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Chapter 9

Audit Sampling – Part b

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Basic steps:1. Specify audit objective

of the test2. Define misstatement3. Define population (and

sampling units)4. Choose sampling

method5. Determine sample size

6. Select sample

7. Audit selected items

8. Evaluate sample results

9. Perform follow-up work as necessary

10. Document sampling procedure and results

Sampling to Test for Account Balance Misstatements (Substantive Testing)

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1. Define Specify Audit ObjectiveSampling 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 eventsProvide 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 useNon-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)

A. Measure of sampling risk Statistical methods provide an objective

measure of sampling risk Non-statistical methods do not provide

such a measure

B. 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)

C. Statistical estimates PPS provides an estimate of the amount of

misstatement in the account Classical methods provide an estimated range of

the account balance

D. 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 balanceA dollar-based sampling approach increases the probability of selecting overstated items

Few or no misstatements expectedIndividual 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 balanceExpects numerous misstatementsIs 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) RFTM = 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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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

Probability Proportional to Size: Sample Evaluation – Cont’d