What is manova When to use manova How to conduct analysis of manova using spss What are the assumptions to be fulfilled

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MANOVA 2023 © Jimma university, Ethiopia
Multivariate Analysis of Variance (MANOVA)
BY:- GROUP 3 MEMBERS

2. Nebiyou
Simegnew
Nafkot Berhanu
Tefera Bala
Sheka Shemsi
Mohammed Ibrahim
Mohamed Oumer
Mesfin Felaha
Group 3 Members

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MANOVA 2023 © Jimma university, Ethiopia
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 by using SPSS.
Objectives of the presentation

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MANOVA 2023 © Jimma university, Ethiopia
Outlines
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What is MANOVA?
When Should MANOVA Is Used?
.
What are the assumptions to be Fulfilled in
MANOVA ?
How to Conduct MANOVA Analysis?

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MANOVA 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 7 pts will be randomly
assigned.
At the end of exercise intervention, the pt’s SBP & FBS will be measured 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 2023 © Jimma university, Ethiopia
Exercise
program
15 mints
30 mints
45 mints
SBP
FBS
1 Independent variable with 3-category 2 continuous dependent
variable
Ho: µ1= µ2= µ3 -on SBP HA: µ1 ≠ µ2 ≠ µ3 –on SBP
Ho: µ1= µ2= µ3 -on FBS HA: µ1 ≠ µ2 ≠ µ3 –on FBS

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MANOVA 2023 © Jimma university, Ethiopia
Normality test
normally
distributed
MANOVA is generally robust to
a moderate violation of
normality

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MANOVA 2023 © Jimma university, Ethiopia
Univariate Outliers (Boxplots)
Not univariate outliers

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MANOVA 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
• 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 2023 © Jimma university, Ethiopia
• Analyze -> General Linear Model -> Multivariate
How to conduct MANOVA Analysis on SPSS?
Looking at Wilk’s lambda, F (4,34) = 13.534, p < .001.
There is a statistically significant difference in SBP and FBS across types of Exercise.

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MANOVA 2023 © Jimma university, Ethiopia
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 2023 © Jimma university, Ethiopia
• 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.
Assumption about normality is violated in the presence of
outliers.
Manova is not recommend if DV is not correlated or highly
correlated.
MANOVA Vs ANOVA

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MANOVA 2023 © Jimma university, Ethiopia
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