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
                   Advantages of
                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
              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
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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