Chapter 16: Multivariate Analysis of Variance (MANOVA)

Question 1

Bartlett’s test of sphericity

Answer 1

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

Question 2

Box test

Answer 2

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

Question 3

Homogeneity of covariance matricies

Answer 3

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.

Question 4

hotelling-lawley trace (T2)

Answer 4

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

Question 5

Identity matrix

Answer 5

a square matrix in which the diagonal elements are equal to 1, and the off diagonal elements are equal to 0

Question 6

matrix

Answer 6

collection of numbers arranged in columns and rows

values are typically referred to as components or elements

Question 7

multivariate

Answer 7

meaning Many Variables

MANOVA is used to look at several dependent variables simultaneously (this term)

Question 8

multivariate analysis of variance (MANOVA)

Answer 8

thought of as an ANOVA for situations in which there are several dependent variables

Question 9

Multivariate normality

Answer 9

an extension of a normal distribution to multiple variables

it is a probability distribution of a set of variables

Question 10

pillai-bartlett trace (V)

Answer 10

a test statistic in MANOVA

it is the sum of the proportion of explained variance on the discriminant function variates of the data

Question 11

Univariate

Answer 11

meaning one variable

ANOVA is used only in situations with only one dependent variable (this term)

Question 12

Wilks’s Lambda (L)

Answer 12

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