Previous research proposes that endorsement of anomalous beliefs is associated with proneness to conjunction error. This supposition ignores important differences between belief types. Correspondingly, the present study examined the degree to which components of statistical bias predicted conspiratorial ideation and belief in the paranormal. Confirmatory factor analysis and structural equation modelling revealed that conjunction error was associated with conspiratorial ideation, whilst perception of randomness most strongly predicted belief in the paranormal. These findings opposed the notion that anomalous beliefs, by virtue of possession of common characteristics, relate similarly to conjunction error. With regard to conspiracy, conjunction‐framing manipulations produced only minor variations in relationship strength. This supported the notion that conspiratorial ideation was associated with a domain‐general susceptibility to conjunction error. Framing, however, did influence the relationship between belief in the paranormal and conjunction; whilst paranormal conjunctions were generally easier to solve, performance declined as level of paranormal belief increased.Copyright © 2017 John Wiley & Sons, Ltd.