# meandigit.benftest: Judge-Schechter Mean Deviation Test for Benford's Law In BenfordTests: Statistical Tests for Evaluating Conformity to 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

 1 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{|μ_k^o-μ_k^e|}{≤ft(9\cdot10^{k-1}\right)-μ_k^e}

where μ_k^o is the observed mean of the chosen k number of digits, and μ_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≤ft(μ=0,σ=σ_B,a=0,b=∞\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

## 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.

pbenf, simulateH0

## Examples

 1 2 3 4 5 6 7 8 #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 

### Example output

	Judge-Schechter Normed Deviation Test for Benford Distribution

data:  X
a_star = 0.0072372, p-value = 0.9417


BenfordTests documentation built on May 1, 2019, 8:07 p.m.