Chapter 16: Multivariate Analysis of Variance (MANOVA) Flashcards
Bartlett’s test of sphericity
examines whether a variance-covariance matrix is proportional to an identity matrix
effectively tests whether the diagonal elements of the variance-covariance matrix are equal and whether the off diagonal elements are approximately 0
Box test
tests the assumption of homogeneity of covariance matrices
this test should be non-significant if the matrices are roughly the same
very susceptible to deviations from multivariate normality, and so may be non-significant not because the variance-covariance matrices are similar across groups, but because the assumption of multivariate normality is not tenable
Homogeneity of covariance matricies
assumption that all variances for each dependent variable are the same across all groups
assumes that the relationships between these dependent variables are roughly equal
tested by comparing the population variance-covariance matrices of the different groups in the analysis.
hotelling-lawley trace (T2)
test statistic in MANOVA
it is the sum of the eigenvalues for each discriminant function variate of the data and so is conceptually the same as the F-ratio in ANOVA
it is the sum of the ratio of systematic and unsystematic variance (SSm/SSr) for each of the variates
Identity matrix
a square matrix in which the diagonal elements are equal to 1, and the off diagonal elements are equal to 0
matrix
collection of numbers arranged in columns and rows
values are typically referred to as components or elements
multivariate
meaning Many Variables
MANOVA is used to look at several dependent variables simultaneously (this term)
multivariate analysis of variance (MANOVA)
thought of as an ANOVA for situations in which there are several dependent variables
Multivariate normality
an extension of a normal distribution to multiple variables
it is a probability distribution of a set of variables
pillai-bartlett trace (V)
a test statistic in MANOVA
it is the sum of the proportion of explained variance on the discriminant function variates of the data
Univariate
meaning one variable
ANOVA is used only in situations with only one dependent variable (this term)
Wilks’s Lambda (L)
test statistic in MANOVA
product of the unexplained variance on each of the discriminant function variates, so it represents the ratio of error variance to total variance (SSr/SSt) for each variate