We examine the variability of peak horizontal and vertical accelerations of the large California strong-motion data set for the time period 1957 to 1991 and find a statistically significant dependence of the standard error on earthquake magnitude. Specifically, the standard error decreases with increasing magnitude. The analysis was conducted using a rigorous methodology that examines both earthquake to earthquake (inter-event) variability and within earthquake (intra-event) variability. The magnitude dependence is stronger for inter-event variability than intra-event variability, and stronger for horizontal peak acceleration than for vertical peak acceleration. The data from the recent Landers, Big Bear, and Northridge earthquakes are consistent with these results.