MUS.evaluation: Evaluate a sample using Monetary Unit Sampling.
In MUS: Monetary Unit Sampling and Estimation Methods, Widely Used in Auditing

Description Usage Arguments Value Author(s) Examples

Evaluate a sample using Monetary Unit Sampling. At the end of the evaluation step, you get to know the audit conclusion for the population. To conduct the evaluation step it is required that you audited the sample and high values before. You can use print() for a comprehensive output.

MUS.evaluation(extract, filled.sample, filled.high.values,
col.name.audit.values, col.name.riskweights,
interval.type, print.advice, tainting.order,
experimental, combined)

`extract`	A MUS.extraction.result object that you got by executing the function MUS.extraction.
`filled.sample`	A data frame or matrix with the sample from the extraction routine that have an additional column with the audit values.
`filled.high.values`	A data frame or matrix with the high value items from the extraction routine that have an additional column with the audit values.
`col.name.audit.values`	Single character with the name of the column containing the audit value in filled.sample respectively filled.high.values. Default is "audit.value".
`col.name.riskweights`	Single character with the name of the column containing the risk weights in filled.sample respectively filled.high.values. Default is NULL, then no risk weights are included in the calcualations (the ordinary MUS case).
`interval.type`	Interval type for high error rate evaluation. Default is "one-sided".
`print.advice`	Boolean. Prints recommendations only if TRUE. Default is "TRUE".
`tainting.order`	Calculates UEL with different tainting orders (increasing, absolute, random). Default is "decreasing".
`experimental`	Boolean. Calculates other bounds, such as momentum, binomial, multinomial. Not ready for production. Default is "FALSE".
`combined`	Boolean. Marks the dataset as a combination of multiple strata. Default is "FALSE".

An object MUS.evaluation.result is returned which is a list containing the following elements:

`MUS.extraction.result elements`	All elements that are contained in MUS.extraction.result object. For auditing acceptability and for further steps all inputs are also returned.
`filled.sample`	dito.
`filled.high.values`	dito.
`col.name.audit.values`	dito.
`Overstatements.Result.Details`	Detail table for overstatements found in the sample.
`Understatements.Result.Details`	Detail table for understatements found in the sample.
`Results.Sample`	Comprehensive results of sample evaluation.
`Results.High.values`	Comprehensive results of individually significant item evaluation.
`Results.Total`	Comprehensive results of both evaluations (sample and individual significant items).
`acceptable`	Boolean, if population is acceptable given results, confidence level and materiality.

Henning Prömpers <henning@proempers.net>

## Simple Example
# Assume 500 invoices, each between 1 and 1000 monetary units
example.data.1 <- data.frame(book.value=round(runif(n=500, min=1,
max=1000)))
# Plan a sample and cache it
plan.results.simple <- MUS.planning(data=example.data.1,
tolerable.error=100000, expected.error=20000)
# Extract a sample and cache it (no high values exist in this example)
extract.results.simple <- MUS.extraction(plan.results.simple)
# Copy book value into a new column audit values
audited.sample.simple <- extract.results.simple$sample
audited.sample.simple <- cbind(audited.sample.simple,
audit.value=audited.sample.simple$book.value)
# Edit manually (if any audit difference occur)
#audited.sample.simple <- edit(audited.sample.simple)
# Evaluate the sample, cache and print it
evaluation.results.simple <- MUS.evaluation(extract.results.simple,
audited.sample.simple)
print(evaluation.results.simple)

## Advanced Example
example.data.2 <- data.frame(own.name.of.book.values=round(runif(n=500,
min=1, max=1000)))
plan.results.advanced <- MUS.planning(data=example.data.2,
col.name.book.values="own.name.of.book.values", confidence.level=.70,
tolerable.error=100000, expected.error=20000, n.min=3)
extract.results.advanced <- MUS.extraction(plan.results.advanced,
start.point=5, seed=1, obey.n.as.min=TRUE)
extract.results.advanced <- MUS.extraction(plan.results.advanced)
audited.sample.advanced <- extract.results.advanced$sample
audited.sample.advanced <- cbind(audited.sample.advanced,
own.name.of.audit.values=audited.sample.advanced$own.name.of.book.values)
#audited.sample.advanced <- edit(audited.sample.advanced)
evaluation.results.advanced <- MUS.evaluation(extract.results.advanced,
audited.sample.advanced,
col.name.audit.values="own.name.of.audit.values")
print(evaluation.results.advanced)

MONETARY UNIT SAMPLING

The sample provides a reasonable basis to conclude that the population
is free of material misstatements (given the parameters below).

The conclusion is based on a calculated Upper Error Limit of 71285 for
overstatements and 71285 for understatements (please be aware that MUS
is not designed to detect understatements, thus they can only be used
as an indicator).

Most important parameters:
- Confidence Level:				0.95
- Tolerable Error (Materiality):		1e+05
- Population gross value:			251781
- Expected Error in population:			20000
- Sample size:					9
- Threshold for individual significant items:	27976

Projected Misstatement:
No misstatements found. Thus, the projected misstatememt is 0.
MONETARY UNIT SAMPLING

The sample provides a reasonable basis to conclude that the population
is free of material misstatements (given the parameters below).

The conclusion is based on a calculated Upper Error Limit of 62638 for
overstatements and 62638 for understatements (please be aware that MUS
is not designed to detect understatements, thus they can only be used
as an indicator).

Most important parameters:
- Confidence Level:				0.7
- Tolerable Error (Materiality):		1e+05
- Population gross value:			240983
- Expected Error in population:			20000
- Sample size:					4
- Threshold for individual significant items:	60246

Projected Misstatement:
No misstatements found. Thus, the projected misstatememt is 0.