We discuss methods to compute significance levels for the existence of quasi-periodic oscillations (QPOs) in active galactic nuclei (AGNs) that take the red-noise character of the X-ray light curves of these objects into account. Applying epoch folding and periodogram analysis to the XMM-Newton observation of the Seyfert galaxy Mrk 766, a possible QPO at a timescale of 4200 s has been reported. Our computation of the significance of this QPO, however, shows that the 4200 s peak is not significant at the 95% level. We conclude that the 4200 s feature is an artifact of the red-noise process and not the result of a physical process within the AGNs.