This function takes a data frame (using sample, bookValues, and auditValues) or summary statistics (using nSumstats and kSumstats) and evaluates the audit sample according to the specified method. The returned object is of class jfaEvaluation and can be used with associated print() and plot() methods.

For more details on how to use this function see the package vignette: vignette("jfa", package = "jfa")

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)

## Arguments

confidence the required confidence level for the bound. Default is 0.95 for 95% confidence. the method that is used to evaluate the sample. This can be either one of poisson, binomial, hypergeometric, mpus, stringer, stringer-meikle, stringer-lta, stringer-pvz, rohrbach, moment, direct, difference, quotient, or regression. an integer specifying the total number of units (transactions or monetary units) in the population. a data frame containing at least a column of Ist values and a column of Soll (true) values. a character specifying the column name for the Ist values in the sample. a character specifying the column name for the Soll values in the sample. a integer vector of the number of times each transaction in the sample is to be evaluated (due to it being selected multiple times for the sample). an integer specifying the number of transactions in the sample. If specified, overrides the sample, bookValues and auditValues arguments and assumes that the data come from summary statistics specified by both nSumstats and kSumstats. a value specifying the sum of taints (proportional errors) found in the sample. If specified, overrides the sample, bookValues and auditValues arguments and assumes that the data come from summary statistics specified by both kSumstats and nSumstats. a value specifying the performance materiality as a fraction of the total value (or size) of the population (a value between 0 and 1). If specified, the function also returns the conclusion of the analysis with respect to the performance materiality. The value is discarded when direct, difference, quotient, or regression method is chosen. a value specifying the required minimum precision. If specified, the function also returns the conclusion of the analysis with respect to the required minimum precision. This value must be specified as a fraction of the total value of the population (a value between 0 and 1). a logical indicating whether to use a prior distribution when evaluating. Defaults to FALSE for frequentist evaluation. If TRUE, the prior distribution is updated by the corresponding likelihood. Chooses a conjugate gamma distribution for the Poisson likelihood, a conjugate beta distribution for the binomial likelihood, and a conjugate beta-binomial distribution for the hypergeometric likelihood. a value for the prior parameter $$\beta$$ (number of transactions in the assumed prior sample). a value for the prior parameter $$\alpha$$ (total tainting in the assumed prior sample). a value specifying $$\Delta$$ in Rohrbach's augmented variance bound (Rohrbach, 1993). a character specifying the type of population for the modified moment method (Dworin and Grimlund, 1984). Can be either one of accounts or inventory. Options result in different methods for calculating the central moments. a value specifying the total value of the transactions in the population. Required when method is one of direct, difference, quotient, or regression, but optional otherwise. if method = "coxsnell", the $$\alpha$$ parameter of the prior distribution on the mean taint. Default is set to 1, as recommended by Cox and Snell (1979). if method = "coxsnell", the $$\beta$$ parameter of the prior distribution on the mean taint. Default is set to 3, as recommended by Cox and Snell (1979). if method = "coxsnell", the mean of the prior distribution on the mean taint. Default is set to 0.5, as recommended by Cox and Snell (1979).

## Value

An object of class jfaEvaluation containing:

confidence

a value specifying the confidence level of the result.

method

the evaluation method that was used.

N

if N is specified, the population size that is used.

n

an integer specifying the sample size used in the evaluation.

k

an integer specifying the number of transactions that contained an error.

t

a value specifying the sum of observed taints.

materiality

if materiality is specified, the performance materiality used.

minPrecision

if minPrecision is specified, the minimum required precision used.

mle

a value specifying the most likely error in the population as a proportion.

precision

a value specifying the difference between the mle and the upper confidence bound as a proportion.

popBookvalue

if specified as input, the total Ist value of the population.

pointEstimate

if method is one of direct, difference, quotient, or regression, the value of the point estimate.

lowerBound

if method is one of direct, difference, quotient, or regression, the value of the lower bound of the interval.

upperBound

if method is one of direct, difference, quotient, or regression, the value of the upper bound of the interval.

confBound

the upper confidence bound on the error percentage.

conclusion

if materiality is specified, the conclusion about whether to approve or not approve the population.

populationK

the assumed total errors in the population. Used in inferences with hypergeometric method.

prior

an object of class 'jfaPrior' to represents the prior distribution.

posterior

an object of class 'jfaPosterior' to represents the posterior distribution.

data

a data frame containing the relevant columns from the sample input.

## Details

This section lists the available options for the methods argument.

• poisson: The confidence bound taken from the Poisson distribution. If combined with prior = TRUE, performs Bayesian evaluation using a gamma prior and posterior.

• binomial: The confidence bound taken from the binomial distribution. If combined with prior = TRUE, performs Bayesian evaluation using a beta prior and posterior.

• hypergeometric: The confidence bound taken from the hypergeometric distribution. If combined with prior = TRUE, performs Bayesian evaluation using a beta-binomial prior and posterior.

• mpu: Mean per unit estimator using the observed sample taints.

• stringer: The Stringer bound (Stringer, 1963).

• stringer-meikle: Stringer bound with Meikle's correction for understatements (Meikle, 1972).

• stringer-lta: Stringer bound with LTA correction for understatements (Leslie, Teitlebaum, and Anderson, 1979).

• stringer-pvz: Stringer bound with Pap and van Zuijlen's correction for understatements (Pap and van Zuijlen, 1996).

• rohrbach: Rohrbach's augmented variance bound (Rohrbach, 1993).

• moment: Modified moment bound (Dworin and Grimlund, 1984).

• coxsnell: Cox and Snell bound (Cox and Snell, 1979).

• direct: Confidence interval using the direct method (Touw and Hoogduin, 2011).

• difference: Confidence interval using the difference method (Touw and Hoogduin, 2011).

• quotient: Confidence interval using the quotient method (Touw and Hoogduin, 2011).

• regression: Confidence interval using the regression method (Touw and Hoogduin, 2011).

## References

Cox, D. and Snell, E. (1979). On sampling and the estimation of rare errors. Biometrika, 66(1), 125-132.

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 1. 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

## Author

Koen Derks, k.derks@nyenrode.nl

## Examples

library(jfa)
set.seed(1)

# Generate some audit data (N = 1000):
data <- data.frame(ID = sample(1000:100000, size = 1000, replace = FALSE),
bookValue = runif(n = 1000, min = 700, max = 1000))

# Using monetary unit sampling, draw a random sample from the population.
s1 <- selection(population = data, sampleSize = 100, units = "mus",
bookValues = "bookValue", algorithm = "random")
s1_sample <- s1$sample s1_sample$trueValue <- s1_sample$bookValue s1_sample$trueValue[2] <- s1_sample$trueValue[2] - 500 # One overstatement is found # Using summary statistics, calculate the upper confidence bound according # to the binomial distribution: e1 <- evaluation(nSumstats = 100, kSumstats = 1, method = "binomial", materiality = 0.05) print(e1) #> # ------------------------------------------------------------ #> # jfa Evaluation Summary (Frequentist) #> # ------------------------------------------------------------ #> # Input: #> # #> # Confidence: 95% #> # Materiality: 5% #> # Minium precision: Not specified #> # Sample size: 100 #> # Sample errors: 1 #> # Sum of taints: 1 #> # Method: binomial #> # ------------------------------------------------------------ #> # Output: #> # #> # Most likely error: 1% #> # Upper bound: 4.66% #> # Precision: 3.66% #> # Conclusion: Approve population #> # ------------------------------------------------------------ # ------------------------------------------------------------ # jfa Evaluation Summary (Frequentist) # ------------------------------------------------------------ # Input: # # Confidence: 95% # Materiality: 5% # Minium precision: Not specified # Sample size: 100 # Sample errors: 1 # Sum of taints: 1 # Method: binomial # ------------------------------------------------------------ # Output: # # Most likely error: 1% # Upper bound: 4.66% # Precision: 3.66% # Conclusion: Approve population # ------------------------------------------------------------ # Evaluate the raw sample using the stringer bound and the sample counts: e2 <- evaluation(sample = s1_sample, bookValues = "bookValue", auditValues = "trueValue", method = "stringer", materiality = 0.05, counts = s1_sample$counts)
print(e2)
#> # ------------------------------------------------------------
#> #             jfa Evaluation Summary (Frequentist)
#> # ------------------------------------------------------------
#> # Input:
#> #
#> # Confidence:               95%
#> # Materiality:              5%
#> # Minium precision:         Not specified
#> # Sample size:              100
#> # Sample errors:            1
#> # Sum of taints:            1
#> # Method:                   stringer
#> # ------------------------------------------------------------
#> # Output:
#> #
#> # Most likely error:        0.59%
#> # Upper bound:              3.95%
#> # Precision:                3.37%
#> # Conclusion:               Approve population
#> # ------------------------------------------------------------
# ------------------------------------------------------------
#             jfa Evaluation Summary (Frequentist)
# ------------------------------------------------------------
# Input:
#
# Confidence:               95%
# Materiality:              5%
# Minium precision:         Not specified
# Sample size:              100
# Sample errors:            1
# Sum of taints:            1
# Method:                   stringer
# ------------------------------------------------------------
# Output:
#
# Most likely error:        0.69%
# Upper bound:              4.12%
# Precision:                3.44%
# Conclusion:               Approve population
# ------------------------------------------------------------