# Audit Sampling Concepts and Techniques

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```					             Audit Sampling

Slide 9- 1
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).

Slide 9- 2
Statistical Sampling

 Design efficient samples
 Measure sufficiency of evidence
 Objectively evaluate sample results

Slide 9- 3
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
Slide 9- 4
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.

Slide 9- 5
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)

Slide 9- 6
Types of Statistical
Sampling Plans

    Attributes sampling
» Discovery sampling
 Classical variables sampling
 Probability-proportional-to-size sampling

Slide 9- 7
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.

Slide 9- 8
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:
Incorrect
Deviation Rate                                  Decision
Exceeds                  Correct
(Risk of Assessing
Tolerable Rate             Decision
Control Risk
Too High)
Incorrect
Deviation Rate
Is Less Than               Decision             Correct
Tolerable Rate         (Risk of Assessing
Decision
Control Risk
Too Low)

Slide 9- 9
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:                                          Planning
»   The risk of assessing control risk too low
»   The tolerable deviation rate
»   The estimated population deviation rate
       Determine the sample size
       Select the sample
Performance
       Test the sample items
       Evaluate the sample results                       Evaluation
       Document the sampling procedure
Documentation

Slide 9- 10
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

Slide 9- 11
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

Slide 9- 12
Audit Sampling for Substantive Tests

    Determine the objective of the test
    Define the population and sampling unit   Planning
    Choose an audit sampling technique
    Determine the sample size
    Select the sample                         Performance
    Test the sample items
    Evaluate the sample results               Evaluation
    Document the sampling procedure           Documentation

Slide 9- 13
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                                 Incorrect
Account Exceeds             Correct             Decision
Tolerable Amount            Decision         (Risk of Incorrect
Rejection)

Misstatement in             Incorrect
Account Is Less                                  Correct
Than Tolerable              Decision
Amount                  (Risk of Incorrect       Decision
Acceptance)

Slide 9- 14
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)

Slide 9- 15
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.

Slide 9- 16
Mean Per-unit (MPU) Estimation
Determining the Sample Size

N = population size
Ur = incorrect rejection coefficient (Table 9-8)
SDE = estimated population standard deviation
A = planned allowance for sampling risk

Slide 9- 17
Mean Per-unit (MPU) Estimation
Determining the Sample Size

Standard deviation

Population SD

Sample SD

Slide 9- 18
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)
Slide 9- 19
MPU Estimation

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
Slide 9- 20
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

Slide 9- 21
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”

Slide 9- 22
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.

Slide 9- 23
PPS Sampling
Determination 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)
Slide 9- 24
PPS Sampling
Sample Selection

Systematic selection is generally used with PPS sampling:

SI = sampling interval
PBV = population book value
n = sample size

Slide 9- 25
PPS Sampling
Evaluation of Sample Results

Allowance for sampling risk

ULM = upper limit on misstatement
PM = projected misstatement
BP = basic precision
IA = incremental allowance

Slide 9- 26
PPS Sampling
Evaluation 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

Slide 9- 27
PPS Sampling
Evaluation 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 < SI, rank order
projected misstatements from largest to smallest,
multiply by corresponding incremental factor
(from Table 9-14) and sum to calculate IA.

Slide 9- 28
PPS Sampling
Evaluation 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.

Slide 9- 29

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 views: 69 posted: 3/28/2011 language: English pages: 29