biostatistics

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MANOVA BY GROUP 3
Multivariate Analysis of Variance (MANOVA)
BY GROUP 3 MEMBERS
 Tefera Bala
 Nebiyou Simegnew
 Sheka Shemsi
 Mohammed
 Mohamed Oumer
 Nafkot Berhanu

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MANOVA BY GROUP 3
outlines
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What is MANOVA?
When Should MANOVA Is Used?
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What are the assumptions to be Fulfilled in MANOVA ?
How to Conduct MANOVA Analysis?

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MANOVA BY GROUP 3
At the end of this presentation you will be able to:
Define MANOVA
List types of MANOVA
List the assumptions of MANOVA
Conduct the MANOVA analysis
Objective of presentation

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MANOVA BY GROUP 3
What is MANOVA?
MANOVA is an extension of the ANOVA
ANOVA deals with only ONE Dependent Variable.
MANOVA accounts for multiple Dependent variable at once.
MANOVA is statistical method for testing if there are mean differences across groups on
multiple DVs.
Tests the hypothesis that one or more independent variables, have an effect on a set of
two or more dependent variables
Similar to ANOVAs, there are between and within subjects in MANOVAs

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MANOVA BY GROUP 3
We do a MANOVA instead of a series of one-at-a-time ANOVAs for two main
reasons:
To reduce the experiment-wise level of Type I error (rejecting the null hypothesis
when it is in fact true) -protects against this inflated error probability only when
the null hypothesis is true.
None of the individual ANOVAs may produce a significant main effect on the DV, but
in combination they might, which suggests that the variables are more meaningful
taken together than considered separately.
MANOVA takes into account the intercorrelations among the DVs.
Why Should We Do a MANOVA?

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MANOVA BY GROUP 3
TYPES OF MANOVA
ONE-WAY MANOVA
TWO-WAY MANOVA
One categorical IDVs
Continuous DV
Categorical IDV
Continuous DV
Continuous DV
Categorical IDV continuous DV
effects
effects
effects

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MANOVA BY GROUP 3
Assumptions to be fulfilled in Manova
1. Normality (Shapiro Wilk)
2. Univariate Outliers (Boxplots)
3. Multivariate Outliers (Mahalanobis Distances)
4. Multicollinearity (Correlation)
5. Linearity (Scatterplot)
6. Homogeneity of variance-covariance matrices (Box’s M)
7. Independency of observation

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MANOVA BY GROUP 3
ONE WAY MANOVA
Eg: If someone is interested to know the effects of exercise on SBP and FBS
among individual who have both HTN and DM.
The exercise program are 15 minutes, 30 minutes and 45 minutes combined
with routine treatment.
The patients will be randomly assigned to each of 3 exercise programs and then
test will be performed to see if there are mean differences across 3 groups on
SBP and FBS.
 If there are 21 patients, for each 3-exercise program pts will 7 be randomly
assigned.
At the end of exercise intervention, the pt’s SBP & FBS will be measure to see if
there are mean differences across the three exercise groups.
1 IDV with 3 category 2 Continuous DV

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MANOVA BY GROUP 3
Normality test
normally distributed
MANOVA is generally robust to a
moderate violation of normality

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MANOVA BY GROUP 3
Univariate Outliers (Boxplots)
Not univariate outliers

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MANOVA BY GROUP 3
This assumption can be tested via the Mahalanobis Distances
Analyze -> Regression -> Linear
Multivariate Outliers
Move ‘SBP’ and ‘FBS’ to the Independent(s) box, and ‘EXERCISE’ to the Dependent
box

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MANOVA BY GROUP 3
Multivariate Outliers
Under Residuals Statistics, Maximum Malal.
Distance = 5.466
This value is smaller than the chi-square
value at df = 2, α = .05, which is 5.99
*Refer to a the critical value in the Chi-Square table; df =
number of DVs
This indicates no multivariate outlier

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MANOVA BY GROUP 3
The assumption of multicollinearity can be checked via a correlation
analysis
• Go to Analyze -> Correlate -> Bivariate
Multicollinearity
In the Correlations table, two DVs are not correlated, r = -.285 (p:0.21)
Therefore, no violation of multicollinearity

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MANOVA BY GROUP 3
This assumption can be tested using scatterplots
Graphs -> Legacy Dialogs -> Scatter/Dot -> Simple Scatter -> Define
linearity
If the lines are roughly straight, we conclude
that the assumption of linearity is satisfied

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MANOVA BY GROUP 3
• Analyze -> General Linear Model -> Multivariate
Homogeneity of variance-covariance matrices
In order to satisfy this assumption, the Box’s M value should be non-significant at α = .001
A significant value of .061 indicates that the assumption has not been violated

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MANOVA BY GROUP 3
• Analyze -> General Linear Model -> Multivariate
How to conduct MANOVA Analysis on SPSS?
Looking at Wilk’s lambda, F(2,34) = 13.534, p < .001.
There is a statistically significant difference in SBP and FBS
across types of Exercise.

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MANOVA BY GROUP 3
To investigate the effects of each DV, look at the Tests of
Between-Subjects Effects table
There is a main effect of exercise (15 or 30 or 45 min) on SBS, p
< .001, but not FBS, p = .180
To investigate which level of the IV significantly affected
the DV? Conduct Post Hoc Comparison
Analyse -> General linear model -> Multivariate -> Post-Hoc -
TUKEY

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MANOVA BY GROUP 3
• MANOVA yields more reliable level of type I error than ANOVA
• MANOVA is statistically more efficient than ANOVA
However, there are some disadvantages of MANOVA
• Complex design, ambiguous analytic results subjected to personal
assumptions.
• One degree of freedom is lost for each additional DV
• Assumption about normality is violated in the presence of outliers.
MANOVA Vs ANOVA