  We have investigated the relationship between the 2-10 keV X-ray variability
amplitude and black hole mass for a sample of 46 radio-quiet active galactic
nuclei observed by ASCA. Thirty-three of the objects in our sample exhibited
variability over a time-scale of ~40 ks, and we found a significant
anti-correlation between excess variance and mass. Unlike most previous
studies, we have quantified the variability using nearly the same time-scale
for all objects. Moreover, we provide a prescription for estimating the
uncertainties in excess variance which accounts both for measurement
uncertainties and for the stochastic nature of the variability. We also present
an analytical method to predict the excess variance from a model power spectrum
accounting for binning, sampling and windowing effects. Using this, we modelled
the variance-mass relation assuming all objects have a universal twice-broken
power spectrum, with the position of the breaks being dependent on mass. This
accounts for the general form of the relationship but there is considerable
scatter. We investigated this scatter as a function of the X-ray photon index,
luminosity and Eddington ratio. After accounting for the dependence of excess
variance on mass, we find no significant correlation with either luminosity or
X-ray spectral slope. We do find an anti-correlation between excess variance
and the Eddington ratio, although this relation might be an artifact owing to
the uncertainties in the mass measurements. It remains to be established that
enhanced X-ray variability is a property of objects with steep X-ray slopes or
large Eddington ratios.
