evaluation {jfa} | R Documentation |
evaluation()
is used to perform statistical inference about the misstatement in an audit population. It allows specification of statistical requirements for the sample with respect to the performance materiality or the precision. evaluation()
returns an object of class jfaEvaluation
which can be used with associated summary()
and plot()
methods.
For more details on how to use this function, see the package vignette:
vignette('jfa', package = 'jfa')
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)
materiality |
a numeric value between 0 and 1 specifying the performance materiality (i.e., the maximum tolerable misstatement) as a fraction of the total number of units in the population. Can be |
min.precision |
a numeric value between 0 and 1 specifying the minimum precision (i.e., upper bound minus most likely error) as a fraction of the total population size. Can be |
method |
a character specifying the inference method. Possible options are |
alternative |
a character indicating the alternative hypothesis and the type of confidence / credible interval. Possible options are |
conf.level |
a numeric value between 0 and 1 specifying the confidence level. |
data |
a data frame containing a data sample. |
values |
a character specifying name of a column in |
values.audit |
a character specifying name of a column in |
times |
a character specifying name of a column in |
x |
a numeric value larger than 0 specifying the sum of (proportional) misstatements in the sample. If specified, overrides the |
n |
an integer larger than 0 specifying the number of items in the sample. If specified, overrides the |
N.units |
an integer larger than 0 specifying the number of units in the population. Only used for methods |
N.items |
an integer larger than 0 specifying the number of items in the population. Only used for methods |
r.delta |
a numeric value specifying |
m.type |
a character specifying the type of population (Dworin and Grimlund, 1984). Possible options are |
cs.a |
a numeric value specifying the |
cs.b |
a numeric value specifying the |
cs.mu |
a numeric value between 0 and 1 specifying the mean of the prior distribution on the mean taint. Only used for method |
prior |
a logical specifying whether to use a prior distribution, or an object of class |
This section lists the available options for the methods
argument.
poisson
: Evaluates the sample with the Poisson distribution. If combined with prior = TRUE
, performs Bayesian evaluation using a gamma prior and posterior.
binomial
: Evaluates the sample with the binomial distribution. If combined with prior = TRUE
, performs Bayesian evaluation using a beta prior and posterior.
hypergeometric
: Evaluates the sample with the hypergeometric distribution. If combined with prior = TRUE
, performs Bayesian evaluation using a beta-binomial prior and posterior.
mpu
: Evaluates the sample with the mean-per-unit estimator.
stringer
: Evaluates the sample with the Stringer bound (Stringer, 1963).
stringer.meikle
: Evaluates the sample with the Stringer bound with Meikle's correction for understatements (Meikle, 1972).
stringer.lta
: Evaluates the sample with the Stringer bound with LTA correction for understatements (Leslie, Teitlebaum, and Anderson, 1979).
stringer.pvz
: Evaluates the sample with the Stringer bound with Pap and van Zuijlen's correction for understatements (Pap and van Zuijlen, 1996).
rohrbach
: Evaluates the sample with Rohrbach's augmented variance bound (Rohrbach, 1993).
moment
: Evaluates the sample with the modified moment bound (Dworin and Grimlund, 1984).
coxsnell
: Evaluates the sample with the Cox and Snell bound (Cox and Snell, 1979).
direct
: Evaluates the sample with the direct estimator (Touw and Hoogduin, 2011).
difference
: Evaluates the sample with the difference estimator (Touw and Hoogduin, 2011).
quotient
: Evaluates the sample with the quotient estimator (Touw and Hoogduin, 2011).
regression
: Evaluates the sample with the regression estimator (Touw and Hoogduin, 2011).
An object of class jfaEvaluation
containing:
conf.level |
a numeric value between 0 and 1 giving the confidence level. |
mle |
a numeric value between 0 and 1 giving the most likely error in the population. |
ub |
a numeric value between 0 and 1 giving the upper bound for the population misstatement. |
lb |
a numeric value between 0 and 1 giving the lower bound for the population misstatement. |
precision |
a numeric value between 0 and 1 giving the difference between the most likely error and the upper bound. |
p.value |
for classical tests, a numeric value giving the one-sided p-value. |
x |
an integer larger than, or equal to, 0 giving the number of sample errors. |
t |
a value larger than, or equal to, 0, giving the sum of proportional sample errors. |
n |
an integer larger than 0 giving the sample size. |
materiality |
if |
min.precision |
if |
alternative |
a character indicating the alternative hypothesis. |
method |
a character indicating the inference method. |
N.units |
if |
N.items |
if |
K |
if |
prior |
an object of class 'jfaPrior' that contains the prior distribution. |
posterior |
an object of class 'jfaPosterior' that contains the posterior distribution. |
data |
a data frame containing the relevant columns from the |
data.name |
a character giving the name of the data. |
Koen Derks, k.derks@nyenrode.nl
Cox, D. and Snell, E. (1979). On sampling and the estimation of rare errors. Biometrika, 66(1), 125-132.
Derks, K., de Swart, J., van Batenburg, P., Wagenmakers, E.-J., & Wetzels, R. (2021). Priors in a Bayesian audit: How integration of existing information into the prior distribution can improve audit transparency and efficiency. International Journal of Auditing, 25(3), 621-636.
Dworin, L. D. and Grimlund, R. A. (1984). Dollar-unit sampling for accounts receivable and inventory. The Accounting Review, 59(2), 218–241
Leslie, D. A., Teitlebaum, A. D., & Anderson, R. J. (1979). Dollar-unit Sampling: A Practical Guide for Auditors. Copp Clark Pitman; Belmont, Calif.: distributed by Fearon-Pitman.
Meikle, G. R. (1972). Statistical Sampling in an Audit Context: An Audit Technique. Canadian Institute of Chartered Accountants.
Pap, G., and van Zuijlen, M. C. (1996). On the asymptotic behavior of the Stringer bound. Statistica Neerlandica, 50(3), 367-389.
Rohrbach, K. J. (1993). Variance augmentation to achieve nominal coverage probability in sampling from audit populations. Auditing, 12(2), 79.
Stringer, K. W. (1963). Practical aspects of statistical sampling in auditing. In Proceedings of the Business and Economic Statistics Section (pp. 405-411). American Statistical Association.
Touw, P., and Hoogduin, L. (2011). Statistiek voor Audit en Controlling. Boom uitgevers Amsterdam.
auditPrior
planning
selection
report
data("BuildIt")
# Draw a sample of 100 monetary units from the population using
# fixed interval monetary unit sampling
sample <- selection(
data = BuildIt, size = 100, units = "values",
method = "interval", values = "bookValue"
)$sample
# Classical evaluation using the Stringer bound
evaluation(
materiality = 0.05, method = "stringer", conf.level = 0.95,
data = sample, values = "bookValue", values.audit = "auditValue"
)
# Classical evaluation using the Poisson likelihood
evaluation(
materiality = 0.05, method = "poisson", conf.level = 0.95,
data = sample, values = "bookValue", values.audit = "auditValue"
)
# Bayesian evaluation using a noninformative gamma prior distribution
evaluation(
materiality = 0.05, method = "poisson", conf.level = 0.95,
data = sample, values = "bookValue", values.audit = "auditValue",
prior = TRUE
)
# Bayesian evaluation using an informed prior distribution
evaluation(
materiality = 0.05, method = "poisson", conf.level = 0.95,
data = sample, values = "bookValue", values.audit = "auditValue",
prior = auditPrior(method = "param", alpha = 1, beta = 10)
)