Chapter 11
Audit Sampling Concepts
Discussion of Audit Procedures
 Nature
Technique (eg. computation,
observation, confirmation etc.)
 Type of evidence (eg. Internal,
external..)

 Timing

when procedures are performed
 Extent

the amount of work done when the
procedures are performed. Many audit
techniques are applied on a test basis
(on only a sample of the population)
Sampling Defined: SAS No 39
= application of an audit
procedure to less than 100 percent
of the items within an account
balance or class of transactions for
the purpose of evaluating some
characteristic of the balance or
class (AU 350.01).
Sample
Population
Audit Sampling Does Not Include:
 Tracing
several transactions through the accounting system
to gain an understanding internal control structure (walkthrough);
 Complete or 100% examination of population items
 Examining all items exceeding some dollar amount, and
testing the remaining items by analytical procedures or, in
some cases, not at all because they are immaterial; and
 Observing employees who are performing a control
procedure that does not leave an audit trail, such as
observing the physical inventory count.
 Enquiry, written representations, and internal control
questionnaires
 Analytical Procedures
Two purposes for audit sampling
Test of controls
Sample:
Purpose:
Usually from a class of transactions
Obtain evidence about client’s
(populations), such as:
control objective compliance:
Cash Receipts
Cash disbursements
Occurrence
Purchases (inventory
Authorization
additions)
Completeness
Inventory issues
Accuracy (valuation)
Sales on credit
Posting, Classification, Timing
Expense details
Examples of tests of controls
For a sample of recorded sales invoices, compare to
bill of lading, price list, quantity shipped, shipping
date and recalculate amounts
 Trace a sample of shipping documents to invoices
 For a sample of cash receipts compare to deposit
slips, check for approval, recalculate cash, trace to
daily report, compare dates, trace postings
 Trace daily reports to cash receipts

Two purposes for audit sampling
Test of Details


Purpose
Obtain evidence about
assertions related to financial
statement balances:
 Existence / Occurrence
 Completeness
 Valuation
 Ownership
 Presentation and disclosure
Sample:
Usually from items in an asset or
liability balance (population)
such as:





Accounts Receivable
Loans receivable
Inventory
Fixed assets
Accounts payable
Tests of Details: Examples



Confirm a sample of the receivables, investigate exceptions and
follow up non-respondents by vouching sales charges and cash
receipts to supporting documents (evidence of existence, rights
and valuation)
Obtain an aged trial balance of the receivables. Audit the aging
accuracy on a sample basis. Calculate and analyze the age status
of the accounts and the allowance for uncorrectable accounts in
the light of current economic conditions and the company’s
collection experience (evidence of valuation)
Vouch a sample of receivable balances to cash received after the
cutoff data (evidence of existence, rights and valuation)
Audit Sampling: Key Decisions

Which population should be tested and for what
(population)?

How many items should be included in the sample (sample
size)?

Which items should be included (selection)?

What does the sample information tell about the population
as a whole (evaluation)?
Non-sampling and Sampling Risk

An auditor can fail to reduce audit risk to an acceptably low
level because of:
Non sampling Risk:
improper assessment of inherent and/or control risk
 failed to apply audit procedures carefully, loss of
control over audit evidence
Inappropriate procedures
Lack of professional skepticism
Sampling Risk:
the probability that an auditor’s conclusion based
on a sample might be different from the conclusion
based on an audit of the entire population.

Non-sampling Risk
 Non-sampling
risk cannot be quantified. It
can only be guarded against.
 Public accounting firms attempt to minimize
non-sampling risk by :
Implementing good quality control
practices of hiring, training, and
supervising competent personnel,
Carefully designing audit program
procedures, and
Assigning appropriately qualified
auditors to each audit.

Sampling Terminology

How to select sample:
 Random selection
 All sampling units have equal chance of
selection. Good, but time-consuming
 Systematic random selection
 Random starting point. Less timcconsuming. Beware of systematically
recurring errors in popn.
 Directed sample selection
 Block sample selection
 Haphazard selection
Sampling Terminology



Whether to subdivide population or not
 Stratified vs. non-stratified sample
How to evaluate results
 Statistical vs. non-statistical
How to define sampling unit /what item to select
 Physical units
 Dollar units (= proportionate to size sampling)
Sampling Techniques

By Physical attribute:  By Dollar Unit:
 physical units are
 dollars are sampling
sampling units
units
 each unit has equal
 larger $ units have
chance of selection
greater chance of
selection
 may need to
compensate for
 no need to
high variability eg.
compensate for high
By stratification
variability or stratify
population by value
Sampling Terminology

What to look at once sample is identified
 Attribute sampling (yes/no)
 Variables sampling
Statistical vs. Non-statistical
 Either
either statistical or non-statistical
methods are permitted under GAAS.
 Objective of both is to enable the auditor to reach a
conclusion about an entire set of data by examining
only a part of it.
 Statistical sampling methods allow the auditor to
express sampling risk in mathematical terms. In
non-statistical sampling, the auditor gives
“thoughtful attention” to this risk
Statistical sampling
Statistical sampling = audit
sampling that uses the laws of
probability for selecting and
evaluating a sample from a
population for the purpose of
reaching a conclusion about the
population.
selected at random
 statistical calculations used to
measure and express the results
 does not require that laws of
probability be used to determine
sample size

Statistical vs. Non-statistical





Statistical:
-precise, definite,
objective description
of results
-requires
quantification of risk
and materiality
-requires a random
sample
-costly, training of
staff
 Non-Statistical:
 Less
rigid approach to
unique problems
 Permits auditors to be
vague about risk and
materiality
 Permits auditors to be
more subjective,
consider outside
factors
Sampling Steps

1. State the objectives of the audit test
 TOC: To ensure key control is operating
effectively, as documented, throughout period
of reliance
 TD: To determine amount of misstatements
related to assertion being addressed
 In both cases, must carefully specify procedure
to be applied and popn that it applies to
Sampling Steps

2. Define error or exception conditions
 TOC: Normally an attribute.


define exceptions advance of test so that the
auditors doing the test will know one when they see
it. Should be related to the key control, and should
be important enough that its exception could lead to
material errors.
TD: Normally an error amount, or audited
value which is compared to book value.
Sampling Steps

3. Define the population
=The set of all elements in the account or
class of transactions.
 Consider objective (eg. Direction of test)
 Ensure all items in population are subject to
selection (timing, physical location, proper
stratification if population is stratified)


4. Define the sampling unit

Physical unit or dollar units?
Sampling Steps

5. Specify your tolerances


TOC: Tolerable exception rate
 Depends on significance of transactions,
significance of control, and consequences of noncontrol
TD: Tolerable misstatement (related to materiality)
These are your benchmarks: if your test results lead you
to conclude that your “problems” (control
deviations/exceptions in TOC, errors in TD) exceed
these amounts, you will act accordingly.
Sampling Steps

6. Specify your sampling risk
TOC: Acceptable risk of assessing control risk
too low (ARACR)
 The lower your control risk, the higher the
reliance on internal controls, the lower this
risk must be
 TD: Acceptable risk of incorrect acceptance
(ARIA)
 From equation: AAR=IR*CR*DR

AAR=IR*CR*APR*ARIA

Sampling Steps

7. Estimate rate of problems in population
TOC: Expected population exception rate
 As this rate increases and approaches your
tolerable exception rate, your sample size
will have to increase
 TD: Expected population error rate
 Same as above

Sampling Steps

7. Determine sample size


TOC:
 TER
 ARACR
 EPER
 Population size if less than 1000
TD:
 Tolerable misstatement (relates to materiality)
 ARIA (relates to other components in risk model)
 Expected errors in population
 Population Size (book is incorrect!!)
 Some methodologies adjust for popn. Variability:
unncessary if DUS is used
Sampling Steps
8. Select sample and perform audit
procedures
 9. Generalize from sample to the
population

TOC:
 Compare sample exception rate to tolerable
exception rate. Consider ARACR.
 TD:
 Compare errors in sample and extrapolate
to population

Misstatements
Type
Definition
Calculation
Known
Actual errors found in the
sample
=sum of errors found
in sample
Most
Likely
Best estimate of errors in
popn, assuming sample is
representative
Possible amount of errors in
popn, given risk that sample
is not representative
-see next slide
Possible
Non stat sampling:
-use judgment
Stat sampling:
-use tables or
computers
Sampling Techniques

By Physical attribute:
 each unit has equal
chance of selection
 may need to
compensate for high
variability
 MLE =
$ amount of error in
sample
/ # of units in sample
* # of units in popn.

By Dollar Unit:
 larger $ units have greater
chance of selection
 no need to compensate
for high variability
 MLE =
 $ recorded amount of
popn
/ # of units in sample
* sum of proportionate
amounts of error in dollar
units in sample in error
Sampling Steps

10. Analyze exceptions or misstatements
TOC: consider:
 Pervasive ?
 Deliberate?
 Misunderstanding ?
 Related to FS balances ?
 TD:
 misunderstanding of GAAP?
 Isolated?
 intentional irregularity
 management override of controls

Sampling Steps

11. Determine acceptabilty of population
TOC: if results are unsatisfactory:
 Increase sample size (will decrease
ARACR)
 Set control risk higher, reduce reliance on
internal control
 TD:
 Increase sample size (will decrease ARIA)
 Have client correct (careful: just correcting
known errors will not affect MLE)
 Qualify audit report
