We investigate the properties of a variability-selected complete sample of AGN in order to identify the mechanisms which cause large amplitude X-ray variability on time scales of years. A complete sample of 24 sources was constructed, from AGN which changed their soft X-ray luminosity by more than one order of magnitude over 5--20 years between ROSAT observations and the XMM Slew Survey. Follow-up observations were obtained with the Swift satellite. After removal of two probable spurious sources, we find that the sample has global properties which differ little from a non-varying control sample drawn from the wider XMM-Slew/ROSAT/Veron sample of all secure AGN detections. A wide range of AGN types are represented in the varying sample. The black hole mass distributions for the varying and non-varying sample are not significantly different. This suggests that long timescale variability is not strongly affected by black hole mass. There is marginal evidence that the variable sources have a lower redshift (2$sigma$) and X-ray luminosity (1.7$sigma$). Apart from two radio-loud sources, the sample have normal optical-X-ray ratios ($alpha_{rm OX}$) when at their peak but are X-ray weak during their lowest flux measurements. Drawing on our results and other studies, we are able to identify a variety of variability mechanisms at play: tidal disruption events, jet activity, changes in absorption, thermal emission from the inner accretion disc, and variable accretion disc reflection. Little evidence for strong absorption is seen in the majority of the sample and single-component absorption can be excluded as the mechanism for most sources.
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