Our earlier work on non-singular effective polarizability and optical activity operators is generalized to remove the condition of well defined time reversal and Hermiticity characteristics of the optical activity operators. This enables depolarized right-angle incident (ICP) and scatteredcircularpolarization (SCP) and polarized right-angle incident (ILP) and scatteredlinearpolarization (SLP) Raman optical activity (ROA) observables to be formulated in terms of matrix elements of the absorptive and dispersive parts of these scattering operators. Stokes ICP and anti-Stokes SCP, and Stokes ILP and anti-Stokes SLP ROA observables are then shown quite generally to be related by thesameandoppositesign, respectively, for scattering from diamagnetic chiral molecules randomly oriented in an optically isotropic phase.