SPSS Series 2 MANOVA and Factorial MANOVA PDF.pdf

8/22/2019 SPSS Series 2 MANOVA and Factorial MANOVA PDF.pdf

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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



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



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.



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



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.



SPSS Outputs: multivariate results

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SPSS Outputs: univariate results

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SPSS Outputs: marginal means



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



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)



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



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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SPSS Series 2 MANOVA and Factorial MANOVA PDF.pdf

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