R: Audit Sampling: Evaluation

evaluation {jfa}

R Documentation

Audit Sampling: Evaluation

Description

evaluation() is used to perform statistical inference about the misstatement in a population after auditing a statistical sample. 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 jfaEvaluation that can be used with associated summary() and plot() methods.

Usage

evaluation(
  materiality = NULL,
  method = c(
    "poisson", "binomial", "hypergeometric",
    "inflated.poisson", "hurdle.beta",
    "stringer.poisson", "stringer.binomial", "stringer.hypergeometric",
    "stringer.meikle", "stringer.lta", "stringer.pvz", "stringer",
    "rohrbach", "moment", "coxsnell", "mpu", "pps",
    "direct", "difference", "quotient", "regression"
  ),
  alternative = c("less", "two.sided", "greater"),
  conf.level = 0.95,
  data = NULL,
  values = NULL,
  values.audit = NULL,
  strata = NULL,
  times = NULL,
  x = NULL,
  n = NULL,
  N.units = NULL,
  N.items = NULL,
  pooling = c("none", "complete", "partial"),
  prior = FALSE
)

Arguments

`materiality`	a numeric value between 0 and 1 specifying the performance materiality (i.e., the maximum tolerable misstatement in the population) as a fraction of the total number of units in the population. Can be `NULL`. Not used for methods `direct`, `difference`, `quotient`, and `regression`.
`method`	a character specifying the statistical method. Possible options are `poisson` (default), `binomial`, `hypergeometric`, `stringer.poisson`, `stringer.binomial`, `stringer.hypergeometric`, `stringer.meikle`, `stringer.lta`, `stringer.pvz`, `rohrbach`, `moment`, `mpu`, `pps`, `direct`, `difference`, `quotient`, or `regression`. See the details section for more information.
`alternative`	a character indicating the alternative hypothesis and the type of confidence / credible interval returned by the function. Possible options are `less` (default), `two.sided`, or `greater`.
`conf.level`	a numeric value between 0 and 1 specifying the confidence level (i.e., 1 - audit risk / detection risk).
`data`	a data frame containing a data sample.
`values`	a character specifying name of a numeric column in `data` containing the book values of the items.
`values.audit`	a character specifying name of a numeric column in `data` containing the audit (i.e., true) values of the items.
`strata`	a character specifying name of a factor column in `data` indicating to which stratum the item belongs.
`times`	a character specifying name of an integer column in `data` containing the number of times an item should be counted due to (not) being selected (multiple times) for the sample. Items for which this value is 0 will not be included in the evaluation.
`x`	a numeric value or vector of values equal to or larger than 0 specifying the sum of (proportional) misstatements in the sample or, if this is a vector, the sum of taints in each stratum. If this argument is specified, the input for the `data`, `values` and `values.audit` arguments is discarded and it is assumed that the data come from summary statistics specified by `x` and `n`.
`n`	an integer or vector of integers larger than 0 specifying the sum of (proportional) misstatements in the sample or, if this is a vector, the sum of taints in each stratum. If this argument is specified, the input for the `data`, `values` and `values.audit` arguments is discarded and it is assumed that the data come from summary statistics specified by `x` and `n`.
`N.units`	a numeric value or vector of values than 0 specifying the total number of units in the population or, if this is a vector, the total number of units in each stratum of the population. This argument is strictly required for the `hypergeometric`, `direct`, `difference`, `quotient`, and `regression` methods, but is also used in stratification to weigh the estimates of each individual stratum to arrive at the population estimate. If `NULL`, each stratum is assumed to be equally represented in the population.
`N.items`	an integer larger than 0 specifying the number of items in the population. Only used for methods `direct`, `difference`, `quotient`, and `regression`.
`pooling`	a character specifying the type of model to use when analyzing stratified samples. Possible options are `none` (default) for no pooling (i.e., no information is shared between strata), `complete` for complete pooling (i.e., all information is shared between strata) or `partial` for partial pooling (i.e., some information is shared between strata). The latter two options fit a Bayesian model to the data using a MCMC sampling procedure whose options can be set globally using `options("mc.iterations")` (otherwise: 2000), `options("mc.warmup")` (otherwise: 1000), `options("mc.chains")` (otherwise: 4) and `options("mc.cores")` (otherwise: 1).
`prior`	a logical specifying whether to use a prior distribution, or an object of class `jfaPrior` or `jfaPosterior`. If this argument is specified as `FALSE` (default), the function performs classical evaluation. If this argument is specified as `TRUE` or as a prior from `auditPrior`, this function performs Bayesian evaluation using the specified prior.

Details

This section lists the available options for the method argument.

poisson: Evaluates the sample with the Poisson distribution. If combined with prior = TRUE, performs Bayesian evaluation using a gamma prior.
binomial: Evaluates the sample with the binomial distribution. If combined with prior = TRUE, performs Bayesian evaluation using a beta prior.
hypergeometric: Evaluates the sample with the hypergeometric distribution. If combined with prior = TRUE, performs Bayesian evaluation using a beta-binomial prior.
inflated.poisson: Inflated Poisson model incorporating the explicit probability of misstatement being zero. If prior = TRUE, performs Bayesian evaluation using a beta prior.
hurdle.beta: Hurdle beta model incorporating the explicit probability of a taint being zero, one, or in between. If prior = TRUE, this setup performs Bayesian evaluation using a beta prior.
stringer.poisson: Evaluates the sample with the Stringer bound using the Poisson distribution.
stringer.binomial: Evaluates the sample with the Stringer bound using the binomial distribution (Stringer, 1963).
stringer.hypergeometric: Evaluates the sample with the Stringer bound using the hypergeometric distribution.
stringer.meikle: Evaluates the sample using the Stringer bound with Meikle's correction for understatements (Meikle, 1972).
stringer.lta: Evaluates the sample using the Stringer bound with LTA correction for understatements (Leslie, Teitlebaum, and Anderson, 1979).
stringer.pvz: Evaluates the sample using the Stringer bound with Pap and van Zuijlen's correction for understatements (Pap and van Zuijlen, 1996).
rohrbach: Evaluates the sample using Rohrbach's augmented variance bound (Rohrbach, 1993).
moment: Evaluates the sample using the modified moment bound (Dworin and Grimlund, 1984).
coxsnell: Evaluates the sample using the Cox and Snell bound (Cox and Snell, 1979).
mpu: Evaluates the sample with the mean-per-unit estimator using the Normal distribution.
pps: Evaluates the sample with the proportional-to-size estimator using the Student-t distribution.
direct: Evaluates the sample using the direct estimator (Touw and Hoogduin, 2011).
difference: Evaluates the sample using the difference estimator (Touw and Hoogduin, 2011).
quotient: Evaluates the sample using the quotient estimator (Touw and Hoogduin, 2011).
regression: Evaluates the sample using the regression estimator (Touw and Hoogduin, 2011).

Value

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 misstatement in the population as a fraction.
`ub`	a numeric value between 0 and 1 giving the upper bound for the misstatement in the population.
`lb`	a numeric value between 0 and 1 giving the lower bound for the misstatement in the population.
`precision`	a numeric value between 0 and 1 giving the difference between the most likely misstatement and the bound relative to `alternative`.
`p.value`	for classical tests, a numeric value giving the p-value.
`x`	an integer larger than, or equal to, 0 giving the number of misstatements in the sample.
`t`	a value larger than, or equal to, 0, giving the sum of proportional misstatements in the sample.
`n`	an integer larger than 0 giving the sample size.
`materiality`	if `materiality` is specified, a numeric value between 0 and 1 giving the performance materiality as a fraction.
`alternative`	a character indicating the alternative hypothesis.
`method`	a character the method used.
`N.units`	if `N.units` is specified, in integer larger than 0 indicating the number of units in the population
`N.items`	if `N.items` is specified, in integer larger than 0 indicating the number of items in the population.
`K`	if `method = 'hypergeometric'`, an integer indicating the assumed total errors in the population.
`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`.
`strata`	a data frame containing the relevant statistical results for the strata.
`data.name`	a character giving the name of the data.

Author(s)

Koen Derks, k.derks@nyenrode.nl

References

Cox, D. and Snell, E. (1979). On sampling and the estimation of rare errors. Biometrika, 66(1), 125-132. doi:10.1093/biomet/66.1.125.

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. doi:10.1111/ijau.12240

Derks, K., de Swart, J., Wagenmakers, E.-J., Wille, J., & Wetzels, R. (2021). JASP for audit: Bayesian tools for the auditing practice. Journal of Open Source Software, 6(68), 2733. doi:10.21105/joss.02733

Derks, K., de Swart, J., Wagenmakers, E.-J., & Wetzels, R. (2021). The Bayesian approach to audit evidence: Quantifying statistical evidence using the Bayes factor. PsyArXiv. doi:10.31234/osf.io/kzqp5

Derks, K., de Swart, J., Wagenmakers, E.-J., & Wetzels, R. (2022). An impartial Bayesian hypothesis test for audit sampling. PsyArXiv. doi:10.31234/osf.io/8nf3e

Derks, K., de Swart, J., Wagenmakers, E.-J., & Wetzels, R. (2022). Bayesian generalized linear modeling for audit sampling: How to incorporate audit information into the statistical model. PsyArXiv. doi:10.31234/osf.io/byj2a

Dworin, L. D. and Grimlund, R. A. (1984). Dollar-unit sampling for accounts receivable and inventory. The Accounting Review, 59(2), 218-241. https://www.jstor.org/stable/247296

Leslie, D. A., Teitlebaum, A. D., & Anderson, R. J. (1979). Dollar-unit Sampling: A Practical Guide for Auditors. Copp Clark Pitman; Belmont, CA. ISBN: 9780773042780.

Meikle, G. R. (1972). Statistical Sampling in an Audit Context. 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. doi:10.1111/j.1467-9574.1996.tb01503.x.

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.

Examples

# Using summary statistics
evaluation(materiality = 0.05, x = 0, n = 100) # Non-stratified
evaluation(materiality = 0.05, x = c(2, 1, 0), n = c(50, 70, 40)) # Stratified

# Using data
data("BuildIt")
BuildIt$inSample <- c(rep(1, 100), rep(0, 3400))
levs <- c("low", "medium", "high")
BuildIt$stratum <- factor(c(levs[3], levs[2], rep(levs, times = 1166)))
sample <- subset(BuildIt, BuildIt$inSample == 1)

# Non-stratified evaluation
evaluation(
  materiality = 0.05, data = sample,
  values = "bookValue", values.audit = "auditValue"
)
# Stratified evaluation
evaluation(
  materiality = 0.05, data = sample, values = "bookValue",
  values.audit = "auditValue", strata = "stratum"
)

[Package jfa version 0.7.1 Index]