AUDITING AND ASSURANCE SERVICES 1

Chapter 6: AUDIT SAMPLING

 LEARNING OBJECTIVES
1) Define audit sampling and its objective and describe the
requirements that apply to all audit samples-statistical and non-
statistical.
2) Identify the various means of gathering audit evidence.
3) Identify factors influencing the determination of sample size.
4) Understand the appropriate methods of selecting sample items.
5) Appreciate the application of audit procedures to a selected sample,
and the evaluation of sample results.
6) Consider sampling approaches to tests of controls, in particular,
attribute sampling.
7) Consider sampling approaches to substantive tests, in particular,
monetary-unit sampling.

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 TEXTBOOKS

1) Auditing and Assurance Services, A

Systematic Approach, by Messier, Glover &
Pruitt, McGraw-Hill, 12th edition, 2022
(Chapters 8, 9)
2) Kiểm toán – NXB Kinh tế TP.HCM – Khoa
Kế toán – Bộ môn Kiểm toán, Đại học Kinh tế
TP.HCM, 2017 (Chapter 4)

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 RELEVANT GUIDANCE

ISA 500 / VSA 500 Audit Evidence

ISA 530 / VSA 530 Audit Sampling

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 Audit Process
Audit Audit Audit Audit Audit
Engagement Planning Evidence Completion Reporting
• Obtain and review • Understanding • Performing tests
financial info the entity and its of controls and
• Evaluate client environment substantive tests
integrity (third parties to collect audit
• Assess RMM
and the previous
• Calculate evidence
auditor)
• Evaluate materiality • (Chap 5, 6)
independence • Response to
• Assess the audit assessed risk,
team’s competence audit strategy,
• Comply with ethical
and plan
requirements
• Decide to accept • (Chap 3, 4)
• Prepare engagement
letter
• (Chap 2) 9/16/2024 5
 1. MEANS OF GATHERING AUDIT EVIDENCE

Selecting items
to test

Audit sampling Non-sampling methods

Selecting specific 100%

items examination
• high value or high risk • used where a
• Items selected will not population consists of
necessarily be only a few items
representative of the
population.

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 2. AUDIT SAMPLING

Importance
❖time and cost do not allow an audit of all the transactions, events,
and balances
❖It provides a reasonable basis for auditors to conclude the
population from which the sample is drawn.
▪ How many items to examine;
▪ Which items to select;
▪ How sample results are evaluated and extrapolated to the
population.

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 Audit Sampling > Definition and Features

The application of an audit procedure to less ❖to understand

than 100% of the items within a population audit sampling,
to obtain audit evidence about particular two features of
characteristics of the population. particular
importance:
Some auditing Many auditing ▪ sampling risk;
procedures can be procedures do not
and
applied by sampling involve sampling
▪ characteristic of
interest.

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 Audit Sampling > Sampling Risk

Sampling risk Non-sampling risk

the risk that an auditor reaches the risk that the auditor
an incorrect conclusion reaches an incorrect conclusion
because the sample is not for any reason not related to
representative of the sampling risk.
population.
Common reasons:

ineffective failure to
audit recognize
procedures exceptions

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 Audit Sampling > Characteristics of Interest

Characteristics of
interest

Tests of control Substantive tests

deviation rate from an monetary misstatement
internal control policy in the balance
or procedure

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 Audit Sampling > Non-statistical versus Statistical Sampling

Non-statistical
Statistical Sampling
Sampling
sampling approach with the sampling approaches that
following characteristics: do not have characteristics
of statistical sampling
Random sample Use of probability
selection – items in theory to evaluate
Haphazard selection –
the population have sample results, including
chosen at will, but guarding
an equal chance of measurement of
against bias in the selection
being selected. sampling risk

Advantage: defensibility, Advantage: greater

thorough quantification application of audit
a matter for
of sampling risk experience
the auditor's
judgment

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 3. ATTRIBUTE SAMPLING FOR TESTS OF CONTROLS

Attribute
Sampling
A sampling
technique that is Involves examination
suitable for tests of documents for
of controls and particular attributes
addresses these related to controls
issues Results can be (e.g. authorization)
used to support or
refute an initial
assessment of
control risk.

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 Attribute Sampling for Tests of Controls

Auditor should consider

Audit objectives Tolerable error Allowable risk of Expected error

– the relationship – maximum error over-reliance – amount of error
between the rate that would – allowable risk of the auditor
sample and the still support assessing control expects to find in
objective of the control risk
risk too low the population
test assessment

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 Attribute Sampling for Tests of Controls

Steps in attribute sampling for tests of controls:

Define the attribute Specify tolerable Select a sample

1 3 deviation rate (TDR) 5 using random or
(audit objective) to
(See next slides) systematic sampling
be tested (See next slides)
e.g., whether purchase
orders have been Determine
properly authorized 4 Test the sample
sample size (n) 6
(See next slides) (See next slides)
Identify population
2 e.g., all purchase orders
in a given period 7 Evaluate the sample results
(See next slides)

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 Attribute Sampling for ToC > Specify Tolerable Deviation Rate

Tolerable deviation rate (TDR)

maximum error rate that would support control risk assessment
• controls at a higher control risk → • Relationship between tolerable
increase tolerable deviation rate deviation rates to associate and
and decrease sample size. planned levels of control risk:
• In practice, auditors usually assess Qualitative level Tolerable
control risk across three levels: of control risk deviation rate
high, medium, and low. Low 1% to 5%
• For 'high', the auditor would omit Medium 5% to 20%
tests of controls. High Omit test

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 Attribute Sampling for ToC > Determine Sample Size

Assume an auditor has specified one Reliability factor (R): Statistical factor extracted
tolerable deviation rate of 7% and a from supporting tables to aid in the calculation
desired level of assurance of 90% and of sample size and evaluation of sample results.
expects to find at most one deviation.
Using the formula, a minimum sample
size of 56 is computed as follows:
R 3.89
n= = = 56
TDR 0.07

n: sample size
R: reliability factor Notice that 3.89 is the reliability factor for one
TDR: tolerable deviation rate expected deviation at a 90% desired level of
assurance, from Table 10.2.
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 Attribute Sampling for ToC > Select Sample

Common sampling methods

Random selection Systematic selection

ensures that all items in the involves selecting items using a constant
population have an equal chance interval between selections, the first
of selection by using computerized
interval having a random start.
random number generators or
random number tables. Number of items
Sample in the population
=
interval Sample size

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 Select Sample > Random Selection > Example 1
An auditor wants a sample of 50 items from a population of sales invoices
numbered from 3689 to 9452. The figure shows the random selection of sales
invoices using https://www.random.org/integers/

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 Select Sample > Systematic Selection > Example 2

An auditor wants a sample of 10 items from a population of sales invoices

numbered from 3689 to 9452.
➢ Step 1: Calculate the sample interval: (9452-3689+1)/10=576.4 or 576

➢ Step 2: Give every item in population chance of selection by choosing a

random number (random start) between 3689 and 4265 (3689+576) to
determine the starting point for the sample, e.g. 4000.
➢ Step 3: Continue to add sampling interval to random start, and identify items
to be sampled, e.g. item nos. 4000, 4576, 5152, 5728, 6304, 6880, 7456,
8032, 8608, 9184.

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 Select Sample > Activity 6-1

1) Present your result using the website below to select a sample of 20

items from a population of cash receipts numbered from 1 to 592.
https://www.random.org/integers/

2) Suppose an auditor uses Systematic Selection to select a sample of 20

items from a population of cash receipts numbered from 1 to 592. What
are the invoices selected by the auditor?

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 Attribute Sampling for ToC > Test the Sample and Evaluate Results

Test the sample Evaluate sample results

Auditors use the audit ▪ The approach in practice is to use sample deviation
procedures to perform testing rate (SDR) as the best estimate of population
on each item selected for the deviation rate (PDR). SDR is also PDR.
presence or absence of the For example, the auditor selects 25 items and finds
attribute. one error => SDR = 4% (= 1/25) => PDR = 4%
Audit procedures for ToC:
1. Inspection ▪ Compared with tolerable deviation rate (TDR). If SDR
2. Observation < TDR, sample results support the auditor’s planned
3. Inquiry
4. Re-performance reliance on internal control.

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 Attribute Sampling for ToC > Example 3

An auditor is testing whether all sales orders are authorized before being
processed. The auditor defines the attribute as “the presence of an authorization
signature on the sales order." A random sample of 100 sales orders is selected,
and the auditor checks each order to see if the signature is present.

▪ The auditor detected that 2 orders lacked proper authorization, i.e. 98 of the
100 orders are signed, and the sample deviation rate is 2% (SDR = 2/100 = 2%).
▪ Compared to the tolerable deviation rate, the auditor can conclude the internal
control is operating effectively because the SDR is lower than 5%.

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 4. MUS SAMPLING FOR SUBSTANTIVE TESTS
MUS is also called dollar-
Monetary-Unit unit sampling (DUS)
Sampling
(MUS)
effective for
a statistical audit
sampling method detecting
primarily used for overstatements,
substantive testing such as inflated
focuses on the
of account balances dollar amounts in a asset values or
population, giving revenue amounts
larger monetary
items a higher
chance of being
selected for testing
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 MUS Sampling for Substantive Tests

Steps in MUS sampling for substantive tests:

Identify audit Determine the Select the sample

1 3 sample size 5 Select the random start then
objective
e.g., to verify that the (See next slides) select the sample that includes
sales are accurate and items based on their monetary
free from material values (see next slides)
Calculate the
misstatements 4 sample interval Test the sample
(see next slides) 6 performs audit procedures
Identify population & on the selected items
2 sample unit
(e.g., the sales amount of $1 Evaluate the results
million consists of 9,000 7 analyzes misstatements identified, and
invoices) projects these to the entire population
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 MUS Sampling for ST > Determine Sample Size

Example 4:
BV × R
n= The sales amount of $1 million consists of 9,000
TM invoices;
n: Sample size Tolerable misstatement $50,000;
BV: Book value (or population value) The expected misstatement is zero and the risk
R: Reliability factor of incorrect acceptance is 5%;
TM: Tolerable misstatements → Reliability factor (R) = 3 (Table 10.2)
$1,000,000 × 3
n = = 60
$50,000

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 MUS Sampling for ST > Calculate Sample Interval

Example 5:
BV The sales amount of $1 million consists of
SI = 9,000 invoices;
n
Tolerable misstatement $50,000;
SI: Sample interval The expected misstatement is zero and the risk
n: sample size of incorrect acceptance is 5%;
BV: Book value (or population value) → Reliability factor (R) = 3 (Table 10.2)
n = 1,000,000*3/50,000 = 60

$1,000,000
SI = = $16,667
60

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 MUS Sampling for ST > Select the Sample > Example 6
Cummulative Items $ Invoice Amount
Invoice no. Amount of items
total selected selected no. $
A1001 $6,000 $6,000
RS $14,068 A1003 $15,000
A1002 $1,000 $7,000
A1003 $15,000 $22,000 RS + SI $30,735 A1005 $12,000
A1004 $5,000 $27,000 RS + 2SI $47,402 A1006 $10,000
A1005 $12,000 $39,000
A1006 $10,000 $49,000 RS + 3SI $64,069 A1008 $17,000
A1007 $9,000 $58,000 RS + 4SI $80,736 A1009 $11,000
A1008 $17,000 $75,000
RS + 5SI $97,403 A1011 $7,000
A1009 $11,000 $86,000
A1010 $8,000 $94,000 …
A1011 $7,000 $101,000 RS + 58SI $980,754 A9999 $9,000
… … …
A9999 $9,000 $986,000 RS + 59SI $997,421 A10000 $10,000
A10000 $14,000 $1,000,000 Total $200,000
Population size (BV) $1,000,000
Sample size (n) 60 The random start is selected at any number
Sampling interval (SI) $16,667 from the first item ($6,000) to the sample
Random start (RS) 9/16/2024 $14,068 interval ($16,667) 27
 MUS Sampling for ST > Evaluate the Results > Example 7
Continue with examples 4, 5 and 6 from
the previous slides: ▪ Calculate the projected misstatements:
Assume that an auditor has examined Projected Misstatements Sample
= × BV ÷
the supporting documentation for the misstatements in the sample value

sales sample and found a net monetary Projected

overstatement in the sample of $2,000. = 2,000 *1,000,000/200,000 = $10,000
misstatements
The information is as follows:
Amount of sales (BV) $1 000 000 ▪ The projected misstatements ($10,000)
Number of invoices 9,000 are lower than the TM ($50,000)
Sample size 60 ▪ The auditor would conclude that the
The value of the sample $200,000
sales are not materially misstated.
Tolerable misstatement (TM) $50,000
Misstatements found in the sample $2,000
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 MUS Sampling for ST > Activity 6-2
An auditor wants to check 5 A/Rs from 10 A/Rs below using MUS. The starting point is
An auditor is conducting the audit using MUS sampling to select a sample of A/R items for
$15,500. What
examination. Theare the A/Rs
auditor selected
established by the auditor?
a tolerable By sending
misstatement confirmation
of $20,000, a reliableletters
factor at 1, and a
to customers, random
the start
auditor at $15,500.
discovers the What areowed
balance the A/Rs selected
by Mr. Tran by theChinh
Van auditor? By
is zero.
sending confirmation letters to customers, the auditor discovered that the balance owed
Suppose
by Mr. Tranthe tolerable
Van Chinh wasmisstatement
zero. What isisthe
$10,000. What
auditor's is the auditor’s
conclusion on the A/Rconclusion
tested? on
the A/R balance tested?
No. Accounts Receivable Amount No. Accounts Receivable Amount
1 Công ty Vận tải Bắc Nam 15,269 6 Công ty Cp Bình Minh 5,125
2 Ông Trần văn Chính 5,689 7 Công ty Giấy Bãi Bằng 13,698
3 Ông Nguyễn Văn An 12,356 8 Công ty Nhựa Hoà An 8,157
4 C ty TNHH Hoà Hương 4,750 9 Công ty TNHH Hoàng Hà 6,753
5 HTX May 10 9,369 10 HTX May mặc Bốn Mùa 2,568
Note: do not re-number the population.
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End of Chapter 6

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