Covariance: Difference

You can choose this command after selecting two objects of type Covariance.

We test the hypothesis that the samples that gave rise to the two covariance matrices M1 and M2, have equal covariances. The test statistic is L′ which is distributed as a χ2 variate with p(p+1)/2 degrees of freedom.

L′ = L · (1 – (2p + 1 – 2 / (p + 1)) / (6 · ( N – 1))),

where,

L = (N – 1) · (ln determinant (M1) – ln determinant (M2)) + trace (M2 · M1–1) – p),

p is dimension of covariance matrix and N is the number of observations underlying the covariance matrix.

For more details on this test, see e.g. page 292 of Morrison (1990).