The performance of an optical system depends on the characteristics manufacturing errors of the mirrors, including aberrations on the primary mirror. When designing a system and evaluating its expected performance, the exact nature of the aberrations is not known beforehand, so approximations and simplifying assumptions need to be made. A common assumption is that aberrations of the primary mirror take the form of correlated Gaussian peaks and valleys about the ideal (perfectly spherical) primary mirror. The effect of such correlated Gaussian imperfections can be calculated in an average sense, using the optical quality factor (OQF) to modify the diffraction-limited modulation transfer function (MTF). Alternatively, a single instantiation of the aberrations can be added as phase variations to the pupil function, followed by calculation of the MTF. In this paper we compare these two methods of modeling the effects of correlated Gaussian aberrations on the MTF and point spread function (PSF). We explore the parameter space within which the OQF approximation is valid and the range of possible MTFs resulting from individual instantiations of the aberrations.