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Slide 9- 1
Audit Sampling
Slide 9- 2
Audit Sampling Defined
SAS No. 39 defines audit sampling as the application of an audit procedure to less than 100 percent of the items within an account balance or class of transactions for the purpose of evaluating some characteristic of the balance or class (AU 350.01).
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Advantages of Statistical Sampling
Design efficient samples Measure sufficiency of evidence Objectively evaluate sample results
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Requirements of Audit Sampling Plans
When planning the sample consider:» The relationship of the sample to the relevant audit objective» Materiality or the maximum tolerable misstatement or deviation
rate» Allowable sampling risk» Characteristics of the population
Select sample items in such a manner that they can be expected to be representative of the population
Sample results should be projected to the population Items that cannot be audited should be treated as
misstatements or deviations in evaluating the sample results Nature and cause of misstatements or deviations should be
evaluated
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Selection of Random Sample
Random number tables Random number generators Systematic selection Haphazard Selection
Note that these methods are often used in conjunction with a stratification process.
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Terminology
Sampling risk» Risk of assessing CR too high / Risk of
incorrect rejection» Risk of assessing CR too low / Risk of
incorrect acceptance
Precision (allowance for sampling risk)
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Types of Statistical Sampling Plans
Attributes sampling» Discovery sampling
Classical variables sampling Probability-proportional-to-size sampling
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Attribute Sampling Applied To Tests Of Controls
Attribute sampling is a statistical method used to estimate the proportion of a characteristic in a population.
The auditor is normally attempting to determine the operating effectiveness of a control procedure in terms of deviations from the prescribed internal control.
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Sampling Risk for Tests of Controls
CorrectDecision
Incorrect Decision
(Risk of Assessing Control Risk
Too High)
IncorrectDecision
(Risk of AssessingControl Risk
Too Low)
Correct Decision
True State of Population
Deviation Rate Deviation Rate Exceeds Is Less Than
Auditors’ Conclusion Tolerable Rate Tolerable RateFrom the Sample Is:
Deviation Rate Exceeds Tolerable Rate
Deviation Rate Is Less Than Tolerable Rate
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Attribute Sampling for Tests of Controls
Determine the objective of the test Define the attributes and deviation conditions Define the population to be sampled Specify:
» The risk of assessing control risk too low» The tolerable deviation rate» The estimated population deviation rate
Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure
Planning
Performance
Evaluation
Documentation
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Discovery Sampling
A modified case of attributes sampling Purpose is to detect at least one deviation (i.e.
critical deviations) Useful in fraud detection Auditor risk and deviation assessments:
» Risk of assessing control risk too low (i.e. 5%)» Tolerable rate (normally set very low, i.e. < 2%)» Expected deviation rate is generally set at 0
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Nonstatistical Attributes Sampling
Determination of required sample size» Must consider risk of assessing control risk too low
and tolerable deviation rate» Need not quantify the risks
Evaluation of results» Compare tolerable deviation rate to sample
deviation rate. Assuming appropriate n:– If SDR somewhat less than TDR, then conclude that risk
of assessing control risk too low is set appropriately.– If SDR approaches TDR it becomes less likely that PDR
< TDR– Must use professional judgment
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Audit Sampling for Substantive Tests
Determine the objective of the test Define the population and sampling unit Choose an audit sampling technique Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure
Planning
Performance
Evaluation
Documentation
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Audit Sampling for Substantive Tests
Sampling Risk
True State of Population
Misstatement in Misstatement in Account Exceeds Account Is Less
Auditors’ Conclusion Tolerable Amount Than Tolerable From the Sample Is: Amount
Misstatement inAccount Exceeds Tolerable Amount
Misstatement inAccount Is LessThan TolerableAmount
CorrectDecision
Incorrect Decision
(Risk of Incorrect Rejection)
IncorrectDecision
(Risk of Incorrect Acceptance)
Correct Decision
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Risk of Incorrect Acceptance (RIA)
Modification of audit risk model:
AR = IR x CR x DRDR comprised of two types of substantive procedures,
each with an associated type of risk: Risk associated with AP and other procedures that do not
involve audit sampling (AP) Risk associated with procedures involving audit sampling (RIA)
AR = IR x CR x AP x RIA
RIA = AR /(IR x CR x AP)
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Classic Variables Sampling
Mean per-unit estimation Difference and Ratio Estimation
» Appropriate when differences between audited and book values are frequent
» Difference estimation is most appropriate when the size of the misstatements does not vary significantly in comparison to book value
» Ratio estimation is most appropriate when the size of misstatements is nearly proportional to the book values of the items.
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Mean Per-unit (MPU) EstimationDetermining the Sample Size
N = population size
Ur = incorrect rejection coefficient (Table 9-8)
SDE = estimated population standard deviation
A = planned allowance for sampling risk
2
A
SDUNn Er
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Mean Per-unit (MPU) EstimationDetermining the Sample Size
N
)Xx( 2
Standard deviation
1
)( 2
n
Xxs
Population SD
Sample SD
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MPU Estimation Determining the Sample Size
Calculation of planned allowance for sampling risk (A):
r
a
UUTM
A
1
TM = tolerable misstatement
Ua = Incorrect acceptance coefficient (Table 9-8)
Ur = incorrect rejection coefficient (Table 9-8)
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MPU Estimation Adjusted Allowance for Sampling
Risk
Calculation of adjusted allowance for sampling risk (A´):
TM = Tolerable misstatementUa = Incorrect acceptance coefficient (Table 9-8)SDC = Sample (calculated) standard deviation n = sample size
n
SDUNTMA Ca
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MPU Estimation
Estimated total audited value = Mean audited value x Number of accounts
Acceptance interval
= Estimated total audited value +/- Adjusted allowance for sampling risk
Projected misstatement = Estimated total audited value – Book value of
population
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Nonstatistical Variables Sampling
Determination of required sample size» Must consider IR, CR and AP risk
Evaluation of results» Compare projected misstatement to tolerable
misstatement. » As PM approaches TM then likelihood of material
misstatement increasing.» Rule-of-thumb: if PM exceeds 1/3 of TM, PM
“becoming too high”
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Probability-proportional-to-size (PPS) Sampling
Applies the theory of attributes sampling to estimate the total dollar amount of misstatement in a population.
Population is defined by the individual dollars comprising the population’s book value ($1 = 1 item).
Relatively easy to use and often results in smaller sample sizes than classical variables approaches.
Assumptions underlying PPS sampling:» Expected misstatement rate in the population is small.» Amount of misstatement in physical unit should not exceed
recorded BV of the item.» PPS focuses on overstatements.
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PPS SamplingDetermination of Sample Size
)(0
EFEMTM
RFPBVn
PBV = population book value
RF = reliability factor (Table 9-14)
TM = tolerable misstatement
EM = expected misstatement
EF = expansion factor (Table 9-15)
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PPS SamplingSample Selection
Systematic selection is generally used with PPS sampling:
n
PBVSI
SI = sampling interval
PBV = population book value
n = sample size
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PPS SamplingEvaluation of Sample Results
IABPPMULM
ULM = upper limit on misstatement
PM = projected misstatement
BP = basic precision
IA = incremental allowance
Allowance for sampling risk
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PPS SamplingEvaluation of Sample Results
Projected misstatement (PM) If BV < SI, PM = TF x SI
TF = tainting factor = (BV – AV) / BV» BV = book value» AV = audit value
If BV > SI, PM = actual misstatement
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PPS SamplingEvaluation of Sample Results
Allowance for sampling risk Basic precision = SI x RF0
Incremental allowanceIf no misstatements in sample found, IA = 0If misstatements found:
For misstatements in which BV < SI, rank order projected misstatements from largest to
smallest, multiply by corresponding incremental factor (from Table 9-14) and sum to calculate IA.
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PPS SamplingEvaluation of Sample Results
Compare ULM to TM: If ULM < TM, conclude that population is not
misstated by more than TM at the specified level of sampling risk.
If ULM > TM, conclude that the sample results do not provide enough assurance that the population misstatement is less than the TM and balance adjustment may be warranted.