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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


1
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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