Chapter 14: Sampling
ACCT620 Internal Auditing
Otto Chang
Professor of Accounting
Advantage of Statistical
Sampling
• It quantifies sampling risk, both the risk of
false alarm and the risk of non-detection
• It assist auditors in designing an efficient
sample
• It is an objective, verifiable technique for
gathering audit evidence
• Many soft wares are developed to make it
easy to do.
The Influence of Audit
Objectives on Sampling Method
• Attribute sampling: focus on the the existence of
some attribute, suited for testing internal control
• Discovery sampling: used when little to no
noncompliance is expected. A subset of attribute
sampling in which the discovery of one error
means noncompliance rate was too high
• Sequential (stop-or-go) sampling: used when low
population error rate is expected to minimize
sample size.
• Variable sampling: used to asses a monetary or any
measure of quantity, i.e, testing A/R, inventory,
fixed assets
• Dollar Unit Sampling or Sampling with Probability
proportional to size (PPS): each dollar is viewed as
a sampling item and is either correct or incorrect. It
is an attribute sampling with conclusion expressed
as a dollar amount rather than an error rate. Used
mostly to test overstatement.
• Multi-stage or layered sampling: non-random
method that tests only certain aspects of
differentially defined population, i.e., select
certain procedures on certain days in certain stores
located in certain regions
• Cluster sampling: non-random method that selects
a group (cluster) of items rather than individual
items, i.e., a barrel of tires, or a filing cabinet
drawer of documents
Sampling Terminology
• Population: the audit universe, the totality of
something auditors want to reach a conclusion
• Sample: a subset of the population, generally
randomly drawn
• Representativeness: similarity between the sample
and the population
• Sampling unit: the item included in the sample
• Sampling size: The number of items in the sample
Sampling Concepts
• Random samples: a sample selected by the use of
– a random number table, if population is pre-numbered
– systematic selection (interval sampling) with multiple
random starts if not pre-numbered
• Stratified sampling: a population is broken into
sub-population to minimize variability within a
particular stratum. It is more efficient than
random sample.
Sample size
• Required sample size increase as population size
increases but at negligible rate
• Required sample size increase dramatically (by the
square of the relative change) as standard
deviation (sample variability) increases. To reduce
sample variability, use difference or ratio approach
rather than mean-per-unit estimation.
• Required sample size increases as required
precision of estimates narrows
Sampling Concepts
• Expected error rates: the error rate expected to be
found in population. A high rate increases required
sample size in attributes sampling
• Precision: desired allowance for sampling risk, tied
into auditor’s evaluation of materiality, usually
indicated as an interval around sample estimates
• Tolerable rate: maximum rate of error auditors
would accept and still assess controls to be effective
Sampling Concepts
• Sampling risks:
– Type I error (Alpha risk): incorrect rejection
while population is reasonably stated.
– Type II error (Beta risk): incorrect acceptance
while population is not reasonably stated.
Related to audit effectiveness, more critical to
auditors.
• Confidence Interval or reliability:is the
complement of risk.
Example of Discovery Sampling
• Objective: to determine if fictitious employee have
been added to the payroll
• Sampling Plan:
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Population: all employees on the payroll last year (9,500)
Sampling unit: each employee
Nature of errors: entering of fictitious employee
Sampling risk: 5%, 95% confidence interval
Sample size: 300 (tolerable error rate at 1%)
Evaluation phase: no fictitious employee were found
Interpretation: fraud is not present (95% of confident)
Attribute Sampling
• Objective: to determine if credit is checked for
sales > $1,000
• Sampling plan:
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Population: all A/R >$1,000 over last year (30,000)
Sampling unit: customer with A/R > $1,000
Nature of errors: credit check was not performed
Sampling risk: 5% or 95% confidence level
Sample size: 300 (expected error rate=2% and tolerable
error rate=4%, precision=2% )
– Evaluation phase: 5 (1.7%) deviations were identified
– Interpretation: true error rate is < 3.9% (95%
confidence level)
Variable Sampling
• Objective: to assess the reasonableness of
recorded CIP at $2,400,000
• Sampling Plan:
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Population; 1,000 homes in CIP
Sampling unit: each home
Nature of error: misstatement of CIP
Sampling risk: 10%, 90% confidence level
Sample size: 286 (standard deviation from pilot sample
of 40 homes = $3,000, desired precision= $247,500,
after a finite correction factor
– Evaluation: $22,000,000 + $244,588
– Interpretation: CIP overstated
Dollar Unit Sampling
• Objective: to assess if A/R are overstated
• Sample plan:
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Population: all (20,000) A/R recorded at $5,600,000
Sampling unit: each dollar in recorded A/R
Nature of error: misstatement of A/R
Method of selection: systematic
Sampling risk: 5%
Sample size: 112 (upper precision limit=$150,000 and
expected errors=3 and percentage of error size=100%)
– Evaluation: $352,800 (population value $5,600,000 x
reliability factor 0.063 from Ex. 14-J)
– Interpretation: A/R is overstated