jfa is an R package for statistical audit sampling. The package
provides the user with five functions for planning, performing,
evaluating, and reporting an audit sample. Specifically, it contains
functions for calculating sample sizes, selecting the transactions
according to standard audit sampling techniques, and calculating various
upper limits for the misstatement from the sample or from summary
statistics. The jfa package also allows the user to create a prior
probability distribution to perform Bayesian audit sampling using these
functions.
For complete documentation of the package, see the package manual or visit the website.
- Koen Derks - Initial work - Website
See also the list of contributors who participated in this project.
This project is licensed under the open-source GPL-3 License.
The following instructions will get the jfa package up and running on
your local machine for use in R and RStudio.
- R - The programming language used for deploying the package.
The jfa package is simple to download and set-up. The most recent
version from CRAN (0.5.0) can
be downloaded by running the following command in R or RStudio:
install.packages("jfa")
Alternatively, you can download the most recent (development) version from GitHub using:
devtools::install.github("koenderks/jfa")
The jfa package can then be loaded in R or RStudio by typing:
library(jfa)
The package vignettes show how to use the jfa package using simple
examples.
- Get started
- The audit sampling workflow
- Constructing a prior distribution
- Estimating the misstatement
- Testing the misstatement
To validate the output, jfa’s results are currently being verified
against the following benchmark(s):
- Audit Sampling: Audit Guide (Appendix A and Appendix C)
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.
The cheatsheet can help you get started with the jfa package and its
workflow. You can download a pdf version
here.
Below you can find a list of the functions in the current version of
jfa sorted by their occurrence in the standard audit sampling
workflow.
The auditPrior() function creates a prior distribution according to
one of several methods, including the audit risk model and assessments
of the inherent and control risk. The returned object is of class
jfaPrior and can be used with associated print() and plot()
methods. jfaPrior results can also be used as input argument for the
prior argument in other functions.
Full function with default arguments:
auditPrior(confidence = 0.95, likelihood = "binomial", method = "none", expectedError = 0, N = NULL, materiality = NULL, ir = 1, cr = 1, pHmin = NULL, pHplus = NULL, factor = 1, sampleN = 0, sampleK = 0)
Supported options for the likelihood argument:
likelihood |
Reference | Description |
|---|---|---|
binomial |
Steele (1992) | Beta prior distribution (+ binomial likelihood) |
poisson |
Stewart (2013) | Gamma prior distribution (+ Poisson likelihood) |
hypergeometric |
Dyer and Pierce (1991) | Beta-binomial prior distribution (+ hypergeometric likelihood) |
Supported options for the method argument:
method |
Reference | Description | Additional arguments |
|---|---|---|---|
none |
Derks et al. (2020) | No prior information | |
arm |
Derks et al. (2020) | Inherent risk and internal control risk (ARM) | ir and cr |
median |
Derks et al. (2020) | Equal prior probabilities for hypotheses | |
hypotheses |
Derks et al. (2020) | Custom prior probabilities for hypotheses | pHmin or pHplus |
sample |
Derks et al. (2020) | Earlier sample | sampleN and sampleK |
factor |
Derks et al. (2020) | Weighted earlier sample | factor, sampleN and sampleK |
The planning() function calculates the required sample size for a
statistical audit sample, based on the Poisson, binomial, or
hypergeometric likelihood. A prior can be specified to combine with the
specified likelihood in order to perform Bayesian planning. The returned
jfaPlanning object has a print() and a plot() method. In the
planning() function, the prior argument can be an object of class
jfaPrior as returned by the auditPrior() function.
Full function with default arguments:
planning(confidence = 0.95, expectedError = 0, likelihood = "poisson", N = NULL, materiality = NULL, minPrecision = NULL, prior = FALSE, kPrior = 0, nPrior = 0, increase = 1, maxSize = 5000)
Supported options for the likelihood argument:
likelihood |
Reference | Description |
|---|---|---|
binomial |
Stewart (2012) | Binomial likelihood |
poisson |
Stewart (2012) | Poisson likelihood |
hypergeometric |
Stewart (2012) | Hypergeometric likelihood |
The selection() function takes a data frame and performs sampling
according to one of three algorithms: random sampling, cell sampling, or
fixed interval sampling in combination with either record sampling or
monetary unit sampling. The returned jfaSelection object has a
print() and a plot() method. In the selection() function, the
sampleSize argument can be an object of class jfaPlanning as
returned by the planning() function.
Full function with default arguments:
selection(population, sampleSize, units = "records", algorithm = "random", bookValues = NULL, intervalStartingPoint = 1, ordered = TRUE, ascending = TRUE, withReplacement = FALSE, seed = 1)
Supported options for the units argument:
units |
Reference | Description | Additional arguments |
|---|---|---|---|
records |
Leslie, Teitlebaum, and Anderson (1979) | Sampling units are transactions | |
mus |
Leslie, Teitlebaum, and Anderson (1979) | Sampling units are monetary units | bookValues |
Supported options for the algorithm argument:
algorithm |
Reference | Description | Additional arguments |
|---|---|---|---|
random |
Random sampling | ||
cell |
Cell sampling | ||
interval |
Systematic sampling / Fixed interval sampling | intervalStartingPoint |
The evaluation() function takes a sample data frame or summary
statistics about an evaluated audit sample and calculates a confidence
bound according to a specified method. The returned jfaEvalution
object has a print() and plot() method. In the evaluation()
function, the prior argument can be an object of class jfaPrior as
returned by the auditPrior() function.
Full function with default arguments:
evaluation(confidence = 0.95, method = "binomial", N = NULL, sample = NULL, bookValues = NULL, auditValues = NULL, counts = NULL, nSumstats = NULL, kSumstats = NULL, materiality = NULL, minPrecision = NULL, prior = FALSE, nPrior = 0, kPrior = 0, rohrbachDelta = 2.7, momentPoptype = "accounts", populationBookValue = NULL, csA = 1, csB = 3, csMu = 0.5)
Supported options for the method argument:
method |
Reference | Description | Additional arguments |
|---|---|---|---|
binomial |
Stewart (2012) | Binomial likelihood | |
poisson |
Stewart (2012) | Poisson likelihood | |
hypergeometric |
Stewart (2012) | Hypergeometric likelihood | |
stringer |
Bickel (1992) | Classical Stringer bound | |
stringer-meikle |
Meikle (1972) | Stringer bound with Meikle’s correction | |
stringer-lta |
Leslie, Teitlebaum, & Anderson (1979) | Stringer bound with LTA correction | |
stringer-pvz |
Pap and van Zuijlen (1996) | Modified Stringer bound | |
rohrbach |
Rohrbach (1993) | Rohrbach’s augmented variance estimator | rohrbachDelta |
moment |
Dworin and Grimlund (1984) | Modified moment bound | momentPoptype |
coxsnell |
Cox and Snell (1979) | Cox and Snell bound | csA, csB, and csMu |
direct |
Touw and Hoogduin (2011) | Direct estimator | populationBookValue |
difference |
Touw and Hoogduin (2011) | Difference estimator | populationBookValue |
quotient |
Touw and Hoogduin (2011) | Quotient estimator | populationBookValue |
regression |
Touw and Hoogduin (2011) | Regression estimator | populationBookValue |
The report() function takes an object of class jfaEvaluation as
returned by the evaluation() function, automatically generates a
html or pdf report containing the analysis results and their
interpretation, and saves the report to your local computer.
Full function with default arguments:
report(object = NULL, file = NULL, format = "html_document")
For an example report, see the following link.
- Bickel, P. J. (1992). Inference and auditing: The Stringer bound. International Statistical Review, 60(2), 197–209. - View online
- Cox, D. R., & Snell, E. J. (1979). On sampling and the estimation of rare errors. Biometrika, 66(1), 125-132. - View online
- Derks, K. (2020). jfa: Bayesian and classical audit sampling. R package version 0.5.0. - View online
- Derks, K., de Swart, J., van Batenburg, P., Wagenmakers, E.-J., & Wetzels, R. (2020). Priors in a Bayesian audit: How integration of existing information into the prior distribution can improve audit transparency and efficiency. Under review. - View online
- Dworin, L. D. and Grimlund, R. A. (1984). Dollar-unit sampling for accounts receivable and inventory. The Accounting Review, 59(2), 218–241. - View online
- Dyer, D., & Pierce, R. L. (1993). On the choice of the prior distribution in hypergeometric sampling. Communications in Statistics - Theory and Methods, 22(8), 2125-2146. - View online
- Meikle, G. R. (1972). Statistical Sampling in an Audit Context. Canadian Institute of Chartered Accountants.
- Leslie, D. A., Teitlebaum, A. D., & Anderson, R. J. (1979). Dollar-unit sampling: A practical guide for auditors. London: Pitman.
- Pap, G., & van Zuijlen, M. C. (1996). On the asymptotic behaviour of the Stringer bound. Statistica Neerlandica, 50(3), 367-389. - View online
- Rohrbach, K. J. (1993). Variance augmentation to achieve nominal coverage probability in sampling from audit populations. Auditing: A Journal of Practice & Theory, 12(2), 79-97.
- Steele, A. (1992). Audit risk and audit evidence: The Bayesian approach to statistical auditing. San Diego: Academic Press.
- Stewart, T. R. (2012). Technical notes on the AICPA audit guide audit sampling. American Institute of Certified Public Accountants, New York. - View online
- Stewart, T. R. (2013). A Bayesian audit assurance model with application to the component materiality problem in group audits. VU University, Amsterdam. - View online
- Touw, P., and Hoogduin, L. (2011). Statistiek voor audit en controlling. Boom uitgevers, Amsterdam.
