If one wishes to test if the correlations in a correlation matrix are statistically significant as a whole group, one can perform a likelihood ratio test of the hypothesis that the correlation matrix is equal to the identity matrix.
The ratio of the restricted and unrestricted likelihood functions is $\alpha = |R|^{N/2}$ , where |R| is the determinant of the correlation matrix (Morrison, 1967).
The test statistic is therefore $-2\log(\alpha)$, which is distributed as $\chi^2$ with $\frac{1}{2}p(p-1)$ df.
My question is, how do you perform the calculation of the observed value $-2\log( \alpha)$?
Best Answer
Do you mean something like this?:
in R:
Or in Excel: Where the matrix is in cells C26:E28, and N is 100:
And the above is in cell D31:
You can also use the sem package:
(sem gives a very slightly different answer, because it multiplies by N-1).