meandigit.benftest {BenfordTests}

Judge-Schechter Mean Deviation Test for Benford's Law

Description

meandigit.benftest 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

meandigit.benftest(x = NULL, digits = 1, pvalmethod = "asymptotic", pvalsims = 10000)

Arguments

x

A numeric vector.

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. Either "asymptotic" or "simulate".

pvalsims

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

Details

A statistical test is performed utilizing the deviation between the mean digit of signifd(x,digits) and pbenf(digits). Specifically:

a^*=\frac{|\mu_k^o-\mu_k^e|}{\left(9\cdot10^{k-1}\right)-\mu_k^e}

where \mu_k^o is the observed mean of the chosen k number of digits, and \mu_k^e is the expected/true mean value for Benford's predictions. a^* conforms asymptotically to a truncated normal distribution under the null-hypothesis, i.e.,

a^*\sim truncnorm\left(\mu=0,\sigma=\sigma_B,a=0,b=\infty\right)

x is a numeric vector of arbitrary length. Values of x should be continuous, as dictated by theory, but may also be integers. digits should be chosen so that signifd(x,digits) is not influenced by previous rounding.

Value

A list with class "htest" containing the following components:

statistic

the value of the a^* test statistic

p.value

the p-value for the test

method

a character string indicating the type of test performed

data.name

a character string giving the name of the data

Author(s)

Dieter William Joenssen [e-mail]

References

Benford, F. (1938) The Law of Anomalous Numbers. Proceedings of the American Philosophical Society. 78, 551–572.

Judge, G. and Schechter, L. (2009) Detecting Problems in Survey Data using Benford's Law. Journal of Human Resources. 44, 1–24.

See Also

pbenf, simulateH0

Examples

#Set the random seed to an arbitrary number
set.seed(421)
#Create a sample satisfying Benford's law
X<-rbenf(n=20)
#Perform a Judge-Schechter Mean Deviation Test
#on the sample's first digits using defaults
meandigit.benftest(X)
#p-value = 0.1458