By Hui Bian Office for Faculty Excellence 1
K-group between-subjects MANOVA with SPSS Factorial between-subjects MANOVA with SPSS How to interpret SPSS outputs How to report results 2
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. 3
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 4
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. 5
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. 6
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. 7
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: 9 th, 10 th, 11 th, and 12 th 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. 8
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. 9
Select Analyze Explore Move Q80 and Q81 Move Q3r Click Plots Descriptive Statistics 10
Stem-and-Leaf Plots (Q80 for 9 th grade) Stem Leaves 11
Stem-and-Leaf Plots (Q81 for 9 th grade) 12
Normal Q-Q Plots: the straight line in the plot represents expected values when the data are normally distributed. 13
Box Plots Kurtosis 75 th percentile Median 25 th percentile Minimum value 14
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 15
Options and Post-hoc 16
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. 17
SPPS Outputs Descriptive statistics 18
SPSS Outputs The non-significant Box s M indicates homogeneity of covariance matrices Significant result indicates sufficient correlation between the dependent variables. 19
SPSS Outputs 20
SPSS Outputs: univariate test results 21
SPSS Outputs: estimated marginal means 22
SPSS Outputs 23
P values SPSS Outputs 24
Plots 25
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 η 2 =.01. Univariate tests showed that there were significant differences across the grade levels on physical activity, F(3,15662) = 24.80, p <.01, partial η 2 =.01, and hours of watching TV, F(3,15662) = 27.00, p <.01, partial η 2 =.01. 26
Results Tamhane post hoc tests suggested 12 th graders (M = 3.96, SD = 2.53) had less days of physical activity than 9 th -11 th graders did. However, 9 th graders (M = 4.43, SD = 2.61) exercised more than 11 th graders (M = 4.24, SD = 2.57). Tukey HSD tests showed 9 th (M = 3.91, SD = 1.76) and 10 th (M = 3.83, SD = 1.76) graders spent more hours of watching TV than 11 th (M = 3.65, SD = 1.71)and 12 th graders (M = 3.61, SD = 1.71)did. 27
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. 28
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: 9 th, 10 th, 11 th, and 12 th 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). 29
Analysis using SPSS Select Analyze Multivariate General Linear Model 30
Options and Plots 31
SPSS Outputs 32
SPSS Outputs So, we don t have homogeneity of variance and covariance matrices across combination of two independent variables. 33
SPSS Outputs: multivariate results 34
SPSS Outputs: univariate results 35
SPSS Outputs: marginal means 36
SPSS Outputs: plots 37
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) 38
Plots Yes No 39
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 40
Type Q28 = 1 & Q3r = 1 (means Yes/9 th grade) 41
Then click Ok. Now you create a new variable with only one category (Yes to smoking and 9 th graders). Next, you need to continue adding other five categories to the same variable. Go to Transform Compute Variable 42
Use If button to change conditions Type Q28 = 1 & Q3r = 2 (Yes/10 th graders) 43
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. 44
Use ANOVA to examine if there is a difference across 8 levels of new variable on Q80. 45
P values Post hoc tests 46
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. 9 th and 10 th graders who had not ever use cigarettes exercised more than other students. 47
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. 48
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