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Chapter 15

Audit Sampling for Tests of Controls (TOC) and Substantive

Tests of Transactions (STOT)

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Representative samples

A representative sample is one in which the attributes in the sample of audit interest (exception rate for TOC or dollar misstatement for STOT) are approximately the same as those of the population.

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Sampling risk

Sampling risk refers to the likelihood that an auditor will reach an incorrect audit conclusion because the sample tested is not representative that of the population.

Sampling risk is an inherent part of audit Sampling risk is an inherent part of audit sampling because auditors did not test all the sampling because auditors did not test all the items in the entire population.items in the entire population. In other words, auditors cannot eliminate the In other words, auditors cannot eliminate the

sample risk entirely no matter how hard he/she sample risk entirely no matter how hard he/she tries.tries.

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Non-sampling risk

Non-sampling risk is the likelihood that an auditor fails to uncover exceptions when testing internal controls or fails to find material monetary misstatements when conducting substantive tests of transactions or tests of detail balances.

Non-sample risk occurs because Auditors choose a sampling plan that is improper to the

audit objective, and/or Auditors do not have proficiency to recognize exceptions

or monetary errors contained in the sample. With proper training and supervision, it is possible for

audit team to eliminate non-sample risk entirely.

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Audit objectives

Transaction-related1. Occurrence2. Completeness3. Accuracy4. Posting and summarization 5. Classification6. Timing

Balance-related1. Existence2. Completeness3. Accuracy4. Classification5. Cutoff6. Detail tie-in7. Realizable value8. Rights and obligations9. Presentation and disclosure

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Direction of tests for sales

CompletenessCompletenessstartstart

Occurrencestart

Customerorder

Shippingdocument

Duplicatesales

invoice

Salesjournal

Generaljournal

Accountsreceivablemaster file

==

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Sampling Approaches

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Sampling can be statistical or non-statistical (whether it relies on statistical theory to make inference)

Similarities: both statistical and non-statistical sampling follow a three-step process: Step 1: Plan the

sample (calculate sample size)

Step 2: Select the sample and perform the tests

Step 3: Evaluate the results.

Differences: Statistical sampling

Each item in the population has a known probability to be selected.

Auditor can rely on central limit theorem in which allows auditors to quantify sampling risk in Step 1 (Plan the sample) and Step 3 (Evaluate the results).

Non-statistical sampling bases on auditor’s judgment in which auditor auditor believes items selected will provide believes items selected will provide the most useful information.the most useful information.

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Probabilistic vs. Nonprobabilistic Sample Selection

Probabilistic sampling A method of

selecting a sample such that each population item has a known probability of being selected.

For instance, 95% confidence level with 5% sampling risk

Non probabilistic sampling A method of selecting a

sample such that each population item does not have a known probability of being selected.

Auditor uses professional judgment rather than implementing probabilistic methods.

Often terms as judgmental sampling.

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Examples of probabilistic and non-probabilistic sample selection

Non-probabilistic: Directed sample

selection (judgmental)

Block sample selection

Haphazard sample selection (costs vs. benefits)

Probabilistic: Random sample Random sample

selectionselection Systematic sample Systematic sample

selectionselection PPS (Probability

proportional to size) sample selection

Stratified sample selection (chapter 17)

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Non-probabilistic sample selection methods

Directed sample selection: An sampling method that the selection of sample item is based on auditor’s the selection of sample item is based on auditor’s judgments directed by the following criteria:judgments directed by the following criteria: Items most likely to contain misstatements (overdue Items most likely to contain misstatements (overdue

accounts, related-party transactions)accounts, related-party transactions) Items containing selected population characteristics (e.g., Items containing selected population characteristics (e.g.,

cash disbursement-month, account, types of transaction)cash disbursement-month, account, types of transaction) Large dollar amountLarge dollar amount

It is clear that directed sample selection method is not It is clear that directed sample selection method is not based on probability distributionbased on probability distribution

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Non-probabilistic sample selection methods Block sample selection: Samples are selected

according to auditor’s judgment using the following steps:1.1. Population is divided into blocksPopulation is divided into blocks2.2. Once the sample in the first block is selected, the Once the sample in the first block is selected, the

remainder of the block is chosen remainder of the block is chosen in sequencein sequence.. More blocks are better than few blocks because it is More blocks are better than few blocks because it is

more likely that sample selected will be representative.more likely that sample selected will be representative. Haphazard sample selection: samples are selected

without any conscious bias on the part of auditorswithout any conscious bias on the part of auditors Realistically, it is difficult for auditors to be completely Realistically, it is difficult for auditors to be completely

unbiased.unbiased.

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Probabilistic sample selection methods

Random sampling: A sample method in which every item in the population has an equal probability to be selected.Auditors who adopt this sample selection method

can use either random number tables or computer generated random numbers to select items from the population.

Random sampling is the most commonly-used probabilistic sampling approach used by auditorsUnder the risk-based audit approach, however,

auditors often relies on professional judgments in sample selection, instead of using random sampling.

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Probabilistic sample selection methods

Systematic sample selection:The interval is determined by dividing the The interval is determined by dividing the

population size by the number of sample items population size by the number of sample items desired [(3,151-651)/125 = 20].desired [(3,151-651)/125 = 20].

Then selects the items (one out of every twenty) Then selects the items (one out of every twenty) for the sample (auditor need to first randomly for the sample (auditor need to first randomly select a number between 0 and 19).select a number between 0 and 19).

Pro and con:Pro and con:Pro: easy to usePro: easy to useCon: sample may not be fully representative Con: sample may not be fully representative

(bias leads to systematic errors)(bias leads to systematic errors)

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Probabilistic sample selection methods

Probability proportional to size (PPS) sample selection method:A sample is taken in which the probability of A sample is taken in which the probability of

selecting any individual population item is selecting any individual population item is proportional to its recorded dollar amount.proportional to its recorded dollar amount.

Sampling unit is per recorded dollar (also called Sampling unit is per recorded dollar (also called monetary unit sampling or MUS) monetary unit sampling or MUS)

MUS is a form of PPS which is a very common MUS is a form of PPS which is a very common method for substantive tests of transactions and method for substantive tests of transactions and tests of detail balances.tests of detail balances.

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Probabilistic sample selection methods

Stratified sample Stratified sample selection (part of PPS):selection (part of PPS):The entire population is The entire population is

divided into sub-divided into sub-populations by size of populations by size of the recorded amountthe recorded amount

Larger sample sizes are Larger sample sizes are taken from the larger taken from the larger sub-populations (strata).sub-populations (strata).

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Sampling for exception rates (TOC)

The The occurrence rate (exception rate or deviation rate) Is the ratio of the items containing the specific attribute Is the ratio of the items containing the specific attribute

(audit interest). (audit interest). Examples of specific attribute (audit interest). Examples of specific attribute (audit interest).

The credit approval was been done prior to issuing a The credit approval was been done prior to issuing a sales ordersales order

The credit approval was done by someone with general The credit approval was done by someone with general and special authorization. and special authorization.

Sales invoices have been verified internally before Sales invoices have been verified internally before sending to customers.sending to customers.

Sales invoices have shipping documents and/or sales Sales invoices have shipping documents and/or sales order attached.order attached.

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Examples of possible exceptions (or dollar misstatements)

Following are types of exceptions may contain in the population: Deviations from client’s established policy

and procedures (i.e., internal controls -- TOC)

Monetary errors (misstatements) contained in the transaction classes (STOT)

Monetary errors (misstatements) contained in account balances (TDB)

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Terms used to plan audit sampling (Table 5-1 on page 485)

Characteristic or attribute (Table 15-2 on page 487 Characteristic or attribute (Table 15-2 on page 487 and Figure 15-2 on page 490)and Figure 15-2 on page 490) Acceptable risk of assessing control risk too low Acceptable risk of assessing control risk too low

(ARACR)(ARACR)Auditors conclude that internal control is effective

but in fact, it is not effective.The probability of over-reliance on internal controls The probability of over-reliance on internal controls

Tolerable exception rate (TER)Tolerable exception rate (TER)The maximum exception rate contains in the sample The maximum exception rate contains in the sample

that auditors will conclude the internal controls in the that auditors will conclude the internal controls in the population are acceptable.population are acceptable.

Estimated population exception rate (EPER)Estimated population exception rate (EPER) Initial sample sizeInitial sample size

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Terms used to evaluate sampling results

Number of Exceptions (1) # of exception from internal control

policies and procedures found in the sample

Sample exception rate (SER) Total exception rate (%) found in

the sample = (1)/sample size Computed upper exception rate

(CUER) Highest possible estimated

exception rate in the population at a given level of ARACR.

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I: Plan the sample

Step 1: State the objectives of the audit test.Step 1: State the objectives of the audit test. Step 2: Decide whether audit sampling applies.Step 2: Decide whether audit sampling applies. Step 3: Define attributes and exception conditions.Step 3: Define attributes and exception conditions. Step 4: Define the population.Step 4: Define the population. Step 5: Define the sampling unit.Step 5: Define the sampling unit. Step 6: Specify the tolerable exception rate.Step 6: Specify the tolerable exception rate. Step 7: Specify acceptable risk of assessing control risk too low Step 7: Specify acceptable risk of assessing control risk too low

(ARACR).(ARACR). Step 8: Estimate the population exception rate.Step 8: Estimate the population exception rate. Step 9: Determine the initial sample size.Step 9: Determine the initial sample size. Step 10: Select the sample.Step 10: Select the sample. Step 11: Perform the audit procedures.Step 11: Perform the audit procedures. Step 12: Generalize from the sample to the population.Step 12: Generalize from the sample to the population. Step 13: Analyze exceptions.Step 13: Analyze exceptions. Step 14: Decide the acceptability of the population.Step 14: Decide the acceptability of the population.

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Effect on sample size when the following factors change

Effect on initialChange in factor sample size

Increase acceptable risk ofIncrease acceptable risk ofassessing control risk too low (ARACR)assessing control risk too low (ARACR) Decrease

Increase tolerable exception rate (TER)Increase tolerable exception rate (TER) Decrease

Increase estimated populationexception rate (EPER) Increase

Increase population sizeIncrease population size Increase (minor)Increase (minor)

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Application of attributes sampling(effect of population size)

Population size is a minor consideration in Population size is a minor consideration in determining sample size.determining sample size.

The degree of representative is ensured by The degree of representative is ensured by the sample selection process more than by the sample selection process more than by sample size.sample size.

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Perform Audit Procedures of Billing of Customers and Recording the Sales in

the Records on Table 15-2

Table 15-2, Table 15-3, Figure 15-2, Figure 15-3, Figure 15-4, Figure 15-5

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Decide whether the population is acceptable

Revise TER or ARACR.Revise TER or ARACR. Expand the sample size.Expand the sample size. Revise assessed control Revise assessed control

risk.risk. Communicate with the Communicate with the

audit committee or audit committee or management.management.

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Any Questions?