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 of variances and covariances in
MANOVA and
linear discriminant analysis
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features ...
. It is named after
George E. P. Box
George Edward Pelham Box (18 October 1919 – 28 March 2013) was a British statistician, who worked in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference. He has been called "one of the gre ...
, 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
References
Multivariate statistics
Statistical hypothesis testing
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