# jpsq.benftest: Joenssen's _JP-square_ Test for Benford's Law In BenfordTests: Statistical Tests for Evaluating Conformity to Benford's Law

## Description

jpsq.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 correlation between the first digits' distribution and Benford's distribution to assert if the data conforms to Benford's law.

## Usage

 1 jpsq.benftest(x = NULL, digits = 1, pvalmethod = "simulate", 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. Currently only "simulate" is available. pvalsims An integer specifying the number of replicates used if pvalmethod = "simulate".

## Details

A statistical test is performed utilizing the sign-preserved squared correlation between
signifd(x,digits) and pbenf(digits). Specifically:

J_P^2=sgn≤ft(cor≤ft(f^o, f^e\right)\right)\cdot cor≤ft(f^o, f^e\right) ^2

where f^o denotes the observed frequencies and f^e denotes the expected frequency of digits
10^{k-1},10^{k-1}+1,…,10^k-1. 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 J_P^2 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 Dieter.Joenssen@googlemail.com

## References

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

Joenssen, D.W. (2013) A New Test for Benford's Distribution. In: Abstract-Proceedings of the 3rd Joint Statistical Meeting DAGStat, March 18-22, 2013; Freiburg, Germany.

Joenssen, D.W. (2013) Two Digit Testing for Benford's Law. Proceedings of the ISI World Statistics Congress, 59th Session in Hong Kong. [available under http://www.statistics.gov.hk/wsc/CPS021-P2-S.pdf]

Shapiro, S.S. and Francia, R.S. (1972) An Approximate Analysis of Variance Test for Normality. Journal of the American Statistical Association. 67, 215–216.

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 Joenssen's \emph{JP-square} Test #on the sample's first digits using defaults jpsq.benftest(X) #p-value = 0.3241 

### Example output

	JP-Square Correlation Statistic Test for Benford Distribution

data:  X
J_stat_squ = 0.52721, p-value = 0.3241


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