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## LECTURE 17 MANOVA

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### Multiple discriminant analysis (MDA) is the part of MANOVA where canonical roots ... violations of the assumption of normality, making the Box's M test less useful ... – PowerPoint PPT presentation

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Title: LECTURE 17 MANOVA

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LECTURE 17MANOVA
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Other Measures
• Pillai-Bartlett trace, V
• Multiple discriminant analysis (MDA) is the part
of MANOVA where canonical roots are calculated.
Each significant root is a dimension on which the
vector of group means is differentiated. The
Pillai-Bartlett trace is the sum of explained
variances on the discriminant variates, which are
the variables which are computed based on the
canonical coefficients for a given root. Olson
(1976) found V to be the most robust of the four
tests and is sometimes preferred for this reason.
• Roy's greatest characteristic root (GCR
• is similar to the Pillai-Bartlett trace but is
based only on the first (and hence most
important) root.Specifically, let lambda be the
largest eigenvalue, then GCR lambda/(1
lambda). Note that Roy's largest root is
sometimes also equated with the largest
eigenvalue, as in SPSS's GLM procedure (however,
SPSS reports GCR for MANOVA). GCR is less robust
than the other tests in the face of violations of
the assumption of multivariate normality.

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--- fixed value From 1st model
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Assumptions- Homoscedasticity
• Box's M Box's M tests MANOVA's assumption of
homoscedasticity using the F distribution. If
p(M)lt.05, then the covariances are significantly
different. Thus we want M not to be significant,
rejecting the null hypothesis that the
covariances are not homogeneous. That is, the
probability value of this F should be greater
than .05 to demonstrate that the assumption of
homoscedasticity is upheld. Note, however, that
Box's M is extremely sensitive to violations of
the assumption of normality, making the Box's M
test less useful than might otherwise appear. For
this reason, some researchers test at the p.001
level, especially when sample sizes are unequal.

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Assumptions-Normality
• Multivariate normal distribution. For purposes of
significance testing, variables follow
multivariate normal distributions. In practice,
it is common to assume multivariate normality if
each variable considered separately follows a
normal distribution. MANOVA is robust in the face
of most violations of this assumption if sample
size is not small (ex., lt20).

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DISCRIMINANT ANALYSIS
• The inverse of the MANOVA problem

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Group 1 mean

Group 3 mean
Group 2 mean
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Group 1 mean

Group 3 mean
Group 2 mean
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