Audit Sampling

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Audit Sampling
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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

• True State of Population
• Deviation Rate Deviation Rate
  Exceeds
  Is Less Than
• Auditors Conclusion Tolerable Rate
  Tolerable Rate
• From the Sample Is
• Deviation Rate
• Exceeds
• Tolerable Rate
• Deviation Rate
• Is Less Than
• Tolerable Rate

Correct Decision
Incorrect Decision (Risk of Assessing Control
Risk Too High)
Incorrect Decision (Risk of Assessing Control
Risk Too Low)
Correct Decision
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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. lt 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 lt 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 in
• Account Exceeds
• Tolerable Amount
• Misstatement in
• Account Is Less
• Than Tolerable
• Amount

Correct Decision
Incorrect Decision (Risk of Incorrect
Rejection)
Incorrect Decision (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 DR
• DR 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

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Mean Per-unit (MPU) EstimationDetermining the
Sample Size
Standard deviation
Population SD
Sample SD
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MPU Estimation Determining the Sample Size

• Calculation of planned allowance for sampling
  risk (A)

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 misstatement
• Ua Incorrect acceptance coefficient (Table 9-8)
• SDC Sample (calculated) standard deviation
• n sample size

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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 populations 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
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

SI sampling interval PBV population book
value n sample size
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PPS SamplingEvaluation of Sample Results
Allowance for sampling risk
ULM upper limit on misstatement PM projected
misstatement BP basic precision IA
incremental allowance
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PPS SamplingEvaluation of Sample Results

• Projected misstatement (PM)
• If BV lt SI, PM TF x SI
• TF tainting factor (BV AV) / BV
• BV book value
• AV audit value
• If BV gt SI, PM actual misstatement

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PPS SamplingEvaluation of Sample Results

• Allowance for sampling risk
• Basic precision SI x RF0
• Incremental allowance
• If no misstatements in sample found, IA 0
• If misstatements found
• For misstatements in which BV lt 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 lt TM, conclude that population is not
  misstated by more than TM at the specified level
  of sampling risk.
• If ULM gt 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.