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

View source: R/Benford_tests.R

`chisq.benftest`

takes any numerical vector reduces the sample to the specified number of significant digits and performs Pearson's chi-square goodness-of-fit test to assert if the data conforms to Benford's law.

1 | ```
chisq.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 to use if |

A *χ^2* goodness-of-fit test is performed on `signifd(x,digits)`

versus `pbenf(digits)`

.
Specifically:

*χ^2 = n\cdot\displaystyle∑_{i=10^{k-1}}^{10^k-1}\frac{≤ft(f_i^o - f_i^e\right)^2}{f_i^e}*

where *f_i^o* denotes the observed frequency of digits *i*, and *f_i^e* denotes the expected frequency of digits *i*.
`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.

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]

Pearson, K. (1900) On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that it can be Reasonably Supposed to have Arisen from Random Sampling. *Philosophical Magazine Series 5*. **50**, 157–175.

1 2 3 4 5 6 7 8 9 | ```
#Set the random seed to an arbitrary number
set.seed(421)
#Create a sample satisfying Benford's law
X<-rbenf(n=20)
#Perform a Chi-squared Test on the sample's
#first digits using defaults but determine
#the p-value by simulation
chisq.benftest(X,pvalmethod ="simulate")
#p-value = 0.6401
``` |

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