Title: Audit Sampling
1Audit Sampling
2Audit 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).
3Advantages of Statistical Sampling
- Design efficient samples
- Measure sufficiency of evidence
- Objectively evaluate sample results
4Requirements 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
5Selection 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.
6Terminology
- 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)
7Types of Statistical Sampling Plans
- Attributes sampling
- Discovery sampling
- Classical variables sampling
- Probability-proportional-to-size sampling
8Attribute 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.
9Sampling 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
10Attribute 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
11Discovery 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
12Nonstatistical 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
13Audit 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
14Audit 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
15Risk 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)
16Classic 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.
17Mean 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
18Mean Per-unit (MPU) EstimationDetermining the
Sample Size
Standard deviation
Population SD
Sample SD
19MPU 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)
20MPU 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
21MPU 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
22Nonstatistical Variables Sampling
- PBV population book value
- RF reliability factor (based on auditors
combined assessment of inherent and control risk
and the risk that other substantive procedures
will fail to detect misstatements) (Table 9-13). - TM tolerable misstatement
23Nonstatistical Variables Sampling
PM projected misstatement SNM sample net
misstatement SBV sample book value PBV
population book value Test compare PM to TM.
Rule-of-thumb if PM exceeds 1/3 of TM, PM
becoming too high
24Probability-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.
25PPS 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)
26PPS SamplingSample Selection
- Systematic selection is generally used with PPS
sampling
SI sampling interval PBV population book
value n sample size
27PPS SamplingEvaluation of Sample Results
Allowance for sampling risk
ULM upper limit on misstatement PM projected
misstatement BP basic precision IA
incremental allowance
28PPS 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
29PPS 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.
30PPS 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.