of our dependent variables
 The plots obtained from SPSS look reasonably normal.
 We judge these variables ready for multivariate analysis.
 MANOVA using SPSS
 Select Analyze
General Linear Model
Multivariate
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 Options and Post-hoc
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 Post hoc tests:
 A follow-up analysis
 Following a significant multivariate effect.
 The purpose of post hoc tests is to discover which
specific dependent variables are affected.
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 SPPS Outputs
 Descriptive statistics
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The non-significant Box’s
M indicates homogeneity
of covariance matrices
 SPSS Outputs
Significant result
indicates sufficient
correlation between the
dependent variables.
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 SPSS Outputs
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 SPSS Outputs: univariate test results
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 SPSS Outputs: estimated marginal means
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 SPSS Outputs
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P values
 SPSS Outputs
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 Plots
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 Results
 The mutivariate analysis of variance (MANOVA) was
conducted to assess grade differences on two sedentary
behaviors: physical activity and hours of watching TV
and. A non-significant Box’s M test (p = .12) indicates
homogeneity of covariance matrices of the dependent
variables across the levels of grade.
 The multivariate effect was significant by grade levels,
F(6,31322) = 28.11, p < .01, partial η2 = .01. Univariate tests
showed that there were significant differences across the
grade levels on physical activity, F(3,15662) = 24.80, p <
.01, partial η2 = .01, and hours of watching TV, F(3,15662) =
27.00, p < .01, partial η2 = .01 .
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 Results
 Tamhane post hoc tests suggested 12th graders (M =
3.96, SD = 2.53) had less days of physical activity
than 9th-11th graders did. However, 9th graders (M =
4.43, SD = 2.61) exercised more than 11th graders (M =
4.24, SD = 2.57).
 Tukey HSD tests showed 9th (M = 3.91, SD = 1.76) and
10th (M = 3.83, SD = 1.76) graders spent more hours
of watching TV than 11th (M = 3.65, SD = 1.71)and 12th
graders (M = 3.61, SD = 1.71)did.
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 Two-way MANOVA design
 The effects of two independent variables on several
dependent variables are examined simultaneously.
 A two-way design enables us to examine the joint effect
of independent variables.
 Interaction effect means that the effect of one
independent variable has on dependent variables is not
the same for all levels of the other independent variable.
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 Example:
 Research design: two-way between-subjects design
 Research question: whether grade levels and ever use
cigarettes jointly affect high school students’ sedentary
behaviors or whether the grade differences on sedentary
behaviors are moderated by ever use.
 Two independent variable: Grade with 4 levels: 9th, 10th, 11th,
and 12th grade (Q3r); ever use cigarettes (Q28) with two
levels: female and male.
 Two dependent variable: sedentary behaviors: Q80 (physical
activity), and Q81 (hours of watching TV).
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 Analysis using SPSS
 Select Analyze
General Linear Model
Multivariate
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 Options and Plots
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 SPSS Outputs
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 SPSS Outputs
So, we don’t have
homogeneity of variance
and covariance matrices
across combination of two
independent variables.
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 SPSS Outputs: multivariate results
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 SPSS Outputs: univariate results
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 SPSS Outputs: marginal means
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 SPSS Outputs: plots
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 Post hoc tests
 If we use ever use (two levels: Yes and No) as a
moderator, we want to know the relationship patterns of
grade and sedentary behaviors from Yes and No groups.
 Run one-way MANOVA for Yes group (select cases: Q28
= 1/Yes).
 Run one-way MANOVA for No group (select cases: Q28
= 2/No)
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 Plots
Yes
No
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 Other analyses
 We want to know which combinations of two independent variables
are significantly different from other combinations.
 Create a new variable: Grade_Smoke
 Go to Transform
Compute Variable
Click If
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 Type Q28 = 1 & Q3r = 1 (means Yes/9th grade)
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 Then click Ok. Now you create a new variable with
only one category (Yes to smoking and 9th graders).
 Next, you need to continue adding other five
categories to the same variable.
 Go to Transform
Compute Variable
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 Use If button to change conditions
 Type Q28 = 1 & Q3r = 2 (Yes/10th graders)
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 After click Continue than OK, you get this small
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
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
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window, click OK.
The same procedure for adding all categories.
Type Q28 = 1 & Q3r = 3
Type Q28 = 1 & Q3r = 4
Type Q28 = 2 & Q3r = 1
Type Q28 = 2 & Q3r = 2
Type Q28 = 2 & Q3r = 3
Type Q28 = 2 & Q3r = 4
A new variable with 8 levels.
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 Use ANOVA to examine if there is a difference across 8
levels of new variable on Q80.
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P values
 Post hoc tests
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 Results
 Similar to the results from one-way MANOVA.
 But we need to report Pillai’s trace multivariate test
result because we don’t have equal variance and
covariance matrices across the groups.
 The grade and ever use significantly affected sedentary
behaviors.
 The relationship of grade and sedentary behaviors were
moderated by ever use behavior.
 9th and 10th graders who had not ever use cigarettes
exercised more than other students.
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Meyers, L. S., Gamst, G., & Guarino, A. J. (2006).
Applied multivariate research: design and
interpretation. Thousand Oaks, CA: Sage Publications,
Inc.
Stevens, J. P. (2002). Applied multivariate statistics for
the social sciences. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc.
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