Tests the hypothesis that the selected SSCP matrix object is diagonal.
The test statistic is |R|N/2, the N/2-th power of the determinant of the correlation matrix. Bartlett (1954) developed the following approximation to the limiting distribution:
|χ2 = -(N - numberOfConstraints - (2p + 5) /6) ln |R||
In the formula's above, p is the dimension of the correlation matrix, N-numberOfConstraints 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 within-group sums of squares and cross-products of k independent groups, numberOfConstraints would equal k.
We return the probability α as
|α = chiSquareQ (χ2 , p(p-1)/2).|
A very low α indicates that it is very improbable that the matrix is diagonal.
© djmw, November 11, 2001