Do people fit to Benford’s law, or do they have a Benford bias?
- Bruce Burns, School of Psychology, The University of Sydney, Sydney, NSW, Australia
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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