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)

confidence | the required confidence level for the bound. Default is 0.95 for 95% confidence. |
---|---|

method | the method that is used to evaluate the sample. This can be either one of |

N | an integer specifying the total number of units (transactions or monetary units) in the population. |

sample | a data frame containing at least a column of Ist values and a column of Soll (true) values. |

bookValues | a character specifying the column name for the Ist values in the sample. |

auditValues | a character specifying the column name for the Soll values in the sample. |

counts | 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). |

nSumstats | an integer specifying the number of transactions in the sample. If specified, overrides the |

kSumstats | a value specifying the sum of taints (proportional errors) found in the sample. If specified, overrides the |

materiality | 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 |

minPrecision | 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). |

prior | a logical indicating whether to use a prior distribution when evaluating. Defaults to |

nPrior | a value for the prior parameter \(\beta\) (number of transactions in the assumed prior sample). |

kPrior | a value for the prior parameter \(\alpha\) (total tainting in the assumed prior sample). |

rohrbachDelta | a value specifying \(\Delta\) in Rohrbach's augmented variance bound (Rohrbach, 1993). |

momentPoptype | a character specifying the type of population for the modified moment method (Dworin and Grimlund, 1984). Can be either one of |

populationBookValue | a value specifying the total value of the transactions in the population. Required when |

csA | if |

csB | if |

csMu | if |

An object of class `jfaEvaluation`

containing:

a value specifying the confidence level of the result.

the evaluation method that was used.

if `N`

is specified, the population size that is used.

an integer specifying the sample size used in the evaluation.

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

a value specifying the sum of observed taints.

if `materiality`

is specified, the performance materiality used.

if `minPrecision`

is specified, the minimum required precision used.

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

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

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

if method is one of `direct`

, `difference`

, `quotient`

, or `regression`

, the value of the point estimate.

if method is one of `direct`

, `difference`

, `quotient`

, or `regression`

, the value of the lower bound of the interval.

if method is one of `direct`

, `difference`

, `quotient`

, or `regression`

, the value of the upper bound of the interval.

the upper confidence bound on the error percentage.

if `materiality`

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

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

method.

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

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

a data frame containing the relevant columns from the `sample`

input.

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).

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.

Koen Derks, k.derks@nyenrode.nl

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 # ------------------------------------------------------------