Box's ''M'' test is a multivariate statistical test used to check the equality of multiple
variance-covariance matrices.
The test is commonly used to test the assumption of
homogeneity
Homogeneity and heterogeneity are concepts relating to the Uniformity (chemistry), uniformity of a Chemical substance, substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, ...
of variances and covariances in
MANOVA
In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is often followed by significance tests ...
and
linear discriminant analysis
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to fi ...
. It is named after
George E. P. Box, who first discussed the test in 1949. The test uses a
chi-squared approximation.
Box's ''M'' test is susceptible to errors if the data does not meet model assumptions or if the sample size is too large or small.
Box's ''M'' test is especially prone to error if the data does not meet the assumption of
multivariate normality.
See also
*
Bartlett's test
*
Levene's test
In statistics, Levene's test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. This test is used because some common statistical procedures assume that variances of the population ...
References
Multivariate statistics
Statistical tests
{{statistics-stub