1. Chapter 14: Sampling ACCT620 Internal Auditing Otto Chang Professor of Accounting

2. 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.

3. 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.

4. 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.

5. 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

6. 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

7. 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.

8. 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

9. 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

10. 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.

11. 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)

12. 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)

13. 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

14. 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