Keywords
first digit law
discrete distribution
goodness of fit
simultaneous confidence intervals
How to Cite
Abstract
The purpose of this methodological article is to clearly present the Newcomb-Benford law, accompanied by an example, to enhance understanding among diverse areas of research in psychology unfamiliar with its use in other disciplines, including cognitive science. This law is primarily applied for detecting fraud in databases and tallying votes in popular elections. The article commences with a historical overview, presenting distributions from the first to the fourth significant digit, as well as the two-digit distribution. Statistical-mathematical explanations of the law are reviewed, followed by the presentation of six goodness-of-fit tests and the calculation of simultaneous confidence intervals to assess compliance with the law. Simulated data following two distributions, namely normal and lognormal, are employed. The former, common in psychology, doesn't conform to the law, while the latter facilitates transforming the normal distribution to adhere to it. Finally, conclusions are drawn, and suggestions are made to detect manipulation of normally distributed data.
References
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