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:– 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:– 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:

– 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:

– 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