People often detect structure and patterns in data that is random. This difficulty in accurately evaluating randomness manifests itself in mistaken beliefs that a fair coin has a bias towards heads or tails, detection of causal relationships between variables that randomly co-occur, or observation of illusory correlations between continuous variables. A computational analysis of an optimal reasoner’s performance on these three tasks suggests that this difficulty does not arise simply because people have an irrational disposition to see meaning in randomness, but because the underlying inference problem is intrinsically hard– for both statistical inference and human intuition. This analysis suggests that randomly produced data is inherently ambiguous, because data which is randomly produced can often also be produced by a systematic process. An experiment is reported which provides evidence that inferences about randomness are inherently difficult.
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