Chapter 15 Audit Sampling for Tests of Controls and Substantive Tests of Transactions

Presentation Outline Representative Sample Statistical vs. Nonstatistical Sampling Terms Used in Sample Planning Terms Related to Evaluating Results Steps in Sampling

I. Representative Sample A representative sample is one in which the characteristics in the sample of audit interest are approximately the same as those of the population. Two things cause a sample to be nonrepresentative: Nonsampling risk Sampling risk

A. Nonsampling Risk Nonsampling risk is the risk that the audit tests do not uncover existing exceptions in the sample. Two causes of this risk are: Auditor failure to recognize exceptions Inappropriate or ineffective audit procedures

B. Sampling Risk Sampling risk is the risk that an auditor reaches an incorrect conclusion because the sample is not representative of the population. This can be controlled by: Adjusting the sample size Using an appropriate method of selecting sample items

II. Statistical vs. Nonstatistical Sampling Probabilistic Sample Selection Nonstatistical Sampling Nonprobabilistic Sample Selection Although statistical sampling uses either sampling with or without replacement, auditors normally sample without replacement.

A. Statistical Sampling Mathematical rules allow the quantification of sampling risk in planning the sample. For example, a 95% confidence level provides a 5% sampling risk. Statistical sampling requires probabilistic sample selection.

B. Probabilistic Sample Selection Probabilistic sample selection selects a sample in a way that each population item has a known probability of being included in the sample and the sample is randomly selected. Simple random number selection – all items of the population have an equal chance of being selected. Can use random number tables and random number generators (see Fig. 15-1 on p. 448). Systematic sample selection – Auditor determines an interval and selects items on the basis of the interval (see example on page 449) Probability Proportional to Size – Probability of selecting an item is proportional to its recorded amount. Stratified sample – Divided population into subpopulations and use different selection criteria for each subpopulation. Note: It is acceptable to make nonstatistical evaluations by using probabilistic selection, but it is never acceptable to evaluate a nonprobabilistic sample as if it were a statistical sample.

Stratification Illustrated The process of dividing a population into subpopulations that have similar characteristics. Strata must be defined so that each sampling unit can only be in one stratum. Accounts Receivable Stratification Stratum Size Composition of Stratum Sample Selection 2 22 All accounts over $5,000 100% examination 121 All accounts between $1,000 and $5,000 Random-number table 3 85 All accounts under $1,000 Systematic selection 4 14 All accounts with credit balances

C. Nonstatistical Sampling In nonstatistical sampling, the auditor does not quantify sampling risk. Instead, those sample items that the auditor believes will provide the most useful information are selected. Since conclusions are based on a judgmental basis, nonprobabilistic sample selection is normally conducted.

D. Nonprobabilistic Sample Selection Nonprobabilistic sample selection is a method of selecting a sample where the auditor uses professional judgment rather than probabilistic methods to select sample items. Directed sample selection – auditor selects items based on a judgmental criteria such as likelihood of misstatement, characteristics such as different time periods, or large dollar amounts. Block sample selection – selection of a number of items in sequence. Auditor must use several blocks to obtain a representative sample. Haphazard sample selection – selection of items without any conscious bias on the part of the auditor. Note: It is acceptable to make nonstatistical evaluations by using probabilistic selection, but it is never acceptable to evaluate a nonprobabilistic sample as if it were a statistical sample.

III. Terms Used in Sample Planning Characteristics or Attribute Acceptable Risk of Assessing Control Risk Too Low (ACACR) Tolerable Exception Rate (TER) Estimated Population Exception Rate (EPER)

A. Characteristics or Attribute The characteristic being tested in the population.

B. Acceptable Risk of Assessing Control Risk Too Low (ARACR) The risk that the auditor is willing to take of accepting a control as effective or a rate of monetary misstatement as tolerable, when the true population exception rate is greater than the tolerable exception rate.

C. Tolerable Exception Rate Exception rate that the auditor will permit in the population and still be willing to use the assessed control risk and/or the amount of monetary misstatements in the transactions established during planning.

D. Estimated Population Exception Rate Exception rate that the auditor expects to find in the population before testing begins.

IV. Terms Related To Evaluating Results Exception Sample Exception Rate (SER) Computed Upper Exception Rate

A. Exception The term exception should be understood to refer to both: deviations from prescribed controls and situations where amounts are not monetarily correct.

B. Sample Exception Rate (SER) Number of exceptions in the sample size divided by the sample size.

C. Computed Upper Exception Rate (CUER) The upper limit of the probable population exception rate; the highest exception rate in the population at a given ARACR.

V. Steps in Sampling Planning the Sample (Steps 1-9) Select the Sample and Perform the Tests (Steps 10-11) Evaluate the Results (Steps 12-14)

A. Planning the Sample Step 1 State the objectives of the audit test. Step 2 Decide whether audit sampling applies. Step 3 Define attributes and exception conditions. Step 4 Define the population. Step 5 Define the sampling unit.

A. Planning the Sample Step 6 Specify the tolerable exception rate. Step 7 Specify acceptable risk of assessing control risk too low. Step 8 Estimate the population exception rate. Step 9 Determine the initial sample size.

B. Select the Sample and Perform the Tests Step 10 Select the sample. Step 11 Perform the audit procedures.

C. Evaluate the Results Step 12 Generalize from the sample to the population. Step 13 Analyze exceptions. Step 14 Decide the acceptability of the population.

Summary Effect of Sampling Risk and Nonsampling Risk a Representative Sample Statistical Sampling Must Use Probabilistic Sample Selection Simple Random Sample Selection Systematic Sample Selection Probability Proportional to Size Sample Selection Stratified Sample Selection Nonstatistical Sampling Often Uses Nonprobabilitic Sample Selection Directed Sample Selection Block Sample Selection Haphazard Sample Selection Sampling Terms The 14 Steps of Sampling