The symmetry test is a test for symmetry about the diagonal of a square contingency table. It is used to test for changes in assessment, and is done with a chi-square test.
If the chi-square test is significant we conclude that at least one cross-diagonal pair is different from the first to the second assessment.
ncg = Frequency in the (c, g) cell
Chi-square has C(C-1)/2 degrees of freedom