jfa
is an R package for statistical audit sampling. The
package provides functions for planning, performing, evaluating, and
reporting an audit sample compliant with the International Standards on
Auditing. Specifically, these functions implement standard audit
sampling techniques for calculating sample sizes, selecting items from a
population, and evaluating misstatement from a data sample or from
summary statistics. Additionally, the jfa
package allows
the user to create a prior probability distribution to perform Bayesian
audit sampling using these functions.
The package and its intended workflow are also implemented with a graphical user interface in the Audit module of JASP, a free and open-source statistical software program.
For complete documentation of jfa
, visit the package website or download
the package
manual.
The most recently released version of jfa
can be
downloaded from CRAN by running the
following command in R:
install.packages('jfa')
Alternatively, you can download the development version from GitHub using:
::install_github('koenderks/jfa') devtools
After installation, the jfa
package can be loaded
with:
library(jfa)
The cheat sheet below can help you get started with the
jfa
package and its intended workflow. You can download a
pdf
version of the cheat sheet here.
Below you can find an explanation of the available functions in
jfa
sorted by their occurrence in the standard audit
sampling workflow. For detailed examples of how to use these functions,
visit the Get started
section on the package website.
auditPrior()
The auditPrior()
function is used to specify a prior
distribution for Bayesian audit sampling. The interface allows a
complete customization of the prior distribution as well as a formal
translation of pre-existing audit information into a prior distribution.
The function returns an object of class jfaPrior
which can
be used with associated summary()
and plot()
methods. Objects with class jfaPrior
can also be used as
input for the prior
argument in other functions. Moreover,
jfaPrior
objects have a corresponding
predict()
function to produce the predictions of the prior
distribution on the data level.
Full function with default arguments:
auditPrior(method = 'default', likelihood = c('poisson', 'binomial', 'hypergeometric'),
N.units = NULL, alpha = NULL, beta = NULL, materiality = NULL, expected = 0,
ir = NULL, cr = NULL, ub = NULL, p.hmin = NULL, x = NULL,
n = NULL, factor = NULL, conf.level = 0.95)
Supported options for the method
argument:
default
: Indifferent / noninformative prior
distribution.strict
: Improper prior distribution (matches classical
results).impartial
: Impartial prior distribution (Derks et al.,
2022).param
: Manually set the prior parameters.hyp
: Manually provide the prior probability for
tolerable misstatement (Derks et al., 2021).arm
: Manually provide the inherent risk and internal
control risk (Derks et al., 2021).bram
: Manually provide the upper bound of the prior
distribution (Touw & Hoogduin, 2011).sample
: Manually provide an equivalent prior sample
(Derks et al., 2021).factor
: Manually provide and weigh an equivalent prior
sample (Derks et al., 2021).Supported options for the likelihood
argument:
poisson
: Poisson likelihood and conjugate gamma prior
distribution (Stewart, 2013).binomial
: Binomial likelihood and conjugate beta prior
distribution (Steele, 1992).hypergeometric
: Hypergeometric likelihood and conjugate
beta-binomial prior distribution (Dyer & Pierce, 1991).Example usage:
# Default beta(1, 1) prior distribution
<- auditPrior(method = 'default', likelihood = 'binomial')
x
# Custom gamma(1, 10) prior distribution
<- auditPrior(method = 'param', likelihood = 'poisson', alpha = 1, beta = 10)
x
# Beta prior distribution incorporating inherent risk (70%) and control risk (50%)
<- auditPrior(method = 'arm', likelihood = 'binomial', materiality = 0.05, ir = 0.7, cr = 0.5)
x
summary(x) # Prints information about the prior distribution
predict(x, n = 20, cumulative = TRUE) # Predictions for a sample of n = 20
planning()
The planning()
function is used to calculate a minimum
sample size for audit samples. It allows specification of statistical
requirements for the sample with respect to the performance materiality
or the precision. The function returns an object of class
jfaPlanning
which can be used with associated
summary()
and plot()
methods. To perform
Bayesian planning, the input for the prior
argument can be
an object of class jfaPrior
as returned by the
auditPrior()
function, or an object of class
jfaPosterior
as returned by the evaluation()
function.
Full function with default arguments:
planning(materiality = NULL, min.precision = NULL, expected = 0,
likelihood = c('poisson', 'binomial', 'hypergeometric'),
conf.level = 0.95, N.units = NULL, by = 1, max = 5000,
prior = FALSE)
Supported options for the likelihood
argument:
poisson
: Poisson likelihood (Stewart, 2012).binomial
: Binomial likelihood (Stewart, 2012).hypergeometric
: Hypergeometric likelihood (Stewart,
2012).Example usage:
# Classical planning using the Poisson likelihood
<- planning(materiality = 0.03, likelihood = 'poisson')
x
# Bayesian planning using a default beta(1, 1) prior and binomial likelihood
<- planning(materiality = 0.03, likelihood = 'binomial', prior = TRUE)
x
# Bayesian planning using a custom beta(1, 10) prior and binomial likelihood
<- planning(materiality = 0.03,
x prior = auditPrior(method = 'param', likelihood = 'binomial', alpha = 1, beta = 10))
summary(x) # Prints information about the planning
selection()
The selection()
function is used to perform statistical
selection of audit samples. It offers flexible implementations of the
most common audit sampling algorithms for attributes sampling and
monetary unit sampling. The function returns an object of class
jfaSelection
which can be used with associated
summary()
and plot()
methods. The input for
the size
argument can be an object of class
jfaPlanning
as returned by the planning()
function.
Full function with default arguments:
selection(data, size, units = c('items', 'values'),
method = c('interval', 'cell', 'random', 'sieve'), values = NULL,
order = NULL, decreasing = FALSE, randomize = FALSE,
replace = FALSE, start = 1)
Supported options for the units
argument:
items
: Sampling units are items (rows) (Leslie,
Teitlebaum, & Anderson, 1979).values
: Sampling units are monetary units (Leslie,
Teitlebaum, & Anderson, 1979).Supported options for the method
argument:
interval
: Select a fixed unit from each interval.cell
: Select a random unit within each interval.random
: Select random units without an interval.sieve
: Select units using modified sieve sampling
(Hoogduin, Hall, & Tsay, 2010).Example usage:
# Selection using random record (attributes) sampling
<- selection(data = BuildIt, size = 100, units = 'items', method = 'random')
x
# Selection using fixed interval monetary unit sampling (using column 'bookValues' in BuildIt)
<- selection(data = BuildIt, size = 100, units = 'values',
x method = 'interval', values = 'bookValues')
summary(x) # Prints information about the selection
evaluation()
The evaluation()
function takes a sample or summary
statistics of the sample and performs evaluation according to the
specified method and sampling objectives. The function returns an object
of class jfaEvalution
which can be used with associated
summary()
and plot()
methods. To perform
Bayesian evaluation, the input for the prior
argument can
be an object of class jfaPrior
as returned by the
auditPrior()
function, or an object of class
jfaPosterior
as returned by the evaluation()
function.
Full function with default arguments:
evaluation(materiality = NULL, min.precision = NULL, method = 'poisson',
alternative = c('less', 'two.sided', 'greater'), conf.level = 0.95,
data = NULL, values = NULL, values.audit = NULL, times = NULL,
x = NULL, n = NULL, N.units = NULL, N.items = NULL,
r.delta = 2.7, m.type = 'accounts', cs.a = 1, cs.b = 3, cs.mu = 0.5,
prior = FALSE)
Supported options for the method
argument:
poisson
: Poisson likelihood (Stewart, 2012).binomial
: Binomial likelihood (Stewart, 2012).hypergeometric
: Hypergeometric likelihood (Stewart,
2012).stringer
: Stringer bound (Bickel, 1992).stringer.meikle
: Stringer bound with Meikle’s
correction (Meikle, 1972).stringer.lta
: Stringer bound with LTA correction
(Leslie, Teitlebaum, & Anderson, 1979).stringer.pvz
: Modified Stringer bound (Pap & van
Zuijlen, 1996).rohrbach
: Rohrbach’s augmented variance estimator
(Rohrbach, 1993).moment
: Modified moment bound (Dworin & Grimlund,
1984).coxsnell
: Cox and Snell bound (Cox & Snell,
1979).mpu
: Mean-per-unit estimator (Touw & Hoogduin,
2011).direct
: Direct estimator (Touw & Hoogduin,
2011).difference
: Difference estimator (Touw & Hoogduin,
2011).quotient
: Quotient (ratio) estimator (Touw &
Hoogduin, 2011).regression
: Regression estimator (Touw & Hoogduin,
2011).Example usage:
# Classical evaluation using the Poisson likelihood (and summary statistics)
<- evaluation(materiality = 0.03, x = 1, n = 100, method = 'poisson')
x
# Bayesian evaluation using a default minimal information prior (and summary statistics)
<- evaluation(materiality = 0.03, x = 1, n = 100, method = 'poisson', prior = TRUE)
x
# Bayesian evaluation using a custom beta(1, 10) prior (and summary statistics)
<- evaluation(materiality = 0.03, x = 1, n = 100,
x prior = auditPrior(method = 'param', likelihood = 'binomial', alpha = 1, beta = 10))
summary(x) # Prints information about the evaluation
report()
The report()
function takes an object of class
jfaEvaluation
as returned by the evaluation()
function and automatically creates a html
or
pdf
report containing the analysis results and their
interpretation.
Full function with default arguments:
report(object, file = 'report.html', format = c('html_document', 'pdf_document'))
Example usage:
# Generate an automatic report
report(object = x, file = 'myReport.html')
For an example report, see the following link.
To validate the statistical results, jfa
’s automated unit
tests regularly verify the main output from the package against the
following benchmarks:
Below you can find several informative tables that contain
statistical sample sizes, upper limits, one-sided p values, and
Bayes factors. These tables are created using the
planning()
and evaluation()
functions provided
in the package.
Sample sizes
Upper limits
One-sided p values
Bayes factors
jfa
is an open-source project that aims to be useful for
the audit community. Your help in benchmarking and extending
jfa
is therefore greatly appreciated. Contributing to
jfa
does not have to take much time or knowledge, and there
is extensive information available about it on the Wiki of this
repository.
If you are willing to contribute to the improvement of the package by adding a benchmark, please check out the Wiki page on how to contribute a benchmark to jfa. If you are willing to contribute to the improvement of the package by adding a new statistical method, please check the Wiki page on how to contribute a new method to jfa.