Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/Benford_tests.R

`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.

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

`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 |

`pvalsims` |
An integer specifying the number of replicates used if |

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.

A list with class "`htest`

" containing the following components:

`statistic ` |
the value of the |

`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 |

Dieter William Joenssen Dieter.Joenssen@googlemail.com

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.

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
``` |

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