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©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 14 - 1

Audit Sampling for Tests ofControls and Substantive

Tests of Transactions

Chapter 15


Learning Objective 1

Explain the concept ofrepresentative (probabilistic)

sampling.


What does this have to do withrepresentative sampling and sampling risk?


Representative Samples

A representative sample (probabilistic) is one in which the characteristics in the sample of audit

interest are approximately the same asthose of the population. Example??Nonsampling risk is the risk that

audit tests do not uncover existingexceptions in the sample. Competence,

Budget, Boredom, Power-ticking. Matching task to worker, realistic budgets, review.

Modesto, CA, students, and a media hungry Professor


Representative Samples

Sampling risk is the risk that an auditor reachesan incorrect conclusion for population because the

sample is not representative of the population.

Sampling risk is an inherent part of sampling thatresults from testing less than the entire population.

How to reduce/measure? Increase sample size / appropriate (statistical) sampling methods. BUT – stat sampling/rep samples could increase nonsampling risk.

Say what????? Why NonStat sampling used.



Distinguish between statistical

and nonstatistical sampling (n?)

and between probabilistic and

nonprobabilistic sample selection

(which n?).


Statistical VersusNonstatistical Sampling

Step 1

Plan the sample: obj., attributes, exception, population, sampling

unit, stat or non-stat to get n.

Step 2Select the sample: (rep or non-rep?)

and perform the tests.

Step 3 Evaluate the results: SERgeneralize to pop., more

sampling?

SimilaritiesSimilarities


Statistical VersusNonstatistical Sampling

Statistical sampling allows the quantification ofsampling risk (ARACR) in planning the sample (Step 1) and evaluating the results (Step 3). Plusmust use Probabilistic (rep) sampling methods

In nonstatistical sampling Sampling risk is not quantified. More discretionwith sampling, more judgmental. Can use either

Prob. or non. Prob. Why use??

DifferencesDifferences


Sample Selection Methods

1. Directed sample selection2. Haphazard sample selectionOnly use w/ nonstat. sampling

Nonprobabilistic/nonrepresentativeNonprobabilistic/nonrepresentative


Sample Selection Methods

1. Simple random sample selection2. Systematic sample selection3. Probability proportional to size sample selection

Use with either stat. or nonstat. sampling.

Probabilistic/representativeProbabilistic/representative


Nonprobabilistic SampleSelection Methods

Item selection based on auditor judgmental criteria

Items most likely to contain misstatements: risk-based

Items containing selected population characteristics:5 shipping docs from each month or

30% of sample from one divisionLarge dollar coverage

Directed Sample SelectionDirected Sample Selection


Nonprobabilistic SampleSelection Methods

Auditor randomly selects sample items.

Haphazard Sample SelectionHaphazard Sample Selection

Me and my Nordstrom dress.



Select representative samples.


Probabilistic SampleSelection Methods – see handout

Simple Random Sample SelectionSimple Random Sample Selection

Every possible combination of elementsin the population has an equal chance

of constituting the sample.

Computer generation of random numbers


Probabilistic SampleSelection Methods

Systematic Sample SelectionSystematic Sample Selection

The auditor calculates an interval andthen selects the items for the sample

based on the size of the interval.

The interval is determined by dividingthe population size by the number of

sample items desired.


Probabilistic SampleSelection Methods

Probability Proportional to SizeSample Selection

Probability Proportional to SizeSample Selection

A sample is taken where the probabilityof selecting any individual population item

is proportional to its recorded amount.



Define and describe audit

sampling for exception rates.


Sampling forException Rates

The exception rate is the ratio of the items NOT containing the

specific attribute to the total numberof population items (e.g. invoice data not

traced to shipping doc. (ToT-occurrence)), daily batch total of qty shipped

NOT compared with qtybilled (I/C-occurrence)).

SER: 3 exceptions / 100 sample = 3%


Sampling forException Rates

Following are types of exceptions inpopulations of accounting data:

– deviations from client’s established controls

– monetary misstatements in populationsof transaction data – no shipping doc for

invoice

– monetary misstatements in populationsof account balance details – A/R not confirmed



Use nonstatistical sampling in

tests of controls and substantive

tests of transactions.


Terms Used inAudit Sampling

Terms Related to Planning: Table 15-1 p. 485Terms Related to Planning: Table 15-1 p. 485

Characteristic or attribute (test)

Acceptable risk of assessing control risk too low or accept ToT results (ARACR) = sampling risk!

Tolerable exception rate (TER)Estimated population exception rate (EPER)

Initial sample size: determined by all 3 above


Terms Used inAudit Sampling

Terms Related to Evaluating ResultsTerms Related to Evaluating Results

Exception

Sample exception rate (SER)

Computed upper exception rate (CUER)Mathematically incorporates (adds) sampling

risk or ARACR to SER (only related to stat. sampling)


I: Plan the Sample - Fig 15-2 p. 490

Step 1State the objectives of the audit test – Ex. ToT accuracy – Attribute 5.

Step 2 Decide whether audit sampling applies.

Step 3 Define attributes and exception conditions.Ex. Table 15-3 p. 488, attribute 5.

Step 4 Define the population– all sales invoices in year

Step 5 Define the sampling unit – sales invoice


I: Plan the Sample - Fig 15-2 p. 490

Specify acceptable risk of assessingcontrol risk too low or accepting ToT.Key – qual. w/ non-stat. quant. w/ stat.

Estimate the population exception rate. How?

Determine the initial sample size – useprofessional judgment, w/ statistical sampling use tables/computers. TER-EPER = precision smaller = bigger sample

Step 7

Step 8

Step 9

Specify the tolerable exception rate. How?Step 6


II: Select the Sample and Perform the Tests

Select the sample = prob. or non prob.

Perform the audit procedures.Fig 15-3 p. 494. Attribute 5:4 ex. / 100 sample- SER = 4%

Step 10

Step 11


III: Evaluate the Results-Fig 15-4 p. 496

Generalize from the sample to the population. SER sig. < TER: CR OK, ToT provides no adjustment: reduce AP and detail testing. SER≥TER: inc. CR, ToT – adj proposed (project to pop. or isolate w/ more sampling): do more AP/detailed tests. Too close to call? → Conservative (not an issue w/ stat)

Analyze exceptions – isolated or distributed?

Decide the acceptability of the population.

Step 12

Step 13

Step 14


Guidelines for ARACR and TER for Tests of Control

Factors:

Preliminary assessed control risk (lower)– ARACR/Sampling Risk (lower)

Significance of the transactions and related accountbalances that the internal controls are intended toaffect (higher) – TER (lower)


Guidelines for ARACR and TER for Tests of Control

Judgment

• Lowest assessed control risk• Moderate assessed control risk• Higher assessed control risk• 100% assessed control risk• Highly significant balances• Significant balances• Less significant balances

Guideline

• ARACR of low• ARACR of med.• ARACR of high• ARACR is N/A• TER of 4%• TER of 5%• TER of 6%


Guidelines for ARACR and TER of Tests of Transactions

Planned Reduction in ARACR for TER forSubstantive Tests of Substantive Tests Substantive TestsDetails of Balances of Transactions of Transactions

Large Low Low

Moderate Medium Medium

Small High High


Effect on Sample Sizeof Changing Factors Table 15-6 p. 493

Type of Change Effect on InitialSample Size

Increase ARACR Decreaseor sampling risk (usually constant)

Increase tolerable exception rate Decrease

Increase estimated populationexception rate Increase

Increase population size Increase (minor)


Decide the Acceptabilityof the Population

Revise TER or ARACR – no-no

Expand the sample size–isolate exceptions (known mist)

Revise assessment control risk, SOX 404?

ToT – book adj. and inc. APand detail testing

Is SER > TER???



Define and describe

attributes (statistical) sampling and

a sampling distribution.


Statistical Audit Sampling

The statistical sampling method mostcommonly used for tests of controlsand substantive tests of transactions

is attributes sampling.


Sampling Distribution

Attributes (statistical) sampling is based on thebinomial distribution (think 2 columns). And since

we quantify sampling risk and useonly representative samples, we can use

tables (like the normal distribution table you haveused for z or t-tests in stat classes)!



Use attributes sampling

in tests of controls and

substantive tests

of transactions.


Application ofAttributes Sampling

EPER and TER the same as non-statisticaltesting – see p. 496. Still judgments!

2 We quantify sampling risk (ARACR) = 5%, We want to be 95% confident in our conclusion.

3 How did we get initial sample size of 93? We judg-mentally selected a sample size of 100 on p. 496

1

See Fig 15-8 p. 506 – Attribute 5 wheredid all this come from?

See Fig 15-8 p. 506 – Attribute 5 wheredid all this come from?



Select the table corresponding to the ARACR.

2 Locate the TER on the top of the table.

3 Locate the EPER on the far left column.

4

1

Read down the appropriate TER column untilit intersects with the appropriate EPER rowin order to get the initial sample size = 93!

Get 93 invoices via a REPRESENTATIVE sample.

Use of the Tables – Table 15-8 (Sample Size) p . 504Use of the Tables – Table 15-8 (Sample Size) p . 504



Samples rounded up to even number–not necessary!

2 # exceptions same as p. 500, SER = 4%

3 Do not compare SER to TER like p. 496, go to Table 15-9 p. 505 to get Computed Upper Exception Rate (CUER) – compare CUER to TER. CUER > TER: I/C - increase CR, ToT – bookadjustment and/or increase AP and detail testing

1

Back to Figure 15-8 p. 506Back to Figure 15-8 p. 506



Use table that corresponds to your ARACR

2 Locate the SER on the top of the table.

3 Locate the Sample Size on the far left column.

4

1

Read down the appropriate TER column untilit intersects with the appropriate EPER row

in order to get the CUER – we are 95% confident that PER for no. 5 is ≤ 9.0, but 9.0 > TER = 5!

Use of the CUER tables – Generalize To Population – Table 15-9 p. 505

Use of the CUER tables – Generalize To Population – Table 15-9 p. 505


End of Chapter 15

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