stringer.bound: Stringer bound
In koenderks/auditR: A Multifunctional R Package for Auditing

Description Usage Arguments Value Details Author(s) References See Also Examples

Calculates the Stringer confidence bound for the maximum error in an audit population.

1	stringer.bound(bookValues, auditValues, confidence = 0.95)

`bookValues`	A vector of book values from sample.
`auditValues`	A vector of corresponding audit values from the sample.
`confidence`	The amount of confidence desired from the bound (on a scale from 0 to 1), defaults to 95% confidence.

An estimate of the mean taint per dollar unit in the population

The Stringer bound is the most well-known and used bound in the accounting practice. Proposed by Stringer (1963), the bound estimates the mean taint per dollar unit. It's formula is defined as:

p(0; 1 - α) + ∑ [ p(j; 1 - α) - p(j-1; 1 - α) ] x Z

where p(j; 1 - α) equals the unique solution to:

∑ (n choose k) p^k (1-p)^{n-k} = 1- α

and is therefore the Clopper-Pearson confidence interval for a binomial parameter (Clopper-Pearson, 1934). The values Z are the proportional taints defined as \frac{bookValues - auditValues}{bookValues} (bookValues - auditValues) / bookValues. Since the upper bound is only defined for integer values of k, when partial taints are observed Stringer performs linear interpolation between the upper bounds that are properly defined. The Stringer bound is often used for its capacity to yield sensible results, even when zero errors are found. This comes with a downside, as the bounds that are given by the Stringer approach are highly conservative bounds due to the attribute sampling method. Additionally, the Stringer bound does not accommodate understatements. However, it can be corrected by using either one of 4 adjustments; Meikle's adjustment (1972), the LTA adjustment (1979), Bickel's adjustment (1992) or the adjustment suggested by Pap and van Zuijlen (1996).

Koen Derks, k.derks@nyenrode.nl

Bickel, P. J. (1992). Inference and auditing: the Stringer bound. International Statistical Review, 197-209.

Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4), 404-413.

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., & van Zuijlen, M. C. (1996). On the asymptotic behaviour of the Stringer bound 1. Statistica Neerlandica, 50(3), 367-389.

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.

stringer.meikle stringer.lta stringer.bickel stringer.modified

# Create an imaginary data set
bookValues   <- rgamma(n = 2400, shape = 1, rate = 0.001)
error.rate   <- 0.1
error        <- sample(0:1, 2400, TRUE, c(1-error.rate, error.rate))
taint        <- rchisq(n = 2400, df = 1) / 10
auditValues  <- bookValues - (error * taint * bookValues)
frame        <- data.frame( bookValues = round(bookValues,2),
                            auditValues = round(auditValues,2))
# Draw a sample
samp.probs   <- frame$bookValues/sum(frame$bookValues)
sample.no    <- sample(1:nrow(frame), 100, FALSE, samp.probs)
sample       <- frame[sample.no, ]
# Calculate Stringer bound
stringer.bound(bookValues = sample$bookValues,
               auditValues = sample$auditValues,
               confidence = 0.95)