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:
devtools::install_github('koenderks/jfa')
After installation, the jfa
package can be loaded with:
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()
function
The auditPrior()
function creates a prior probability distribution according to one of several methods, including a translation of the assessments of the inherent risk and control risk from the audit risk model. 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
object 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
: Noninformative prior distribution based on minimal information.strict
: Strict prior distribution (with classical properties).param
: Manual prior parameters.impartial
: Equal prior probabilities for (in)tolerable misstatement (Derks et al., 2021).hyp
: Manual prior probability for tolerable misstatement (Derks et al., 2021).arm
: Assessments of inherent risk and internal control risk (Derks et al., 2021).bram
: x-% upper bound for the prior distribution (Touw & Hoogduin, 2011).sample
: Information from an earlier sample (Derks et al., 2021).factor
: Weigh information from an earlier 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:
# A gamma prior distribution based on minimal information
x <- auditPrior(method = 'default', likelihood = 'poisson')
# A custom beta(1, 10) prior distribution
x <- auditPrior(method = 'param', likelihood = 'binomial', alpha = 1, beta = 10)
# A beta prior distribution which incorporates inherent risk (70%) and control risk (50%)
x <- auditPrior(method = 'arm', likelihood = 'binomial', materiality = 0.05, ir = 0.7, cr = 0.5)
summary(x) # Prints information about the prior distribution
predict(x, n = 20, cumulative = TRUE) # Predictions for a sample of n = 20
planning()
function
The planning()
function calculates the minimum sample size for a statistical audit sample based on the Poisson, binomial, or hypergeometric likelihood. 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
x <- planning(materiality = 0.03, likelihood = 'poisson')
# Bayesian planning using a default minimal information prior
x <- planning(materiality = 0.03, likelihood = 'poisson', prior = TRUE)
# Bayesian planning using a custom beta(1, 10) prior
x <- planning(materiality = 0.03,
prior = auditPrior(method = 'param', likelihood = 'binomial', alpha = 1, beta = 10))
summary(x) # Prints information about the planning
selection()
function
The selection()
function takes a data frame and performs statistical sampling according to one of three algorithms: fixed interval sampling, cell sampling, or random sampling in combination with either record (attributes) sampling or monetary unit sampling (MUS). 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 sampling unit from each interval.cell
: Select a random sampling unit from each interval.random
: Select random sampling units.sieve
: Select units using modified sieve sampling (Hoogduin, Hall, & Tsay, 2010).Example usage:
# Selection using random record (attributes) sampling
x <- selection(data = BuildIt, size = 100, units = 'items', method = 'random')
# Selection using fixed interval monetary unit sampling (using column 'bookValues' in BuildIt)
x <- selection(data = BuildIt, size = 100, units = 'values', method = 'interval', values = 'bookValues')
summary(x) # Prints information about the selection
evaluation()
function
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 (Dworing & 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)
x <- evaluation(materiality = 0.03, x = 1, n = 100, method = 'poisson')
# Bayesian evaluation using a default minimal information prior (and summary statistics)
x <- evaluation(materiality = 0.03, x = 1, n = 100, method = 'poisson', prior = TRUE)
# Bayesian evaluation using a custom beta(1, 10) prior (and summary statistics)
x <- evaluation(materiality = 0.03, x = 1, n = 100,
prior = auditPrior(method = 'param', likelihood = 'binomial', alpha = 1, beta = 10))
summary(x) # Prints information about the evaluation
report()
function
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:
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.