Title:	Tests for Detecting Irregular Digit Patterns
Version:	0.1.2
Date:	2022-06-16
Description:	Provides statistical tests and support functions for detecting irregular digit patterns in numerical data. The package includes tools for extracting digits at various locations in a number, tests for repeated values, and (Bayesian) tests of digit distributions.
BugReports:	https://github.com/koenderks/digitTests/issues
URL:	https://koenderks.github.io/digitTests/, https://github.com/koenderks/digitTests
Imports:	graphics, stats
Suggests:	benford.analysis, BenfordTests, BeyondBenford, knitr, rmarkdown, testthat
Language:	en-US
License:	GPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.0
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2022-06-16 14:38:22 UTC; derksk
Author:	Koen Derks [aut, cre]
Maintainer:	Koen Derks <k.derks@nyenrode.nl>
Repository:	CRAN
Date/Publication:	2022-06-16 16:10:12 UTC

digitTests: Tests for Detecting Irregular Data Patterns

Description

digitTests is an R package providing tests for detecting irregular data patterns.

The package and its analyses are also implemented with a graphical user interface in the Audit module of JASP, a free and open-source statistical software program.

Author(s)

Please use the citation provided by R when citing this package. A BibTex entry is available from citation("digitTests").

See Also

Useful links:

• The issue page to submit a bug report or feature request.

Examples

# Load the digitTests package
library(digitTests)

############################################
### Example 1: Benford's Law ####
############################################

data('sinoForest')
distr.test(sinoForest$value, check = 'first', reference = 'benford')

###################################
### Example 2: Repeated Values ####
###################################

data('sanitizer')
rv.test(sanitizer$value, check = 'lasttwo', method = 'af', B = 1000)

Bayesian Test of Digits against a Reference Distribution

Description

This function extracts and performs a Bayesian test of the distribution of (leading) digits in a vector against a reference distribution. By default, the distribution of leading digits is checked against Benford's law.

Usage

distr.btest(x, check = 'first', reference = 'benford', 
            alpha = NULL, BF10 = TRUE, log = FALSE)

Arguments

Details

Benford's law is defined as p(d) = log10(1/d). The uniform distribution is defined as p(d) = 1/d.

The Bayes Factor BF_{10} quantifies how much more likely the data are to be observed under H_{1}: the digits are not distributed according to the reference distribution than under H_{0}: the digits are distributed according to the reference distribution. Therefore, BF_{10} can be interpreted as the relative support in the observed data for H_{1} versus H_{0}. If BF_{10} is 1, there is no preference for either H_{1} or H_{0}. If BF_{10} is larger than 1, H_{1} is preferred. If BF_{10} is between 0 and 1, H_{0} is preferred. The Bayes factor is calculated using the Savage-Dickey density ratio.

Value

An object of class dt.distr containing:

Author(s)

Koen Derks, k.derks@nyenrode.nl

References

Benford, F. (1938). The law of anomalous numbers. In Proceedings of the American Philosophical Society, 551-572.

See Also

distr.test rv.test

Examples

set.seed(1)
x <- rnorm(100)

# Bayesian digit analysis against Benford's law
distr.btest(x, check = 'first', reference = 'benford')

# Bayesian digit analysis against Benford's law, custom prior
distr.btest(x, check = 'first', reference = 'benford', alpha = 9:1)

# Bayesian digit analysis against custom distribution
distr.btest(x, check = 'last', reference = rep(1/9, 9))

Test of Digits against a Reference Distribution

Description

This function extracts and performs a test of the distribution of (leading) digits in a vector against a reference distribution. By default, the distribution of leading digits is checked against Benford's law.

Usage

distr.test(x, check = 'first', reference = 'benford')

Arguments

Details

Benford's law is defined as p(d) = log10(1/d). The uniform distribution is defined as p(d) = 1/d.

Value

An object of class dt.distr containing:

Author(s)

Koen Derks, k.derks@nyenrode.nl

References

Benford, F. (1938). The law of anomalous numbers. In Proceedings of the American Philosophical Society, 551-572.

See Also

distr.btest rv.test

Examples

set.seed(1)
x <- rnorm(100)

# Digit analysis against Benford's law
distr.test(x, check = 'first', reference = 'benford')

# Digit analysis against custom distribution
distr.test(x, check = 'last', reference = rep(1/9, 9))

Methods for da objects

Description

Methods defined for objects returned from the distr.test, distr.btest, and rv.test functions.

Usage

## S3 method for class 'dt.distr'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'dt.rv'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'dt.distr'
plot(x, ...)

## S3 method for class 'dt.rv'
plot(x, ...)

Arguments

Value

The print methods simply print and return nothing.

Extraction of First or Last Digits

Description

This function extracts the first (and optionally second) or last digits in a vector.

Usage

extract_digits(x, check = 'first', include.zero = FALSE)

Arguments

Value

A vector of first (and optionally second) or last digits.

Author(s)

Koen Derks, k.derks@nyenrode.nl

Examples

set.seed(1)
x <- rnorm(100)

# Extract first digits (without zero)
extract_digits(x, check = 'first')

# Extract last digits (including zero)
extract_digits(x, check = 'last', include.zero = TRUE)

Test of Repeated Values

Description

This function analyzes the frequency with which values get repeated within a set of numbers. Unlike Benford's law, and its generalizations, this approach examines the entire number at once, not only the first or last digit.

Usage

rv.test(x, check = 'last', method = 'af', B = 2000)

Arguments

Details

To determine whether the data show an excessive amount of bunching, the null hypothesis that x does not contain an unexpected amount of repeated values is tested against the alternative hypothesis that x has more repeated values than expected. The statistic can either be the average frequency (AF = sum(f_i^2)/sum(f_i)) of the data or the entropy (E = - sum(p_i * log(p_i)), with p_i=f_i/n) of the data. Average frequency and entropy are highly correlated, but the average frequency is often more interpretable. For example, an average frequency of 2.5 means that, on average, your observations contain a value that appears 2.5 times in the data set.To quantify what is expected, this test requires the assumption that the integer portions of the numbers are not associated with their decimal portions.

Value

An object of class dt.rv containing:

Author(s)

Koen Derks, k.derks@nyenrode.nl

References

Simohnsohn, U. (2019, May 25). Number-Bunching: A New Tool for Forensic Data Analysis. Retrieved from https://datacolada.org/77.

See Also

distr.test distr.btest

Examples

 
set.seed(1)
x <- rnorm(50)

# Repeated values analysis shuffling last digit
rv.test(x, check = 'last', method = 'af', B = 2000)

Factory Workers' use of Hand Sanitizer

Description

Data from a study on factory workers' use of hand sanitizer. Sanitizer use was measured to a 100th of a gram.

Usage

data(sanitizer)

Format

A data frame with 1600 rows and 1 variable.

References

[Retracted] Li, M., Sun, Y., & Chen, H. (2019). The decoy effect as a nudge: Boosting hand hygiene with a worse option. Psychological Science, 30, 139–149.

Examples

data(sanitizer)

Financial Statemens of Sino Forest Corporation's 2010 Report

Description

Financial Statemens numbers of Sino Forest Corporation's 2010 Report.

Usage

data(sinoForest)

Format

A data frame with 772 rows and 1 variable.

References

Nigrini, M. J. (2012). Benford's Law: Application for Forensic Accounting, Auditing and Fraud Detection. Wiley and Sons: New Jersey.

Examples

data(sinoForest)