Do people fit to Benford’s law, or do they have a Benford bias?

AbstractSmith (2015) describes an explosion of interest in Benford’s law, that for data from many domains the first digits have a log distribution. Few studies have similarly asked whether the numbers people generate fit to Benford’s law, but recent data show a reasonable fit. This paper argues that testing for fit to Benford’s law is the wrong question for behavioural data, instead we should think in terms of a “Benford bias” in which the first-digit distribution is distorted towards Benford’s law. We propose calculating the effect size of this bias by testing a linear contrast weighted by Benford’s law. Analyses of existing data sets yielded effect sizes of 0.43-0.52. Applying this approach to a new task extended the scope of Benford bias to predicting outputs of a linear system and found an effect size of .40. Benford bias may be a ubiquitous influence on judgments and decisions based on numbers.

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