Box's M Test

Box's M test is a test of whether several groups share the same population covariance matrix, as assumed by MANOVA, Hotelling's T-squared and linear discriminant analysis.

Box M 검정은 여러 집단의 모집단 공분산행렬이 같은지를 검정하는 방법으로, MANOVA·Hotelling T²·선형판별분석의 가정을 확인할 때 쓴다.

How do I check the equal covariance matrix assumption before running MANOVA?

MANOVA 를 하기 전에 공분산행렬이 같다는 가정을 어떻게 확인하나요?

Box's M compares the log determinant of the pooled covariance matrix with those of the group covariance matrices and converts the result to an approximate chi-square statistic. Because it is very sensitive to non-normality and large samples, a significance level of .001 is usually used.

When to use Box's M Test

• You plan a MANOVA, Hotelling's T² or linear discriminant analysis.
• Groups are compared on two or more continuous variables.
• Each group has more observations than variables.

When to use something else

• The data are clearly non-normal; rely on Pillai's trace, which is robust to unequal covariances, rather than on this test.
• Only one outcome is involved; use Levene's test instead.

Assumptions and requirements

• Variables are multivariate normal within each group.
• Observations are independent.
• Each group has more observations than variables.

What the analysis reports

• M statistic
• Chi-square approximation with df and p-value
• Log determinant of each group covariance matrix

How to report it

Box's M test [indicated/did not indicate] a violation of homogeneity of covariance matrices, M = [value], χ²([df]) = [value], p = [value].

Related methods

• MANOVA
• Hotelling's T-squared Test
• Levene's Test

Run Box's M Test on Quorant