Other hypothesis used with the Mauchly's sphericity test is on the orthonormalized contrasts,
H0: C’SC = s^2I , where C is any full-rank (p-1) x p matrix of orthonormal contrasts.
A is the nonorthonormalized contrasts matrix.
C = GMO(A’) is a (p-1) × p column-orthonormal matrix (by the Gram-Schmidt orthonormalization procedure)
L = q^q|C’SC|/[tr(C’SC)]^q
LL = - (N – 1 – ((2q^2 + q + 2)/(6q)) ln L
= - (N – 1 – ((2q^2 + q + 2)/(6q)) [ln|C’SC| – q ln [tr(C’SC)/q]]
This statistic has an approximate Chi-square distribution with 0.5q(q + 1) – 1 = q(q + 1)/2 – 1 degrees of freedom.
Inputs:
X - multivariate data matrix.
alpha - significance level (default = 0.05).
Output:
Complete table results |
