Audit sampling for tests of controls and substantive tests of transactions

©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 14


Representative Samples

A representative sample is one in whichthe characteristics in the sample of auditinterest are approximately the same as

those of the population.

Nonsampling risk is the risk thataudit tests do not uncover existing

exceptions in the sample,resulting in nonsampling errors.



Sampling risk is the risk that an auditor reachesan incorrect conclusion because the sample is

not representative of the population,resulting in sampling error.

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

Note: A 95% confidence level = 5% sampling risk.



Reducing Nonsampling Risk –Careful design of audit procedures,

Proper instruction, supervision, and review.

Reducing Sampling Risk – Adjust sample size,

Use appropriate method for selecting sample items.


Statistical VersusNonstatistical Sampling

Step 1 Plan the sample.

Step 2Select the sample

and perform the tests.

Step 3 Evaluate the results.

SimilaritiesSimilarities


Statistical VersusNonstatistical Sampling

Statistical sampling allows the quantification ofsampling risk in planning the sample (Step 1)

and evaluating the results (Step 3).

In nonstatistical sampling those items that theauditor believes will provide the most useful

information are selected. Conclusions are judgmental = judgmental sampling

DifferencesDifferences


Probabilistic Versus Nonprobabilistic Sample Selection

Probabilistic Sample Selection – Selecting a sample such that each population item has a known probability of being included in the

sample and the sample is selected by a random process.

Nonprobabilistic Sample Selection – Selecting a sample in which the auditor uses professional judgment rather than probabilistic

methods to select sample items.


Sample Selection Methods

1. Directed sample selection2. Block sample selection3. Haphazard sample selection

NonprobabilisticNonprobabilistic


Sample Selection Methods

1. Simple random sample selection2. Systematic sample selection3. Probability proportional to size sample selection4. Stratified sample selection

ProbabilisticProbabilistic


Nonprobabilistic SampleSelection Methods

Item selection based on auditor judgmental criteria

Items most likely to contain misstatements

Items containing selected population characteristics

Large dollar coverage

Directed Sample SelectionDirected Sample Selection


Nonprobabilistic SampleSelection Methods

Selection of several items in sequenceforming “blocks” of items

Selection without regard to size, source, or Distinguishing characteristics

Block Sample SelectionBlock Sample Selection

Haphazard Sample SelectionHaphazard Sample Selection


Probabilistic SampleSelection Methods

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

Random number tables



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.



Systematic Sample Selection ExampleSystematic Sample Selection Example

Population of sales invoices 652 – 3151Desired sample size = 125

Interval = (3151 – 651) / 125 = 20

Select a random start between 1 & 19 (ex. 9)First item in sample is invoice # 661 (652 + 9)

Remaining 124 items = 681 (661+20), 701 (681+20),721 (701+20) etc.



Probability Proportional to SizeSample Selection – for emphasis on

large dollar items

Probability Proportional to SizeSample Selection – for emphasis on

large dollar items

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

is proportional to its recorded amount (PPS).

Evaluated using monetary unit samplingDiscussed in Chapter 16



Stratified Sample SelectionFor emphasis on large dollar items

Stratified Sample SelectionFor emphasis on large dollar items

The population is divided into subpopulationsby size and larger samples are taken of the

larger subpopulations.

Evaluated using variables samplingDiscussed in Chapter 16


Sampling for Tests of Controlsand Substantive Tests of Transactions

The occurrence rate, or exception rate,is the ratio of the items containing thespecific attribute to the total number

of population items.Ex. invoices are not properly verified 3 percent of the time

Estimate the proportion (ratio) of itemsin a population containing a

characteristic or attribute of interest.


Sampling forException Rates

Following are types of exceptions inpopulations of accounting data:

– deviations from client’s established controls

– monetary misstatements in populationsof transaction data

– monetary misstatements in populationsof account balance details (requires a dollar estimate)


Sampling forException Rates

Exceptions versus Deviations

Difference between sample exception rate andpopulation exception rate is Sampling Error

Reliability of sampling error estimate isSampling Risk

Ex. Find a 3% sample exception rate and sampling error of 1%With a sampling risk of 10%. We conclude that the populationException rate is between 2 – 4% at a 10% risk of being wrong

(or 90% chance of being right)


I: Plan the Sample

Step 1 State the objectives of the audit test.

Step 2 Decide whether audit sampling applies.

Step 3 Define attributes and exception conditions.

Step 4 Define the population.

Step 5 Define the sampling unit.


I: Plan the Sample

Specify acceptable risk of assessingcontrol risk too low.

Estimate the population exception rate.

Determine the initial sample size.

Step 7

Step 8

Step 9

Specify the tolerable exception rate.Step 6


II: Select the Sample and Perform the Tests

Select the sample.

Perform the audit procedures.

Step 10

Step 11


III: Evaluate the Results

Generalize from the sampleto the population.

Analyze exceptions.

Decide the acceptability of the population.

Step 12

Step 13

Step 14


Plan the Sample: TER, ARACR, EPER

TER = Tolerable Exception Rate The exception rate that the auditor will permit in the

population and still be willing to use the assessed control risk (CR) and/or amount of monetary misstatements in the transactions (tolerable materiality).

Result of auditor judgment; affected by materiality. What amount of exceptions is material to reject a control? More controls operating for an audit objective results in

higher TER. High TER => low sample size; low TER => high sample size


Plan the Sample:TER, ARACR, EPER

ARACR = Acceptable Risk of Assessing Control Risk too low The risk the auditor is willing to take of accepting a control

as effective (or monetary amount as tolerable) when the true population exception rate is greater than TER.

ARACR = measure of sampling risk The lower the assessed control risk => the lower the

ARACR => the fewer tests of detailed balances.


Plan the Sample:TER, ARACR, EPER

EPER = Expected Population Error Rate A judgmental estimate based on knowledge of client. Used to determine appropriate sample size. Low EPER => low sample size As EPER approaches TER, more precision is needed and

larger sample size is needed.


Guidelines for ARACR and TER 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%


Effect on Sample Sizeof Changing Factors

Type of Change Effect on InitialSample Size

Increase acceptable risk ofassessing control risk too low Decrease

Increase tolerable exception rate Decrease

Increase estimated populationexception rate Increase

Increase population size Increase (minor)


Generalize Sample to Population

SER = Sample exception rate = exceptions/sample size

Subtract SER from TER = sampling error If sampling error is sufficiently large, then true

population exception rate is acceptable.


Decide the Acceptabilityof the Population

Revise TER or ARACR

Expand the sample size

Revise assessment control risk

Communicate with the auditcommittee or management

(good for all 3 options)


Statistical Audit Sampling

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

is attributes sampling.


Sampling Distribution

It is a frequency distribution of the resultsof all possible samples of a specified sizethat could be obtained from a population

containing some specific parameters.

Attributes sampling is based on thebinomial distribution.


Application ofAttributes Sampling

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 row

in order to get the initial sample size.

Use of the TablesUse of the Tables



Population size is a minor considerationin determining sample size.

Representativeness is ensured by the sampleselection process more than by sample size.

Effect of Population SizeEffect of Population Size



Select the table corresponding to the ARACR.

2 Locate the actual number of exceptions on the top of the table.

3 Locate the sample size on the far left column.

4

1

Read down the appropriate exceptions column untilit intersects with the appropriate sample size row

in order to get the CUER (calculated upper exception rate).

Use of the TablesUse of the Tables


End of Chapter 14

Audit sampling for tests of controls and substantive tests of transactions

Economy & Finance

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