Studies exploring relationships between belief in the paranormal and vulnerability to cognitive bias suggest that believers are liable to misperception of chance and conjunction fallacy. Research investigating misperception of chance has produced consistent findings, whilst work on conjunction fallacy is less compelling. Evidence indicates also that framing biases within a paranormal context can increase believers' susceptibility. The present study, using confirmatory factor analysis and structural equation modelling, examined the contribution of each bias to belief in the paranormal and assessed the merits of previous research. Alongside, the Revised Paranormal Belief Scale, participants completed standard and paranormal framed perception of randomness and conjunction problems. Perception of randomness was more strongly associated with belief in the paranormal than conjunction fallacy. Inherent methodological issues limited the usefulness of framing manipulations; presenting problems within a paranormal context weakened their predictive power.Copyright © 2016 John Wiley & Sons, Ltd.