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## Chapter 9

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**Chapter 9**Audit Sampling – Part b**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 Sampling to Test for Account Balance Misstatements (Substantive Testing)**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)**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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.**Probability Proportional to Size: Sample Evaluation –**Cont’d Evaluation: • 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