BenfordTests (version 0.5)

J_S_avg_dev_benford: Judge-Schechter Mean Deviation for Benford's Law

Description

J_S_avg_dev_benford takes any numerical vector reduces the sample to the specified number of significant digits and performs a goodness-of-fit test based on the deviation in means of the first digits' distribution and Benford's distribution to assert if the data conforms to Benford's law.

Usage

J_S_avg_dev_benford(x = NULL, first_digits = 1, pvalmethod = "simulate", pvalsims = 10000)

Arguments

x

A numeric vector.

first_digits

An integer determining the number of first digits to use for testing, i.e. 1 for only the first, 2 for the first two etc.

pvalmethod

Method used for calculating the p-value. Currently only "simulate" is available.

pvalsims

An integer specifying the number of replicates used if pvalmethod = "simulate".

Value

• A list with class "code{htest}" containing the following components:
• statistic
  the value of the a-star test statistic
• p.value
  the p-value for the test
• method
  a character string indicating the type of test performed

Details

A statistical test is performed utilizing the deviation beteen the mean digit of leading_digits(x,first_digits) and pbenf(first_digits). The resulting statistic is normalized to [0,1]. x is a numeric vector of arbitrary length. Values of x should be continuous, as dictated by theory, but may also be integers. first_digits should be chosen so that leading_digits(x,first_digits) is not influenced by previous rounding.

References

Benford F. The law of anomalous numbers. Proceedings of the American Philosophical Society. 1938;78:551-572. Judge G, Schechter L. Detecting problems in survey data using Benford's law. Journal of Human Resources. 2009;44:1-24.

See Also

pbenf