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Chapter 9 Audit Sampling – Part b

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**Sampling to Test for Account Balance Misstatements (Substantive Testing)**

Basic steps: Specify audit objective of the test Define misstatement Define population (and sampling units) Choose sampling method Determine sample size Select sample Audit selected items Evaluate sample results Perform follow-up work as necessary Document sampling procedure and results

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**1. Define Specify Audit Objective**

Sampling always relates to one specific procedure usually testing one specific assertion Specifying the audit objective determines the population to test For example: If objective is to determine existence, the sample should be selected from recorded information - On the other hand, if the objective is to determine completeness, the sample should be selected from a complementary population such as source documents (or cash disbursements if testing for unrecorded payables)

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2. Define Misstatements Misstatement is usually defined as difference that affects the correctness of the overall account balance Misstatements should be defined before sampling to: Preclude auditor from rationalizing away misstatements as isolated events Provide guidance to the audit team

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3. Define the Population Group of items in an account balance that the auditor wants to test. It does not include: Items the auditor has decided to examine 100% Items that will be tested separately Important to properly define the population: Sample results can be projected only to the group from which the sample is selected The population must be directly related to the audit objective

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**3. Define the Sampling Unit**

Sampling units are the individual auditable elements that make up the population Example: sampling units for confirming accounts receivable could be the individual customer's balance or individual unpaid invoices

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**Identify Individually Significant Items**

Many account balances are comprised of a few large dollar items and many smaller items Dividing a population into two or more subgroups based on dollar amount can increase audit efficiency Items in excess of a specified dollar amount (top stratum items) are examined 100% Items less than the specified amount (lower stratum items) are sampled This process (stratification) allows the auditor to examine a significant portion ($ value) of an account balance even though s/he examines a relatively few items

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**4. Choosing a Sampling Method**

There are a number of sampling methods an auditor may use Non-statistical Probability proportional to size (PPS) Classical sampling methods (not covered in this text/course) Mean-per-unit Ratio estimation Difference estimation

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**4. Choosing a Sampling Method – Cont’d - Differences between methods)**

Measure of sampling risk Statistical methods provide an objective measure of sampling risk Non-statistical methods do not provide such a measure Tests for account balance PPS is designed to test for overstatement of an account balance Classical methods test for both overstatement and understatement

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**4. Choosing a Sampling Method – Cont’d (differences between methods)**

Statistical estimates PPS provides an estimate of the amount of misstatement in the account Classical methods provide an estimated range of the account balance Sample selection PPS is a dollar-based approach; each dollar is a sampling unit Classical samples are selected using a variety of sampling units e.g. balances or items

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**4. Choosing a Sampling Method – Cont’d**

Use of PPS would be appropriate if Auditor is testing for overstatements in an account balance A dollar-based sampling approach increases the probability of selecting overstated items Few or no misstatements expected Individual book values (like a subsidiary ledger) are available

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**4. Choosing a Sampling Method – Cont’d**

One of the classical methods would be appropriate if the auditor Is concerned about understatements in an account balance Expects numerous misstatements Is examining an account balance based on estimates rather than a total of individual items Is trying to estimate an account balance

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**5 – 8. Determining Sample Size, Selecting Sample, Evaluating Results**

Sample size, method of selecting the sample, and the approach to evaluating sample results all depend on the sampling method used Whichever sampling method is used, consideration must be given to the risk of misstatement, sampling risk, and the auditor's assessment of tolerable and expected misstatement Tolerable misstatement Maximum misstatement an auditor will accept before deciding the recorded account balance is materially misstated Expected misstatement Based on results of other substantive tests and auditor's prior experience with the client Expected misstatement should be less than tolerable misstatement

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**Steps in non-statistical sampling?**

Determine sample size All significant items should be tested No way to mathematically control sampling risk Select the sample Sample must be representative of population Could use random-based method or haphazard selection Evaluate sample results Project misstatements to the population Consider sampling error Make judgment as to whether account is likely to be materially misstated

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**Probability Proportional to Size (PPS) Sampling**

Dollar-based sampling approach where the population is the number of dollars in the account balance examined Using dollars as sampling units means larger dollar items in the account balance are more likely to be selected in the sample PPS is an effective sampling approach when the auditor is testing for overstatements Appropriate when few misstatements are expected and individual book values are available

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**Probability proportional to size (PPS) sampling: TD risk**

To use PPS, the auditor must determine the allowable risk of the sample failing to detect a material misstatement (test of details risk) and tolerable and expected misstatements for the account balance Detection risk is the risk that the substantive audit procedures will fail to detect material misstatements There are two types of substantive audit procedures - those that use sampling, and other (non-sampling) substantive procedures Test of details (TD) risk is the part of detection risk related to sampling; the risk that substantive sampling procedures will fail to detect a material misstatement Other substantive procedures risk (OSPR) is the risk that the non-sampling procedures will fail to detect a material misstatement

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**Probability Proportional to Size (PPS) Sampling: TD risk– Cont’d:**

The relation between TD risk and inherent and control risks and OSPR is inverse High inherent risk means the auditor is examining transactions that are susceptible to misstatement High control risk means the client controls are weak High OPSR means the non-sampling audit procedures are not effective in detecting material misstatements

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**Probability Proportional to Size (PPS) Sampling: TD risk– Cont’d:**

In each of these situations, the auditor would want to be more careful with his/her sampling procedures The auditor would want lower TD risk; less chance of failing to detect material misstatements with sampling procedures Lower TD risk means the auditor wants a lower risk of sampling procedures failing to detect material misstatements To achieve this lower risk of failing to detect, the sample size must increase

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**Probability Proportional to Size (PPS) Sampling: Sample Size**

PPS samples are usually selected using a fixed interval sampling approach The sampling interval (I) is calculated as I = TM - (EM x EEF) RF TM = Tolerable misstatement (in population) EM = Expected misstatement (in population) EEF = Error expansion factor (derived form tables) RF = Reliability factor (derived form tables) Error expansion and reliability factors are based on TD risk

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**Probability Proportional to Size (PPS) Sampling: Sample Size**

Sample size (n) is computed by dividing the account book value by the sampling interval n = Population Book Value Sampling Interval

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**Probability Proportional to Size (PPS) Sampling - Sample Selection**

Sample items are often selected using a fixed interval approach Every nth dollar after a random start A random start is required to give every dollar in the population an equal chance to be included in the sample The first sample item is the one that first causes the cumulative total (cumulative book value + random start) to equal or exceed the sampling interval Successive sample items are those first causing the cumulative total to equal or exceed multiples of the interval Sample composition: All top stratum items will be included in the sample Lower stratum items will be sampled

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**Probability Proportional to Size: Zero or Negative Balances**

Zero balances Items with zero balances have no chance of being selected using PPS If evaluation is necessary, zero balance items should be audited as a different population Two approaches to deal with population items with negative balances: Exclude them from the selection process and test them as a separate population Include them in the selection process and ignore the negative sign

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**Probability Proportional to Size: Sample Evaluation**

Based on sample results, the auditor computes the upper misstatement limit Upper misstatement limit (UML) Maximum dollar overstatement that might exist in the population Given the misstatements detected in the sample, at the specified TD risk level, UML is the sum of three components: Basic precision Most likely misstatement Incremental allowance for sampling error.

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**Probability Proportional to Size: Sample Evaluation – Cont’d**

If the UML is less than the tolerable misstatement, the account balance is considered fairly presented If the UML exceeds the tolerable misstatement, the account balance is not fairly presented and further work is necessary

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