
Tests the hypothesis that the selected SSCP matrix object is diagonal.
The test statistic is R^{N/2}, the N/2th power of the determinant of the correlation matrix. Bartlett (1954) developed the following approximation to the limiting distribution:
χ^{2} = (N  numberOfConstraints  (2p + 5) /6) ln R 
In the formula's above, p is the dimension of the correlation matrix, NnumberOfConstraints is the number of independent observations. Normally numberOfConstraints would equal 1, however, if the matrix has been computed in some other way, e.g., from withingroup sums of squares and crossproducts of k independent groups, numberOfConstraints would equal k.
We return the probability α as
α = chiSquareQ (χ^{2} , p(p1)/2). 
A very low α indicates that it is very improbable that the matrix is diagonal.
© djmw, November 11, 2001