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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 SurveillanceSystem (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 variablessimultaneously.
Dependent variables are correlated and share acommon 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 variableintercorrelations.
MANOVA helps indentify dependent variables thatproduce 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 highschool students’ sedentary behaviors. One independent variable: Grade with 4 levels: 9th, 10th, 11th,
and 12th grade (Q3r).
Two dependent variables: sedentary behaviors: Q80 (physicalactivity) 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 arenormally distributed.
Box Plots: is used to identify outliers.
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Select Analyze Descriptive StatisticsExplore
Move Q80 and Q81
Move Q3r Click Plots
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Stem-and-Leaf Plots (Q80 for 9th grade)
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Stem
Leaves
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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
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Median
Minimum value
25th percentile
75th percentile
Kurtosis
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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 whichspecific dependent variables are affected.
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SPPS Outputs Descriptive statistics
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SPSS Outputs
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The non-significant Box’s M indicates homogeneity
of covariance matrices
Significant resultindicates sufficientcorrelation between thedependent 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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SPSS Outputs
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P values
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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) indicateshomogeneity 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 thegrade 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) and10th ( 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 notthe 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 usecigarettes 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 twolevels: female and male.
Two dependent variable: sedentary behaviors: Q80 (physicalactivity), 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
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So, we don’t havehomogeneity of varianceand covariance matrices
across combination of twoindependent 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
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Yes No
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Other analyses We want to know which pairs of combinations of two
independent variables are significantly different.
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 withonly one category (Yes to smoking and 9th graders).
Next, you need to continue adding other fivecategories 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 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 8levels of new variable on Q80.
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Post hoc tests
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P values
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Results Similar to the results from one-way MANOVA.
But we need to report Pillai’s trace multivariate testresult 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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