BenfordTests (version 1.2.0)

jpsq.benftest: Joenssen's JP-square Test for 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

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".

Value

• A list with class "code{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

Details

A statistical test is performed utilizing the sign-preserved squared correlation between signifd(x,digits) and pbenf(digits). Specifically: $$J_P^2=sgn\left(cor\left(f^o, f^e\right)\right)\cdot cor\left(f^o, f^e\right) ^2$$ where $f^o$ denotes the observed frequencies and $f^e$ denotes the expected frequency of digits $10^{k-1},10^{k-1}+1,\ldots,10^k-1$. 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.

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.

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