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

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

1. Representative Sample
2. Statistical vs. Nonstatistical Sampling
3. Terms Used in Sample Planning
4. Terms Related to Evaluating Results
5. Steps in Sampling

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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

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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

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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

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II. Statistical vs. Nonstatistical Sampling

1. Statistical Sampling
2. Probabilistic Sample Selection
3. Nonstatistical Sampling
4. Nonprobabilistic Sample Selection

Although statistical sampling uses either
sampling with or without replacement, auditors
normally sample without replacement.
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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.

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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.
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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
2 121 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 100 examination
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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.

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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.
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III. Terms Used in Sample Planning

1. Characteristics or Attribute
2. Acceptable Risk of Assessing Control Risk Too Low
   (ACACR)
3. Tolerable Exception Rate (TER)
4. Estimated Population Exception Rate (EPER)

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A. Characteristics or Attribute

• The characteristic being tested in the population.

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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.

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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.

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D. Estimated Population Exception Rate

• Exception rate that the auditor expects to find
  in the population before testing begins.

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IV. Terms Related To Evaluating Results

1. Exception
2. Sample Exception Rate (SER)
3. Computed Upper Exception Rate

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A. Exception

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

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B. Sample Exception Rate (SER)

• Number of exceptions in the sample size divided
  by the sample size.

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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.

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V. Steps in Sampling

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

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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.
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A. Planning the Sample
Specify the tolerable exception rate.
Step 6
Specify acceptable risk of assessing control risk
too low.
Step 7
Estimate the population exception rate.
Step 8
Determine the initial sample size.
Step 9
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B. Select the Sample and Perform the Tests
Select the sample.
Step 10
Perform the audit procedures.
Step 11
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C. Evaluate the Results
Generalize from the sample to the population.
Step 12
Analyze exceptions.
Step 13
Decide the acceptability of the population.
Step 14
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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