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Presentation Outline
I. Representative Sample
II. Statistical vs. Nonstatistical Sampling
III. Terms Used in Sample Planning
IV. Terms Related to Evaluating Results
V. 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:
A. Nonsampling risk
B. 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
A. Statistical Sampling
B. Probabilistic Sample Selection
C. Nonstatistical Sampling
D. 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 SelectionProbabilistic 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
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
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
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 SelectionNonprobabilistic 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
A. Characteristics or Attribute
B. Acceptable Risk of Assessing Control Risk Too Low (ACACR)
C. Tolerable Exception Rate (TER)
D. Estimated Population Exception Rate (EPER)
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
A. Exception
B. Sample Exception Rate (SER)
C. Computed Upper Exception Rate
A. Exception
The term exception should be understood to refer to
both:deviations from
prescribed controls andsituations where
amounts are not monetarily correct.
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
A. Planning the Sample (Steps 1-9)
B. Select the Sample and Perform the Tests (Steps 10-11)
C. 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
Specify acceptable risk of assessingcontrol risk too low.
Estimate the population exception rate.
Determine the initial sample size.
Step 7
Step 8
Step 9
Specify the tolerable exception rate.Step 6
B. Select the Sample and Perform the Tests
Select the sample.
Perform the audit procedures.
Step 10
Step 11
C. Evaluate the Results
Generalize from the sampleto the population.
Analyze exceptions.
Decide the acceptability of the population.
Step 12
Step 13
Step 14
Summary
Effect of Sampling Risk and Nonsampling Risk a Representative Sample
Statistical Sampling Must Use Probabilistic Sample SelectionSimple Random Sample Selection
Systematic Sample SelectionProbability Proportional to Size Sample Selection
Stratified Sample Selection Nonstatistical Sampling Often Uses Nonprobabilitic Sample
SelectionDirected Sample SelectionBlock Sample Selection
Haphazard Sample Selection Sampling Terms
The 14 Steps of Sampling
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