SECTION 400:

Testing Phase:

Figure 400.1: Methodology Overview 

Planning Phase:   

* Understand the entity's operations: Section 220:
 
* Perform preliminary analytical procedures: Section 225:
 
* Determine planning, design, and test materiality: Section 230:
 
* Identify significant line items, accounts, assertions, and RSSI: 
Section 235:
 
* Identify significant cycles, accounting applications, and financial 
management systems: Section 240:
 
* Identify significant provisions of laws and regulations: Section 245:
 
* Identify relevant budget restrictions: Section 250:
 
* Assess risk factors: Section 260:
 
* Determine likelihood of effective information system controls: 
Section 270:
 
* Identify relevant operations controls to evaluate and test: Section 
275:
 
* Plan other audit procedures: Section 280:
 
* Plan locations to visit: Section 285:

Internal Control Phase: 

* Understand information systems: Section 320:
 
* Identify control objectives: Section 330:
 
* Identify and understand relevant control activities: Section 340:
 
* Determine the nature, timing, and extent of control tests and of 
tests for systems’ compliance with FFMIA requirements: Section 350:
 
* Perform nonsampling control tests and tests for systems’ compliance 
with FFMIA requirements: Section 360:
 
* Assess controls on a preliminary basis: Section 370:

Testing Phase:
 
* Consider the nature, timing, and extent of tests: Section 420:
 
* Design efficient tests: Section 430:
 
* Perform tests and evaluate results: Section 440:
 
** Sampling control tests: Section 450:
 
** Compliance tests: Section 460:
 
** Substantive tests: Section 470:
 
*** Substantive analytical procedures: Section 475:
 
*** Substantive detail tests: Section 480:

Reporting Phase:

* Perform overall analytical procedures: Section 520:
 
* Determine adequacy of audit procedures and audit scope: Section 530:
 
* Evaluate misstatements: Section 540:
 
* Conclude other audit procedures: Section 550:
 
** Inquire of attorneys: 

** Consider subsequent events: 

** Obtain management representations: 

** Consider related party transactions: 

* Determine conformity with generally accepted accounting principles: 
560:
 
* Determine compliance with GAO/PCIE Financial Audit Manual: Section 
570:

* Draft reports: Section 580:

[End of figure]

410 - OVERVIEW: 

.01: 
During the testing phase, the auditor gathers evidence to report on the 
financial statements, internal control, whether the entity's systems 
are in substantial compliance with the three requirements of FFMIA, and 
the entity's compliance with significant provisions of laws and 
regulations. (See figure 400.1.) The following types of tests are 
performed in the testing phase:

* Sampling control tests may be performed to obtain evidence about the 
achievement of specific control objectives. If the auditor obtains 
sufficient evidence regarding control objectives through the use of 
nonsampling control tests (such as observation, inquiry, and 
walkthroughs including inspection of documents), sampling control tests 
are not necessary, as discussed in section 350. Further guidance on 
sampling control tests begins in section 450.

* Compliance tests are performed to obtain evidence about compliance 
with significant provisions of laws and regulations. Further guidance 
on compliance tests is in section 460.

* Substantive tests are performed to obtain evidence that provides 
reasonable assurance about whether the financial statements and related 
assertions are free of material misstatement. Further guidance on 
substantive tests is in section 470.

.02: 
Sampling is often used in these tests. Sampling requires the exercise 
of professional judgment as well as knowledge of statistical sampling 
methods. The following sections provide a framework for applying 
sampling to financial audit situations, but are not meant to be a 
comprehensive discussion. Additional background and guidance on 
sampling is provided in the Audit Guide Audit Sampling (2001 
issue),[Footnote 1] published in 1999 by the American Institute of 
Certified Public Accountants and in Using Statistical Sampling 
published by GAO (accession number 129810). The auditor should consider 
whether he or she needs to consult with the Statistician for assistance 
in designing and evaluating samples. The auditor should consider the 
costs and benefits in determining which type of sampling to use.

.03: 
During this phase, the auditor performs the following activities for 
each type of test:

* Consider the nature, timing, and extent of tests:

* Design efficient tests:

* Perform tests:

* Evaluate results:

Each of these processes is discussed below.

[End of section]

420 - CONSIDER THE NATURE, TIMING, AND EXTENT OF TESTS: 

CONSIDER THE NATURE OF TESTS:

.01: 
The auditor determines the testing methods that will best achieve the 
audit objectives for sampling control tests, compliance tests, and 
substantive tests. Testing methods generally can be classified as 
either analytical procedures or detail tests. Analytical procedures 
involve the comparison of the recorded test amount with the auditor's 
expectation of the recorded amount and the investigation of any 
significant differences between these amounts. Detail tests can be 
classified in two general categories: sampling and nonsampling. 
Sampling methods involve the selection of individual items from a 
population with the objective of reaching a conclusion on all the items 
in the population (including those not selected for testing). 
Nonsampling methods involve selections to reach a conclusion only on 
the items tested. Nonsampling requires the auditor to assess the risk 
of misstatement in the items not tested.

.02: 
The testing method selected by the auditor is a matter of the auditor's 
judgment, considering the objectives of the test, the nature of the 
population, the results of procedures performed during the planning and 
internal control phases (including combined risk assessment and test 
materiality), and possible efficiencies. For tests that involve 
sampling, efficiencies can be achieved by using a common sample for 
each test. These potential efficiencies are discussed further in 
section 430.

CONSIDER THE TIMING OF TESTS:

.03: 
As discussed in section 295 D, the auditor may choose to conduct tests 
before or after the balance sheet date (interim testing) or to conduct 
all tests as of the balance sheet date. Section 495 C provides guidance 
on interim testing, tests of the period between the interim date and 
the balance sheet date (the rollforward period), and related 
documentation.

CONSIDER THE EXTENT OF TESTS:

.04: 
For each type of test, the auditor determines, based on judgment, the 
extent of tests to be performed. Generally, the extent of sampling 
control tests is a function of the auditor's preliminary assessment of 
the effectiveness of controls and the number of control deviations 
expected. The extent of compliance tests is a function of the 
effectiveness of compliance controls. The extent of substantive tests 
is a function of combined risk and test materiality.

[End of section]

430 - DESIGN EFFICIENT TESTS: 

.01: 
After considering the general nature, timing, and extent of the tests 
to be performed, the auditor should design specific tests. The auditor 
should coordinate similar tests to maximize efficiency. For tests that 
involve sampling, efficiencies can be realized by performing numerous 
tests on a common sample (multipurpose testing).[Footnote 2] The 
auditor generally should minimize the number of separate sampling 
applications performed on the same population by attempting to 
effectively achieve as many objectives as possible using the items 
selected for testing.

.02: 
As discussed in section 480, there are several methods of selecting 
items for testing. When determining the selection method to use during 
a multipurpose test, the auditor generally should use the method 
considered most appropriate for substantive detail tests in the 
particular situation. Use of this selection method is usually the most 
efficient because sampling control and compliance tests generally can 
be based on any type of sample.

.03: 
For example, the auditor might use a sample of property additions to 
(1) substantively test the amount of additions and (2) test financial 
reporting controls over property acquisition. If a substantive test 
would require 135 sample items and if the test of financial reporting 
controls would require 45 sample items, the auditor should select 135 
items in the sample but test controls relating only to 45. The 45 items 
for control testing should be selected randomly or systematically (with 
a random start) from the 135 sample items. For example, beginning from 
a random start, every third item selected for substantive testing 
should be tested for controls. If appropriate, the auditor may test 
controls relating to all sample items to provide additional assurance 
concerning controls.

[End of section]

440 - PERFORM TESTS AND EVALUATE RESULTS: 

.01: 
The auditor should perform the planned tests and should evaluate the 
results of each type of test separately, without respect to whether the 
items were chosen as part of a multipurpose test. Guidance on 
performing and evaluating the results is presented for each type of 
test in the following sections:

* Section 450 - Sampling control tests,

* Section 460 - Compliance tests, and

* Section 470 - Substantive tests.

.02: 
Sometimes, tests performed with the expectation of obtaining certain 
results give other results. When this happens, the auditor may wish to 
expand a sample to test additional items. Unless planned for in 
advance, this generally cannot be done simply, as discussed in 
paragraphs 450.17, 460.02, and 480.28; the auditor should consult with 
the Statistician in such cases.

.03: 
The auditor should keep in mind that the consideration of the risk of 
material misstatement due to fraud (discussed in section 260 for 
planning) is a cumulative process that should be ongoing throughout the 
audit. During testing, the auditor may become aware of additional fraud 
risk factors or other conditions that may affect the auditor's 
consideration of fraud risk factors identified during planning, such as 
discrepancies in the accounting records, conflicting or missing 
evidential matter, or problematic or unusual relationships between the 
auditor and the entity being audited. The auditor should consider 
whether fraud risk factors or other conditions identified require 
additional or different audit procedures. (See section 540.):

.04: 
For CFO Act agencies and components listed in OMB audit guidance the 
auditor is required to report on the substantial compliance of their 
financial management systems with the requirements of FFMIA. The 
auditor should conclude on substantial compliance at the completion of 
the audit work based on work done in the internal control and testing 
phases, as discussed in section 540.

[End of section]

450 - SAMPLING CONTROL TESTS: 

.01: 
Controls that leave documentary evidence of their existence and 
application may be tested by inspecting this evidence. If sufficient 
evidence cannot be obtained through walkthroughs in combination with 
other observation and inquiry tests, the auditor generally should 
obtain more evidence by inspecting individual items selected using 
sampling procedures. The auditor may use multipurpose testing to use 
the same sample to test controls and/or compliance and/or balances 
(substantive test). This is usually more efficient. Alternatively, the 
auditor may design a sample to test controls alone. In this case, the 
auditor generally should use random attribute sampling (described 
beginning in paragraph 450.05) to select items for sampling control 
tests.

.02: 
When planning sampling control tests, the auditor should determine (1) 
the objectives of the test (including what constitutes a deviation), 
(2) the population (including sampling unit and frame), (3) the method 
of selecting the sample, and (4) the sample design and resulting sample 
size. The auditor should document the sampling plan in the workpapers. 
See section 495 E for example workpapers for documenting samples.

OBJECTIVES OF THE TEST:

.03: 
The auditor should clearly indicate the objectives of the specific 
control test. In designing samples for control tests, the auditor 
ordinarily should plan to evaluate operating effectiveness in terms of 
the rate of deviations in units or dollars from prescribed controls. 
This involves defining (1) the specific control to be tested and (2) 
the deviation conditions. The auditor should define control deviations 
in terms of control activities not followed. For example, the auditor 
might define a deviation in cash disbursements as "invoice not approved 
and initialed by authorized individual.":

POPULATION:

.04: 
In defining the population, the auditor should identify the whole set 
of items on which the auditor needs to reach a conclusion and from 
which the sample should be drawn. This includes (1) describing the 
population, (2) determining the source document or the transaction 
documents to be tested, and (3) defining the period covered by the 
test. When multiple locations are involved, the auditor may consider 
all or several locations as one population for sampling if the controls 
at each location are components of one overall control system. Before 
combining locations into one population, the auditor should consider 
such factors as (1) the extent of uniformity of the controls and their 
applications at each location, (2) whether significant changes can be 
made to the controls or their application at the local level, (3) the 
amount and nature of centralized oversight or control over local 
operations, and (4) whether there could be a need for separate 
conclusions for each location. If the auditor concludes that the 
locations should be separate populations, he or she should select 
separate samples at each location; he or she should evaluate the 
results of each sample separately.

METHOD OF SELECTION:

.05: 
The auditor should select a sample that he or she expects to be 
representative of the population. For tests of controls, attribute 
sampling achieves this objective. Attribute sampling requires random 
selection of sample items without considering the transactions' dollar 
amount or other special characteristics. IDEA or other software may be 
used to make random selections.

SAMPLE SIZE:

.06: 
In designing attribute samples for which inspection is the principal 
source of evidence of control effectiveness, the auditor should 
determine the objectives of the sample. For financial reporting control 
tests, the objective is to support the preliminary assessment of 
control risk as either moderate or low. For compliance and operations 
control tests, the objective is to support the preliminary assessment 
of the control as effective. In addition, for financial reporting and 
compliance control tests, there is an objective of obtaining evidence 
to support the auditor's report on internal control.

.07: 
To determine the sample size, the auditor uses judgment to determine 
three factors: the confidence level, the tolerable rate (maximum rate 
of deviations from the prescribed control that the auditor is willing 
to accept without altering the preliminary assessment of control 
effectiveness), and the expected population deviation rate (expected 
error rate). Once the auditor determines these factors, he or she may 
use software (such as IDEA) or tables to determine sample size and to 
determine how many deviations the auditor may find without having to 
change the control risk assessment. GAO uses Tables I and II. Table I 
on the following page may be used to determine the sample sizes 
necessary to support these preliminary assessments of controls and to 
conclude on the effectiveness of the controls. Tables I and II are used 
to evaluate the test results. The AICPA has other examples in its 
guidance, and the GAO factors are within the range of the AICPA 
examples. If an auditor chooses to use factors other than Tables I and 
II, he or she should consult with the Statistician.

.08: 
Tables I and II are based on a 90 percent confidence level. (This 
confidence level used at GAO is generally appropriate because the 
auditor obtains additional satisfaction regarding controls through 
other tests such as substantive tests, inquiry, observation, and 
walkthroughs.):

.09: 
Tables I and II are each based on different tolerable rates. Table I is 
based on a tolerable rate of 5 percent, and Table II is based on a 
tolerable rate of 10 percent. Each table shows various sample sizes and 
the maximum number of deviations that may be detected in each sample to 
rely on the controls at the determined control risk level. (See 
paragraphs 450.13-.15 for a discussion of the evaluation of test 
results.)[Footnote 3]

Figure 450.1: Sample Sizes and Acceptable Numbers of Deviations; (90% 
Confidence Level).

TABLE I: (Tolerable rate of 5%): 

(Use for determining sample sizes in all cases):

Sample size: 45; Acceptable Number of Deviations: 0.

Sample size: 78; Acceptable Number of Deviations: 1

Sample size: 105; Acceptable Number of Deviations: 2.

Sample size: 132; Acceptable Number of Deviations: 3.

Sample size: 158; Acceptable Number of Deviations: 4.

Sample size: 209; Acceptable Number of Deviations: 6

[End of table]

TABLE II: (Tolerable rate of 10%)

(Use for evaluating sample results only if preliminary assessment of
financial reporting control risk is low and deviations exceed Table I):

Sample size: 45; Acceptable Number of Deviations: 1.

Sample size: 78; Acceptable Number of Deviations: 4.

Sample size: 105; Acceptable Number of Deviations: 6.

Sample size: 132; Acceptable Number of Deviations: 8.

Sample size: 158; Acceptable Number of Deviations: 10.

Sample size: 209; Acceptable Number of Deviations: 14.

[End of table]










[End of table]

.10: 
For financial reporting controls, if the preliminary assessment of 
control risk is low or moderate, Table I may be used to determine 
sample size. OMB audit guidance requires the auditor to perform 
sufficient control tests to justify a low assessed level of control 
risk, if controls have been properly designed and placed in operation.

.11:
For compliance and operations controls, sample sizes may also be 
determined using Table I.

.12: 
The auditor may use the sample size indicated for 0 acceptable 
deviations (45 items). If no deviations are expected, the sample size 
will be the most efficient for assessing control effectiveness; if no 
deviations are found, the sample will be sufficient to support the 
assessment of control risk. However, the auditor may use a larger 
sample size if control deviations are expected to occur but not exceed 
the acceptable number of deviations for the table.

EVALUATING TEST RESULTS:

Financial Reporting Controls:

.13: 
To evaluate sample results, the auditor needs the sample size, the 
number of deviations, and the confidence level. The auditor may use 
software (such as IDEA) or tables to evaluate results.[Footnote 4] If 
the auditor used Table I to determine sample size, and deviations are 
noted that exceed the acceptable number for the sample size, the 
auditor should follow the guidance below in deciding how to revise the 
preliminary assessment of control risk:

* Low control risk: If the preliminary assessment of control risk is 
low and if deviations are noted that exceed the acceptable number for 
Table I, but not Table II, control risk may be assessed as moderate. 
For example, if the original sample was 45 items, the auditor may 
reduce the assessment of control risk to a moderate level if there is 
not more than 1 deviation. If the auditor finds more than 1 deviation 
with a sample size of 45 items, the auditor concludes that the 
controls being tested are not operating effectively and should 
reassess control risk as high.

* Moderate control risk: If the preliminary assessment of control risk 
is moderate and if control deviations exceed the acceptable number for 
Table I, the auditor should conclude that control risk is high. The 
preliminary assessment of control risk is based on the assumption that 
the controls operate as designed. If the preliminary assessment of 
control risk is moderate and if control tests indicate that the control 
is not operating as designed (deviations exceed the acceptable number 
in Table I), the auditor should conclude that the control is 
ineffective and revise the control risk assessment to high.

Compliance Controls:

.14: 
If Table I is used to determine sample size and deviations are noted 
that exceed the acceptable number for the sample sizes shown in Table 
I, the auditor should conclude that the compliance control is not 
effective. The auditor also should determine whether any deviations 
noted ultimately resulted in noncompliance with a budget-related or 
other law or regulation.

Operations Controls:

.15: 
If Table I is used to determine sample size and deviations are noted 
that exceed the acceptable number for the sample sizes shown in Table 
I, the auditor should conclude that the operations control is not 
effective. The auditor should not place reliance on ineffective 
operations controls when performing other auditing procedures.

OTHER CONSIDERATIONS:

.16: 
If, during the testing of sample items, the number of deviations 
exceeds the acceptable number of deviations in Table I or II (as 
applicable), the auditor concludes that the controls are not operating 
as designed. However, the auditor should consider whether there are 
other reasons for continuing to test the remaining sample items. For 
example, audit team management should determine whether additional 
information (such as an estimate of the population rate of occurrence) 
is needed to report control weaknesses as described in paragraphs 
580.31-.57. The significance of the weakness will determine how the 
auditor reports the finding and, therefore, which elements of the 
finding (condition, cause, criteria, possible effect, and 
recommendation or suggestion) need to be developed. Or, the auditor may 
want to include an interval estimate in the report. The auditor should 
consult with audit team management and the Statistician in deciding 
whether to complete the testing of the sample.

.17: 
If an unacceptable number of deviations is noted in the original sample 
and the auditor believes the use of a larger sample size might result 
in an acceptable number of deviations, the auditor should consult with 
the Statistician before selecting additional sample items. The 
selection and evaluation of additional sample items cannot be based on 
Tables I or II or on the formulas used by IDEA.

.18: 
The auditor should consult with the Statistician when projecting the 
rate of sample control deviations to a population for disclosure in a 
report. While typically stated as a percentage of transactions, the 
deviation rate is expressed as a percentage of dollars in the 
population if sampling control tests are performed on a sample selected 
using DUS (see paragraphs 480.14-.23).

[End of section]

460 - COMPLIANCE TESTS: 

.01: 
The type of provision of a law or regulation and the assessment of the 
effectiveness of compliance controls affect the nature and extent of 
compliance testing. Based on the type of provision (as discussed in 
paragraph 245.01) the compliance tests discussed below should be 
performed.

TRANSACTION-BASED PROVISIONS:

.02: 
To test transaction-based provisions, the auditor should use sampling 
to select specific transactions for testing compliance. The selection 
of transactions to test may be combined with tests of financial 
reporting, compliance, or operations controls and/or with substantive 
tests, as appropriate. If the selection is solely for compliance 
testing, the auditor generally should use a random attribute sample 
(see paragraph 450.05). To determine sample size, the auditor needs to 
make judgments as to confidence level, tolerable rate, and expected 
population deviation rate. Confidence level should be related to 
compliance control risk. For example, if the auditor determines 
compliance controls are effective, he or she may use an 80 percent 
confidence level; if ineffective, a 95 percent confidence level. 
Tolerable rate is the rate of transactions not in compliance that could 
exist in the population without causing the auditor to believe the 
noncompliance rate is too high. GAO auditors should use 5 percent for 
this. Since the auditor will assess the impact of all identified 
noncompliance, many auditors use zero as the expected population 
deviation rate. Using the above factors yields the following sample 
sizes:

[See PDF for image]

[End of figure]

Since the auditor usually reports compliance on an entitywide basis, 
the auditor may use these sample sizes on an entitywide basis. 
Evaluation of test results is discussed in paragraph 460.07. The 
auditor should test the entire sample, even if instances of 
noncompliance are detected. If compliance controls were assessed on a 
preliminary basis as effective and the results of testing indicated 
that this assessment is not appropriate, in the above example, the 
auditor should consult with the Statistician to determine the 
appropriate sample size and selection procedures. The auditor cannot 
merely choose the other sample size, but may, for example, increase the 
sample size from 32 to 65 by using sequential sampling and randomly 
selecting 33 additional items. The Statistician should also evaluate 
the results when a test is expanded.

QUANTITATIVE-BASED PROVISIONS:

.03: 
Generally, effective compliance controls should provide reasonable 
assurance that the accumulation/summarization of information is 
accurate and complete. If the compliance controls do not provide such 
reasonable assurance, the auditor should test the accumulation of 
information directly for existence, completeness, and summarization. 
Such tests may be either samples or nonsampling selections and 
generally should be designed to detect misstatements that exceed an 
auditor-determined percentage of the total amount of the summarized 
information or the amount of the restriction stated in the provision, 
if any (GAO generally uses 5 percent for this test materiality). (The 
amount of the restriction is described in paragraph 245.01.) Such tests 
may be discontinued if significant misstatements are noted that would 
preclude compliance. The test for compliance is the comparison of the 
accumulated/summarized information with any restrictions on the amounts 
stated in the identified provision.

.04: 
For example, if provisions of budget-related laws and regulations are 
considered significant and if related budget and consequently 
compliance controls are ineffective, the auditor should test the 
summarized information directly for the following potential 
misstatements in budget execution information:

* Validity: Recorded amounts are not valid. (See section 395 F for 
validity criteria for obligations, expended authority, and outlays.):

* Completeness: Not all amounts are recorded.

* Cutoff: Obligations, expended authority, and outlays are not recorded 
in the proper period.

* Recording: Obligations, expended authority, and outlays are not 
recorded at the proper amount.

* Classification: Obligations, expended authority, and outlays are not 
recorded in the proper account by program and by object, if applicable, 
including the proper appropriation year if the account has multiple 
years. (Examples of program and object classifications are provided in 
section 395 F.):

* Summarization: Transactions are not properly summarized to the 
respective account totals.

.05: 
An example of audit procedures to test for these misstatements is 
included in section 495 B.

PROCEDURAL-BASED PROVISIONS:

.06: 
In testing compliance controls relating to a procedural-based 
provision, the auditor generally would obtain sufficient evidence to 
conclude whether the entity performed the procedure and therefore 
complied with the provision. For example, the auditor's tests of 
compliance controls concerning receipt of information from grantees 
generally would provide evidence of whether such information was 
received and therefore whether the entity complied. If compliance 
control tests do not provide sufficient evidence to determine 
compliance, the auditor should perform additional procedures, as 
considered necessary, to obtain such evidence.

EVALUATING TEST RESULTS:

.07: 
For any possible instances of noncompliance noted in connection with 
the procedures described above or other audit procedures, the auditor 
should:

* discuss such possible instances with OGC and, when appropriate, the 
Special Investigator Unit and conclude whether noncompliance has 
occurred and the implications of any noncompliance;

* identify the weakness in compliance controls that allowed the 
noncompliance to occur, if not previously identified during compliance 
control testing;

* report the nature of any weakness in compliance controls and consider 
modification of the report on internal control as appropriate (see 
paragraphs 580.31-.55);

* consider the implications of any instances of noncompliance on the 
financial statements; and:

* report instances of noncompliance, as appropriate. (See paragraphs 
580.67-.75.):

[End of section]

470 - SUBSTANTIVE TESTS - OVERVIEW: 

.01: 
In the internal control phase, the auditor preliminarily assesses the 
level of combined (inherent and control) risk for each significant 
assertion within each significant line item or account (see section 
370). Substantive audit procedures should be applied to all significant 
assertions in significant financial statement line items and accounts. 
The auditor's objective during substantive tests is to determine 
whether the assertions are materially misstated and to form an opinion 
about whether the financial statements are presented fairly in 
accordance with GAAP. To determine if significant assertions are 
misstated, the auditor should consider designing substantive tests to 
detect each of the potential misstatements in assertions that were 
developed in the internal control phase (see section 330). In addition, 
the auditor should consider whether efficiencies can be achieved by 
using the concepts of directional testing, as discussed in paragraphs 
470.14-.16.

.02: 
Based on the level of expected overall audit assurance determined in 
the planning phase of the audit (see paragraph 260.04), the auditor 
should establish the minimum levels of substantive assurance for each 
level of combined risk. For example, based on the audit risk model in 
AU 350 and a desired overall audit assurance of 95 percent, GAO 
considers the following minimum levels of substantive assurance for 
each level of combined risk to be appropriate:

Low combined risk: 63%:

Moderate combined risk: 86%:

High combined risk: 95%:

Substantive assurance is the auditor's judgment that all of the 
auditor's substantive tests will detect misstatements that in total 
exceed materiality. Substantive assurance, which relates to the entire 
audit and correlates directly with the level of combined risk, is not 
the same as confidence level, which is for a specific sample. The 
higher the risk, the more substantive assurance required.

TYPES OF SUBSTANTIVE TESTS:

.03: 
There are two general types of substantive tests: (1) substantive 
analytical procedures and (2) tests of details. To achieve the required 
substantive assurance (discussed above) the auditor may use either of 
these tests or a combination of the two. The type of test to use and 
the amount of reliance to place on each type of procedure, within the 
framework of the audit matrix (discussed in paragraph 470.10), is a 
matter of the auditor's judgment and should be based on effectiveness 
and efficiency considerations.

Substantive analytical procedures:

.04: 
Substantive analytical procedures involve the comparison of a recorded 
amount with the auditor's expectation of that amount and investigation 
of any significant differences to reach a conclusion on the recorded 
amount. Analytical procedures involve a study of plausible 
relationships among both financial and nonfinancial data. A basic 
premise is that plausible relationships among data may reasonably exist 
and continue in the absence of errors, fraud, or changes in 
circumstances. (See AU 329.):

.05: 
Substantive analytical procedures may be performed at one of three 
levels for an assertion, as follows:

* Complete: The auditor relies solely on analytical procedures for all 
of the assurance required from substantive procedures. The procedure 
is so persuasive that the auditor believes that it will detect any 
aggregate misstatements that exceed test materiality.

* Partial: The auditor relies on a combination of analytical procedures 
and tests of details to obtain an appropriate level of substantive 
assurance. For partial assurance, the auditor believes that the 
analytical procedures should detect any aggregate misstatements that 
exceed test materiality.

* None: The auditor does not rely on analytical procedures for 
substantive assurance. All substantive assurance will be obtained from 
tests of details. In this situation, supplemental analytical 
procedures may be performed to increase the auditor's understanding of 
account balances and transactions, but not to provide any additional 
substantive assurance. These procedures are similar in scope to those 
performed on an overall basis at the financial statement level (see 
section 520).

.06: 
To determine whether to perform complete or partial substantive 
analytical procedures, the auditor should consider the effectiveness or 
persuasiveness and efficiency of such procedures. In so doing, the 
auditor should consider the factors discussed in detail in section 495 
A.

Detail tests:

.07: 
Detail tests are test procedures that are applied to individual items 
selected for testing and include:

* Confirming a balance or transaction or the related terms, such as 
accounts receivable or accounts payable, by obtaining and evaluating 
direct communication from a third party.

* Physically observing, inspecting, or counting tangible assets, such 
as inventory or property, plant, and equipment, and applying related 
procedures.

* Examining supporting documents to determine whether a balance is 
properly stated. For example, the auditor might examine invoices for 
property and equipment purchases.

* Recalculating, or checking mathematical accuracy of entity records by 
footing or crossfooting or by recomputing amounts and tracing journal 
postings, subsidiary ledger balances, and other details to 
corresponding general ledger accounts. For example, the auditor might 
recalculate unit cost extensions in an inventory list, foot the list 
(whether prepared manually or by computer), and trace the total to the 
general ledger amount.

.08: 
Detail tests are generally used in combination to provide sufficient 
substantive assurance about an assertion. For example, to test the 
valuation of accounts receivable, the auditor might confirm balances, 
recalculate the aging schedule, examine documents supporting the aging 
and specific delinquent accounts, and discuss collectibility with 
management. On the other hand, a single detail test procedure might 
provide substantive assurance about more than one of the five financial 
statement assertions. For example, a physical observation of inventory 
might provide evidence about existence, valuation, and presentation and 
disclosure.

.09: 
The minimum extent of detail testing to be performed is based on the 
combined risk assessment and the amount of assurance obtained from 
substantive analytical procedures, as illustrated in the Audit Matrix 
(figure 470.1).

DETERMINING MIX OF SUBSTANTIVE TESTS:

.10: 
In determining an appropriate mix of analytical procedures and detail 
tests, the auditor should consider the following matrix (figure 470.1) 
which illustrates the integration of such tests for each level of 
combined risk, when the auditor is using a desired overall audit 
assurance of 95 percent. GAO auditors should use this audit matrix.

Figure 470.1: Audit Matrix:

Assessed combined risk level: Low; Substantive assurance: 63%; 
Substantive assurance from analytical procedures[A]: Complete; Minimum
substantive assurance from detail tests: 0%; Substantive assurance 
from analytical procedures[A]: Partial; Minimum substantive assurance 
from detail tests: 50%; Substantive assurance from analytical 
procedures[A]: None; Minimum substantive assurance from detail tests: 
86%. 

Assessed combined risk level: Moderate; Substantive assurance: 86%; 
Substantive assurance from analytical procedures[A]: Complete; Minimum
substantive assurance from detail tests: 0%; Substantive assurance 
from analytical procedures[A]: Partial; Minimum substantive assurance 
from detail tests: 77%; Substantive assurance from analytical 
procedures[A]: None; Minimum substantive assurance from detail tests: 
86%.

Assessed combined risk level: High; Substantive assurance: 95%; 
Substantive assurance from analytical procedures[A]: Complete; Minimum
substantive assurance from detail tests: 0%; Substantive assurance 
from analytical procedures[A]: Partial; Minimum substantive assurance 
from detail tests: 92%; Substantive assurance from analytical 
procedures[A]: None; Minimum substantive assurance from detail tests: 
95%.

[A] Complete assurance from analytical procedures requires procedures 
that are extremely effective and persuasive to serve as the sole source 
of audit evidence for achieving the audit objective. This level of 
effectiveness or persuasiveness is very difficult to achieve when 
combined risk is assessed as high. Therefore, complete reliance on 
analytical procedures for substantive assurance in these situations is 
rare, particularly for balance sheet accounts.

[End of table]

.11: 
Additional factors to consider in determining an appropriate mix of 
analytical procedures and detail tests include the following:

* The nature and significance of the assertion being tested: Analytical 
procedures are generally more likely to be effective for assertions 
related to net cost statement accounts than for those related to 
balance sheet accounts. Significant assertions generally require more 
or higher quality audit evidence that may not be available from 
analytical procedures.

* The nature of the combined risk: Substantive tests should be designed 
to address the specific type and level of combined risk for each 
assertion. For example, for certain loss claim liabilities, detail 
tests might be used to search subsequent claim payments for potential 
liabilities in testing the completeness assertion, while analytical 
procedures might be applied to test the related valuation assertion by 
evaluating the amounts per claim.

* The availability of different types of evidence: Using evidence that 
can be readily obtained may be more efficient. For example, in federal 
government audits, the availability of budgets and other information 
may assist in performing analytical procedures.

* The quality of the respective types of evidence available: The higher 
the quality of a type of evidence, the greater the level of assurance 
the auditor may derive from that type (see paragraph 470.13).

* The anticipated effectiveness of analytical procedures: Detail tests 
should be used if analytical procedures are not expected to be 
effective.

.12: 
When determining the types of substantive tests to use, the auditor's 
goal should be to choose the mix of effective procedures that are 
considered to be the most efficient in combination with sampling 
control tests and compliance tests. The auditor should exercise 
judgment when assessing the effectiveness or persuasiveness of all 
audit procedures, particularly analytical procedures.

.13: 
When considering a procedure's relative effectiveness, the auditor is 
concerned about the expected quality of the evidence. The quality of 
evidence obtained in a substantive test depends highly on the 
circumstances under which it is obtained and should be evaluated with 
professional skepticism. The following are generalizations about 
evidence:

* Evidence obtained from independent third parties provides a higher 
level of assurance than that obtained from sources in the entity.

* Evidence obtained directly by the auditor through confirmation, 
physical examination, vouching, or recalculation provides a higher 
level of assurance than that obtained indirectly, such as through 
inquiry.

* Documentary evidence provides a higher level of assurance than oral 
representations.

* Evidence obtained at or near the balance sheet date concerning an asset 
or liability balance provides a higher level of assurance than that 
obtained before or after the balance sheet date, because the audit risk 
generally increases with the length of the intervening period.

* The lower the control risk associated with an entity's internal 
control, the higher the assurance concerning the information subject to 
that internal control.

OTHER EFFICIENCIES:

.14: In planning tests, the auditor should consider the relationships 
between recorded amounts to help in achieving efficiencies. For 
example, in double-entry accounting, a misstatement in one account 
affects at least one other (related) account. This relationship gives 
rise to the opportunity for testing more than one account with a single 
test. Similarly, the relationship between budgetary and 
proprietary[Footnote 6] accounts may provide the opportunity for 
efficiencies in testing.

.15: 
In double-entry accounting, a misstatement in one account affects at 
least one other (related) account. For example, a misstatement of 
accrued payroll typically results in a misstatement of payroll expense. 
In this example, a substantive test of accrued payroll should detect 
misstatements in both accrued payroll and payroll expense. In designing 
substantive tests, after considering combined risk and developing an 
understanding of each related account, the auditor should consider the 
effect of such tests on related accounts. For example, a test of 
revenue for completeness may provide substantive evidence about the 
completeness of accounts receivable. In many instances where double-
entry accounting is used, it may be efficient to (1) design an overall 
strategy that tests certain accounts substantively for either existence 
or completeness (the two assertions most affected by testing related 
accounts) and (2) rely on such tests to detect misstatements in the 
related accounts. For example, the auditor might test (1) assets and 
expenses directly for existence and (2) liabilities, equity, and 
revenue for completeness, thereby indirectly testing the related 
accounts for existence or completeness, as applicable. This logic is 
called a directional testing approach.

.16: 
In some instances, the auditor may need to supplement a directional 
testing approach to address specific combined risks. For example, if 
inherent and control risk factors warrant, the auditor might test both 
existence and completeness in a test of cutoff as of the balance sheet 
date. During initial financial statement audits, the auditor generally 
should test both existence and completeness directly, when those 
assertions are significant, because the cumulative knowledge about the 
interaction of accounts may be limited.

.17: 
The audit assurance that can be obtained from directional testing is 
diminished in balance-sheet-only audits if related accounts are not 
also tested and in audits of entities having single-entry accounting 
systems (since double-entry account interrelationships do not exist). 
In these instances, the auditor should test both existence and 
completeness directly when those assertions are significant.

.18: 
To maximize efficiency, the auditor should combine the testing of 
budgetary and proprietary accounts where the combination is 
appropriate. For example, the auditor may combine tests of outlays (on 
the statement of budgetary resources) with tests of cash disbursements 
(used to test net costs).

.19: 
If an entity has budget accounting records but does not maintain 
separate proprietary accounting records, or the proprietary records are 
incomplete, the auditor should directly test expended authority 
produced by the budget system and the items necessary to reconcile the 
budget to the proprietary accounts.

.20: 
Also, if (1) relevant budget restrictions relate to significant 
quantitative-based provisions of laws and regulations and (2) budget 
controls are not effective, the auditor should test the accumulation of 
budget amounts (see paragraphs 460.03-.05).

[End of section]

475 - SUBSTANTIVE ANALYTICAL PROCEDURES:

.01: 
This section provides guidance on the application of substantive 
analytical procedures. Analytical procedures are sometimes referred to 
as fluctuation analysis, flux analysis, predictive tests, or analytical 
review. These procedures consist of comparing recorded account balances 
with the auditor's expectations. The auditor develops an expectation or 
estimate of what the recorded amount should be based on an analysis and 
understanding of relationships between the recorded amounts and other 
data. This estimate is then used to form a conclusion on the recorded 
amount. A basic premise underlying analytical procedures is that 
plausible relationships among data may reasonably be expected to 
continue unless conditions are known that would change the 
relationship. (For further information, refer to AU 329 or the Audit 
Guide Analytical Procedures.):

.02: 
Scanning account detail and recomputation are two other audit 
procedures related to analytical procedures. Scanning consists of 
searching for unusual items in the detail of account balances. Scanning 
is an appropriate tool to investigate the cause of a significant 
fluctuation, but it is not considered a substantive analytical 
procedure on its own. Unusual items identified through scanning should 
be investigated to obtain substantive assurance about the unusual 
items. The auditor may independently compute an estimate of an account 
balance, which is sometimes referred to as recomputation or an overall 
test of reasonableness. These recomputations are considered substantive 
analytical procedures. When making recomputations, the auditor should 
assess the reliability of the data used and should follow the steps 
used for performing substantive analytical procedures.

.03: 
The risk of forming the incorrect conclusion on the account balance 
tested may be higher for substantive analytical procedures than for 
detail tests because of the procedures' extensive use of the auditor's 
judgment. Accordingly, quality control is of critical importance. To 
help maintain a high level of quality in these procedures, the 
assessment of the amount of reliance to place on the procedures, the 
design of the procedures, and the formulation of conclusions on the 
results of these procedures should be performed or closely supervised 
and reviewed by experienced audit team personnel.

PERFORMING SUBSTANTIVE ANALYTICAL PROCEDURES:

.04: 
If substantive analytical procedures are used, the auditor should 
perform steps a. through l. below:

a. Determine the amount of the limit. The limit is the amount of 
difference between the auditor's expectation and the recorded amount 
that the auditor will accept without investigation. The determination 
of the limit is a matter of the auditor's judgment; some guidelines are 
provided in paragraph 475.05. The guidelines consider the amount of 
substantive assurance desired from analytical procedures.

b. Identify a plausible, predictable relationship and develop a model 
to calculate an expectation of the recorded amount. Consider the type 
of misstatements that could occur and how those misstatements would be 
detected by the model.

c. Gather data for developing the expectation, and perform appropriate 
procedures to establish the reliability of the data. The reliability of 
these base data is subject to the auditor's judgment. The reliability 
of data is discussed further in section 495 A.

d. Develop the expectation of the recorded amount using the information 
obtained during the previous steps. The preciseness of the expectation 
is subject to the auditor's judgment and is discussed further in 
section 495 A.

e. Compare the expectation with the recorded amount, and note the 
difference.

f. Obtain explanations for differences that exceed the limit, since such 
differences are considered significant.

g. Corroborate explanations for significant differences.

h. Determine whether the explanations and corroborating evidence 
provide sufficient evidence for the desired level of substantive 
assurance. If unable to obtain a sufficient level of substantive 
assurance from analytical procedures, perform additional procedures as 
discussed in paragraphs 475.12-.17 and consider whether the difference 
represents a misstatement.

i. Consider whether the assessment of combined risk remains appropriate, 
particularly in light of any misstatements identified. Revise the 
assessment of combined risk, if necessary, and consider the effects on 
the extent of detail tests.

j. Document (on the Summary of Possible Adjustments as discussed in 
540.04) the amount of any misstatements detected by substantive 
analytical procedures and their estimated effects. The limit (the 
amount of the difference between the recorded amount and the 
expectation that does not require explanation) is not considered a 
known or likely misstatement and is not posted to the Summary of 
Possible Adjustments.

k. Conclude on the fair presentation of the recorded amount.

l. Include documentation of work performed, results, and conclusions in 
the workpapers. Required documentation is discussed in section 490.

GUIDELINES FOR ESTABLISHING THE LIMIT:

.05: 
As discussed above, the limit is the amount of the difference between 
the expected and recorded amounts that can be accepted without further 
investigation. GAO uses the following guidelines in establishing the 
limit for each level of reliance on analytical procedures for 
substantive assurance:

* Complete reliance: The limit is 20 percent or less of test 
materiality.

* Partial reliance: The limit is 30 percent or less of test materiality.

* No reliance: Substantive analytical procedures are not needed.

Auditors using different limits should document the basis for the limit 
used.

INVESTIGATING SIGNIFICANT DIFFERENCES:

Causes of significant differences:

.06: 
Differences between the expectation and the recorded amount typically 
relate to either factors not included in the model (such as specific 
unusual transactions or changes in accounting policies), a lack of 
preciseness of the model, or misstatements (either errors or fraud).

Amount of Difference to Be Explained:

.07: 
When obtaining explanations, it is usually helpful to review with 
entity personnel the model and assumptions used to develop the 
expectation. Entity personnel will then be in a better position to 
provide the auditor with a relevant explanation. If the amount of the 
difference exceeds the limit, the auditor generally should try to 
obtain an explanation for the entire difference between the recorded 
amount and the expectation. The portion of the difference that exceeds 
the limit must be explained (see figure 475.1). If the difference does 
not exceed the limit, an explanation is not required. The auditor 
should identify and corroborate all significant factors that may cause 
the expectation to differ from the actual amount, regardless of whether 
the factors increase or decrease the difference.

Figure 475.1: Amount of Difference Explained When:

Recorded Amount Exceeds Limit:

[See PDF for image]

[End of figure]

Corroboration of explanations:

.08: 
The relevance and reliability of corroborating evidence may vary 
significantly; therefore, the extent of corroboration of explanations 
is left to the auditor's judgment. Corroboration may consist of 
examining supporting documentation or corroborating explanations 
received from accounting department personnel with personnel from the 
appropriate operating department, who should be knowledgeable about the 
entity's operations. The explanations for the fluctuations should be 
quantified and should address the direction and magnitude of the event 
causing the fluctuation. The auditor should corroborate all 
explanations received. In determining whether sufficient corroborating 
evidence has been obtained, the auditor should consider the guidelines 
for complete and partial assurance discussed in paragraph 470.05. In 
evaluating explanations the auditor should consider whether the 
difference could be caused by error or fraud.

Example of an adequate explanation for a significant fluctuation:

.09: 
Assume that the auditor determined test materiality to be $25 million. 
Additionally, assume that the auditor has determined, after considering 
any inherent and control risks, that a substantive analytical procedure 
should be performed with a limit of $5 million. The auditor estimated 
interest expense at $80 million by multiplying the average loan balance 
of $1 billion by the average interest rate of 8 percent. Both of these 
averages were computed through a simple average of beginning-of-year 
and end-of-year amounts. The recorded amount of interest expense, $94.5 
million, is higher than the estimated amount by $14.5 million and 
exceeds the limit by $9.5 million.

.10: 
An explanation from entity personnel that "we borrowed more money this 
year and interest rates are higher than last year" would not be 
adequate. This explanation needs to be quantified and corroborated.

.11: 
An example of an adequate explanation follows:

Based on a review of correspondence from lenders, interest rates 
increased during the year and then fell and were computed to average 9 
percent based on a monthly average. Additionally, loan statements from 
lenders indicate that $100 million was borrowed and repaid during the 
year, and the additional borrowings were outstanding for 6 months. 
Therefore, the average loan balance was actually $50 million higher and 
the average interest rate was 1 percent higher than the figures used in 
the auditor's original estimate.

Therefore, the interest expense in excess of the expectation can be 
explained as follows (in thousands):

$1,000,000 X 1% = $10,000 + 50,000 X 9% = 4,500:

Total difference explained: $14,500:

Course of action in the event of inadequate explanations or 
corroborating evidence:

.12: 
If an explanation and/or corroborating evidence does not adequately 
explain the fluctuation sufficient to provide either complete or 
partial assurance, the auditor must perform additional substantive 
procedures. These procedures may consist of:

* increasing the effectiveness of the substantive analytical procedures 
by making the expectation more precise in order to obtain the amount of 
desired assurance,

* performing tests of details and placing no reliance on the 
substantive analytical procedures that were ineffective, or:

* treating the difference as a misstatement.

.13: 
The auditor should consider the relative efficiency of each of these 
options. Deciding whether to perform additional substantive procedures 
is a matter of the auditor's judgment. The additional procedures must 
provide the auditor with adequate assurance that aggregate 
misstatements that exceed test materiality have been identified.

.14: 
To increase the persuasiveness or effectiveness of an analytical 
procedure, the auditor generally needs to make the expectation more 
precise. The auditor can do so by:

* building a more sophisticated model by identifying more key factors 
and relationships,

* disaggregating the data (such as using monthly instead of annual 
data[Footnote 7]), or

* using more reliable data or obtaining greater confidence in the 
data's reliability by corroborating the data to a greater extent.

Measuring the precision of the expectation and the impact of changing 
each of these factors on the procedure's effectiveness is difficult and 
is left to the auditor's judgment.

.15: 
If detail tests are used to test the account balance because adequate 
explanations cannot be obtained or corroborated, the auditor still must 
obtain an overall understanding of the current-year financial 
statements when applying the required overall analytical procedures at 
the financial statement level. As discussed in section 520, 
significantly less work is needed to obtain this overall understanding 
of the financial statements than when using analytical procedures as a 
substantive test.

.16: 
Additionally, if analytical procedures originally performed as a 
substantive test do not provide the required assurance, the auditor may 
be able to use those procedures to supplement an understanding of the 
account balances or transactions after obtaining substantive assurance 
through detail tests.

.17: 
When the auditor places no reliance on substantive analytical 
procedures, all substantive assurance is provided by detail tests. In 
this situation, less rigorous, supplemental analytical procedures may 
be used to increase the auditor's understanding of the account balances 
and transactions after performing the detail tests. When using 
supplemental analytical procedures, the auditor uses judgment to 
determine which fluctuations require explanations.

[End of section]

480 - SUBSTANTIVE DETAIL TESTS: 

POPULATION TO BE TESTED:

.01: 
In designing detail tests, the assertion tested affects the choice of 
the population (an account balance or a portion of an account balance) 
from which items are selected. For example, the existence assertion 
deals with whether recorded assets or liabilities exist as of a given 
date and whether recorded transactions have occurred during a given 
period. To detail test the existence assertion, the auditor should test 
the recorded account balance by (1) selecting items from those that 
compose the account balance and (2) then testing those items to 
evaluate whether such inclusion in the account balance is proper. For 
example, to test an expense account for existence, the auditor might 
select individual expense amounts included in the balance from a detail 
general ledger and then examine invoices that support the expense 
amount. It would be inappropriate to select invoices directly and then 
trace invoice amounts to inclusion in the general ledger balance.

.02:
For the existence assertion, the test population should agree with or 
be reconciled to the recorded amount of the account balance being 
tested. The auditor should test reconciling items, if any, in an 
appropriate manner. If this is not done, the conclusion applies only to 
the test population (the available items), not the recorded population.

.03: 
Conversely, the completeness assertion deals with whether all 
transactions and accounts that should be presented in the financial 
statements are so included. To detail test the completeness assertion, 
the auditor should select from an independent population of items that 
should be recorded in the account. The auditor should (1) select items 
that should be recorded from a source that is likely to contain all the 
items that should be recorded and (2) determine whether they are 
included in the recorded balance. For example, to test completeness of 
recorded revenue, the auditor might select shipments from a shipping 
log (which is believed to be reasonably complete), trace them to 
recorded revenue amounts, and then test the summarization of those 
amounts to inclusion in the general ledger revenue balance. To test 
completeness of recorded accounts payable, the auditor might select 
from payments made subsequent to year-end plus invoices on hand but not 
yet paid and trace those in which the receipt of goods or services 
occurred before year-end to inclusion in year-end accounts payable 
(those where the receipt occurred after year-end should be tested for 
exclusion from accounts payable).

SELECTION METHODS FOR DETAIL TESTS:

.04: 
Detail tests may be applied to any of the following:

* all items composing the population;

* a nonrepresentative selection (nonsampling selection) of items; and:

* a representative selection (sample) of items composing the population.

Flowchart 1 (section 495 E) illustrates the process of deciding the 
selection method.

.05: 
Detail testing of all items composing the population is generally most 
appropriate for populations consisting of a small number of large 
items. For example, several large accounts receivable or investments 
might compose an entire balance.

.06: 
Detail testing of a nonrepresentative selection (nonsampling selection) 
is appropriate where the auditor knows enough about the population to 
identify a relatively small number of items of interest, usually 
because they are likely to be misstated or otherwise have a high risk. 
(Nonrepresentative selections may also be used to test controls by 
using inquiry, observation, and walkthrough procedures and to obtain 
planning information, for example, by performing a walkthrough to 
understand the items in the population.) While the dollar amount is 
frequently the characteristic that indicates that an item is of 
interest, other relevant characteristics might include an unusual 
nature (such as an item identified on an exception report), an 
association with certain entities (such as balances due from high-risk 
financially troubled entities), or a relationship to a particular 
period or event (such as transactions immediately before and after the 
year-end date). The effects of any misstatements found should be 
evaluated; however, unlike sampling, the results of procedures applied 
to items selected under this method apply only to the selected items 
and must not be projected to the portion of the population that was not 
tested. Accordingly, the auditor must apply appropriate analytical and/
or other substantive procedures to the remaining items, unless those 
items are immaterial in total or the auditor has already obtained 
enough assurance that there is a low risk of material misstatement in 
the population.

.07: 
Detail testing of a representative selection (sample) of items 
composing the population is necessary where the auditor cannot 
efficiently obtain sufficient assurance (based on the assessed combined 
risk and other substantive procedures including analytical procedures) 
about the population from nonrepresentative selections. The auditor 
selects sample items in such a way that the sample and its results are 
expected to be representative of the population. Each item in the 
population must have an opportunity to be selected, and the results of 
the procedures performed are projected to the entire population. (In 
random selection, each item has an equal chance of selection (see 
glossary for further discussion of definition); in dollar-unit sampling 
(DUS), each dollar has an equal chance of selection; in classical 
variables estimation sampling, each item in a stratum has an equal 
chance of selection.):

.08: 
The auditor may use a nonrepresentative selection for part of the 
population and a sample for the remainder of the population. For 
example, the auditor might select all inventory items with a book 
amount greater than $10,000,000, all items that have not had any 
activity in the previous 6 months, and a statistical sample of the 
balance of the population. The auditor would project the misstatements 
in the statistical sample to the population of items less than 
$10,000,000 with activity in the last 6 months. The auditor would also 
compute a combined evaluation for the three selections by adding the 
results of the 100 percent selections to the conclusion for the 
statistical selections.

.09:
The auditor should document in the workpapers (usually in the audit 
program) whether a selection is intended to be a representative 
selection (a sample projectable to the population) or a 
nonrepresentative selection (not projectable to the population); if it 
is a nonrepresentative selection, the auditor also should document the 
basis for concluding that enough work has been done to obtain 
sufficient assurance that the items not tested are free from aggregate 
material misstatement.

REPRESENTATIVE SELECTIONS (SAMPLING):

.10: 
The following paragraphs provide an overview of sampling, primarily 
with respect to the existence and valuation assertions. Similar 
concepts and methods apply to the completeness assertion, except that 
the population for selection differs. (See paragraphs 480.01-.03.):

.11: 
AU 350.45 indicates that samples may be either statistical or 
nonstatistical. In statistical sampling, the auditor uses probability 
theory to determine sample size, select the sample, and evaluate the 
results for the purpose of reaching a conclusion about the population. 
Statistical sampling permits the auditor to objectively determine 
sample size (based on subjective decisions about risk and materiality), 
objectively select the sample items, and objectively evaluate the 
results; thus, the auditor using statistical sampling determines 
objectively whether enough work has been performed. Because of these 
advantages, when a sample is necessary, the auditor should use 
statistical sampling. Software such as Interactive Data Extraction and 
Analysis (IDEA)[Footnote 8] allows the auditor to quickly perform the 
calculations necessary for statistical sampling.

.12:
In nonstatistical sampling, the auditor considers statistical concepts, 
but does not explicitly use them to determine sample size, select the 
sample,[Footnote 9] or evaluate the results. Because the auditor using 
statistical sampling objectively considers the same factors that the 
auditor using nonstatistical sampling should subjectively consider, the 
size of a nonstatistical sample should not be less than the size of a 
properly calculated statistical sample.

.13:
The auditor who uses nonstatistical sampling generally should first 
calculate a statistical sample size (generally using dollar-unit 
sampling), then add at least 25 percent. The 25 percent is protection 
because the nonstatistical sample is not as objective as the 
statistical sample. The auditor who wishes to use nonstatistical 
sampling for a particular test should obtain the approval of the 
Reviewer, in consultation with the Statistician, before performing the 
test. Approval is not needed to use nonrepresentative selections 
(nonsampling) since they do not involve projections.

.14:
In sampling, the sample must be selected from all the items that 
compose the population so that each item has an opportunity for 
selection (in statistical sampling, the auditor can determine the 
probability of selection). For example, the auditor might select sample 
items from a list of all accounts receivable balances that is 
reconciled to the related account balance. Selecting sample items from 
file drawers is not a valid selection method for any type of sampling 
unless the auditor has determined that all items composing the 
population are included in the drawers.

.15:
For statistical samples, sample items should be selected using random 
or dollar-unit selection methods. Computer software may be used. Manual 
selection should be based on random number tables, a computer-based 
random number generator, or through use of systematic selection (every 
nth item with a random start between 1 and n). For example, the auditor 
might begin with a random start and then choose every nth item, where n 
is the sampling interval. The sampling interval would be determined by 
dividing the number of items in the population by the desired number of 
selections.

.16:
The sample size is a function of the size of the population, the 
desired confidence level (based on the amount of substantive assurance 
the auditor requires from detail tests, as shown on the audit matrix in 
section 495 D), test materiality (based on design materiality, expected 
misstatements, and other factors discussed in paragraph 230.13), and 
the sample selection method.

.17:
Once the auditor decides that a sample is necessary, the choice of the 
sample selection method to be used is a matter of the auditor's 
judgment concerning the most efficient method to achieve the audit 
objectives. The following methods of sample selection are available for 
substantive testing:

* dollar-unit sampling (DUS)--see paragraph 480.21,

* classical variables estimation sampling--see paragraph 480.32, and:

* classical probability proportional to size (PPS) sampling (evaluating a 
PPS sample using a classical variables sampling approach)--see 
paragraph 480.34.

Attributes sampling may be used for tests of controls and for tests of 
compliance with laws and regulations. To use any sampling method for 
substantive testing that is not listed in this paragraph, the auditor 
should consult with the Statistician. (Stratification and/or use of 
ratio estimates and regression estimates often lead to smaller sample 
sizes. Multistage samples may reduce time and travel costs.):

.18:
Each of these methods yields a valid projected (likely) misstatement, 
and a valid upper limit at the desired confidence level. In addition, 
classical PPS and classical variables sampling yield a valid two-sided 
confidence interval (DUS yields a valid upper limit). The auditor 
chooses the method based on the test objectives and efficiency.

.19:
When deciding the sampling method, the auditor should consider whether 
the dollar amounts of the individual items composing the population are 
available (such as on a detail listing or a computer file), the 
expected amount of misstatements, and the relative cost and efficiency 
of each appropriate sampling method. Flowchart 2 (section 495 E) 
summarizes the process of choosing the sampling method once the auditor 
has decided a sample is necessary. The subsequent pages of the 
flowchart indicate the steps that the auditor generally should perform 
for each sampling method. Example workpapers to document attribute, 
dollar-unit, and classical variables sampling are in section 495 E.

.20:
If the dollar amounts of the individual items composing the population 
are known, the auditor should use DUS, classical PPS, or classical 
variables estimation sampling. If dollar amounts of these individual 
items are not known, see paragraph 480.36.

SAMPLE SELECTION:

Dollar-unit sampling (DUS):

.21:
Dollar-unit sampling (DUS)[Footnote 10] is a type of statistical 
sampling that the auditor generally should use when:

a. the dollar amounts of individual items in the population are known,

b. the primary objective is to test the overstatement of the population 
(see below for testing a population related to the line item),

c. the auditor expects that the total dollar amount of misstatement in 
the population is not large,[Footnote 11] and:

d. the amount of misstatement in an individual item cannot exceed the 
selected amount.[Footnote 12]

DUS is also known as probability proportional to size (PPS) and 
monetary unit sampling (MUS). DUS works best in populations where the 
total misstatement is not large and where the objective is to test for 
overstatement of a population. When the objective is understatement of 
a line item, the auditor often is able to define a related population 
to test for overstatement. For example, to test for understatement of 
accounts payable, the auditor would select a DUS of subsequent 
disbursements. See also paragraph 480.36.

.22:
In a manually applied DUS, a sampling interval (n) is used to select 
every nth dollar from the dollars in the individual items that compose 
the population. These items might be recorded amounts for individual 
receivable balances, inventory items, invoices, or payroll expenses. 
The item that contains the nth dollar is selected for testing. DUS is 
representative of all dollars in the population; however, larger items 
have a higher probability of selection (for example, a $2,000 item has 
an approximately twenty times greater probability of selection than a 
$100 item).

.23:
When the total misstatement in the population is not large, DUS will 
yield the smallest sample size for a given population, test 
materiality, and desired confidence level when all statistical sampling 
methods are considered. When the auditor expects that the population 
contains a large amount of misstatement, he or she should use classical 
variables sampling (see footnote 3 and paragraph 480.33).

.24:
In DUS, the auditor may compute the sample size manually (paragraphs 
480.24-.26) or by using computer software (paragraph 480.27). To 
calculate a dollar-unit sample size manually, the auditor uses the 
dollar amount of the population, test materiality (see section 230), 
and required confidence level. The auditor calculating sample size 
manually may use the statistical risk factor from figure 480.1 to 
determine sample sizes for the appropriate confidence level, as 
discussed below.

Figure 480.1: Statistical Risk Factors:

Confidence Level: 50%; Statistical; Risk Factor[A]: 0.7.

Confidence Level: 63%; Statistical; Risk Factor[A]: 1.0.

Confidence Level: 77%; Statistical; Risk Factor[A]: 1.5.

Confidence Level: 86%; Statistical; Risk Factor[A]: 2.0.

Confidence Level: 92%; Statistical; Risk Factor[A]: 2.5.

Confidence Level: 95%; Statistical; Risk Factor[A]: 3.0.

[A] These are based on the Poisson distribution, which approximates the 
binomial distribution. Therefore, the sample size computed using this 
table may differ slightly from the sample size computed using IDEA.

[End of table]

Section 495 D contains the audit matrix with the appropriate risk 
factor for each level of combined risk and reliance on substantive 
analytical procedures. See paragraph 480.27 for guidance on using IDEA 
to compute sample size.

.25: 
The statistical risk factors are used in the following formulas to 
determine the sampling interval and sample size for DUS:

1. sampling interval = test materiality ÷ statistical risk factor:

2. sample size = recorded amount ÷ sampling interval:

Sample sizes should be stated in whole numbers. Uneven amounts should 
be rounded up to the next whole number. For example, a sample size of 
40.2 items should be rounded up to 41 items.

.26:
For example, to test a recorded amount of $30 million with a test 
materiality of $900,000 and a 95 percent confidence level, the 
statistical risk factor would be 3.0. The sampling interval would be 
$300,000 (test materiality of $900,000 divided by the statistical risk 
factor of 3.0). Essentially, from a random start, every 300,000th 
dollar is selected. Therefore, the preliminary estimate of sample size 
of 100 items is calculated by dividing the recorded amount of $30 
million by the sampling interval of $300,000. Because the amount of 
certain items might equal or exceed the sampling interval, a selection 
might include more than 1 sample item (for example, a $600,000 
selection would include 2 of the 100 estimated sample items: $600,000/
$300,000 = 2), thereby making the actual number of items tested fewer 
than 100.

.27: 
When the auditor uses the IDEA software to calculate sample size, the 
inputs are materiality, expected total dollar amount of misstatements 
in the population, confidence level, and the dollar amount of the 
population. Whether the auditor should input design materiality or test 
materiality depends on why the auditor reduced design materiality to 
get test materiality (see paragraph 230.13). If the auditor reduced 
design materiality to test materiality because not all entity locations 
are being tested or because the area is sensitive to financial 
statement users, the auditor should input test materiality. If the 
auditor reduced design materiality to test materiality solely because 
misstatements were expected, the auditor should input design 
materiality rather than test materiality. The reason for this is that 
the auditor inputs the expected dollar amount of misstatements in the 
population, and the software considers it in adjusting materiality (if 
the auditor inputs test materiality, the adjustment will have been made 
twice).

.28: 
It is difficult to select additional items for a dollar-unit sample 
after the original sample is selected. If the auditor believes that 
extension of the sample might be necessary, the auditor generally 
should plan for that possibility and consult with the Statistician. For 
example, the auditor might use a 95 percent confidence level 
(statistical risk factor of 3.0) to select the sample but test only the 
number of items necessary to achieve the planned confidence level. The 
items tested should be spread evenly throughout all of the items 
selected. For example, in a manual selection, if a statistical risk 
factor of 1.5 is appropriate based on the planned confidence level, the 
auditor would make selections using a statistical risk factor of 3.0 
(twice as many selections as the factor of 1.5) and initially test 
every other selection (beginning with a random start).

.29: 
If the preliminary assessment of combined risk or reliance on 
substantive analytical procedures is not supported by the results of 
testing, the substantive assurance needed from detail tests increases, 
and the auditor would then test the additional items selected in the 
initial sample.

.30:
If additional sample items are not selected during the initial sample 
and it is necessary to select additional items, the auditor should 
consult with the Statistician to determine how to select the additional 
sample items. Selection of these additional items may be more complex 
and less efficient than if they were chosen during the initial sample.

.31: 
Section 495 F describes how to manually select items using DUS. 
Computer software, such as IDEA, generally should be used to select a 
dollar-unit sample.[Footnote 13] The choice of selection method used 
should be based on efficiency considerations.

Classical variables estimation sampling:

.32: 
Classical variables estimation sampling is a type of statistical 
sampling that the auditor should consider when the auditor expects that 
one or more of the following exist in the population: the dollar amount 
of misstatement in the population is large (see footnote 3); individual 
misstatements may exceed the selected amount of sampling units; 
significant understatements cannot be identified using other tests; 
there are no book amounts for each sampling unit; or the auditor cannot 
add the dollar amounts in the population (see flowchart 2 in section 
495 E).

.33: 
Classical variables estimation sampling is useful because it frequently 
results in smaller sample sizes in higher misstatement situations than 
those that would be obtained using DUS. Because applying this method is 
somewhat complex, the auditor should consult with the Statistician 
before using it. Classical variables sampling and classical PPS require 
knowledge of the population to determine sample size. In many audits, 
the auditor learns about the population over several audits and 
improves the plan each time.

Classical PPS Sampling:

.34: 
Classical PPS Sampling is a type of statistical sampling that the 
auditor should use when he or she is testing for overstatement of the 
defined population and finds a large misstatement rate. The sample is 
selected the same way as a dollar-unit sample (proportional to size). 
Since there is no exact way to determine sample size, the auditor uses 
DUS to calculate sample size. However, since classical PPS sampling is 
used when there are large misstatement rates, the auditor uses a 
conservative (high) estimate of the expected misstatement to avoid 
needing subsequently to expand the sample size to obtain a sufficient 
sample size.

.35: 
Since classical PPS yields a valid measure of likely misstatement and 
precision, it may be used whenever the only reason for using classical 
variables sampling otherwise is the expected large misstatement rate.

Sampling when dollar amounts are not known:

.36: 
DUS cannot be used if the dollar amounts of individual items in the 
population are not known. Classical variables estimation sampling might 
be used, but this has some difficulties: there is no way to accurately 
calculate the sample size without the individual dollar amounts, and 
the method is inefficient unless the auditor finds a large misstatement 
rate. Lack of individual dollar amounts usually occurs when testing the 
completeness assertion where the selection is made from a population 
independent of the population being tested (see paragraphs 480.01-.03). 
In one approach, the auditor might select a random or systematic sample 
of the individual items. For example, items might be randomly selected 
from a shipping log to test the completeness assertion for revenue.

.37: 
For this type of test, the sample size may be approximated from the 
total dollar amount of either the population that the auditor is 
sampling from (the total dollars of the shipping log if the total 
dollar amount is available) or the dollar amount of the population that 
the auditor is testing (the total recorded revenue). Because this 
method is less efficient than DUS, the preliminary estimate of sample 
size for this sample should exceed the sample size that would result 
from using DUS. GAO auditors should use at least a 25 percent increase 
in sample size.[Footnote 14]

.38: 
The auditor should consult with the Statistician in performing the 
evaluation. If the misstatement rate is large, they should consider 
using classical variables estimation sampling. While attribute sampling 
may be used to estimate the misstatement rate in the population, this 
will yield acceptable results only if just one or two misstatements are 
found. The auditor generally should use the upper limit of the 
misstatement rate to make a conservative estimate of the dollar amount 
of misstatement in the population. If the upper limit is less than 
materiality, the auditor has evidence that the population is free of 
material misstatement.

EVALUATION OF SAMPLE RESULTS:

.39: 
Evaluation involves several steps:

a. Projecting the results of the sample to the population (for 
nonstatistical samples, making a judgment about likely misstatement in 
the population).

b. Calculating either the upper limit of misstatement in the 
population or an interval estimate of misstatement or of the 
population audited value at the desired confidence level (for 
nonstatistical samples, considering the risk of further misstatement).

c. Considering the qualitative aspects of misstatements.

d. Reaching a conclusion as to whether the population is fairly stated.

e. Considering the effect of misstatements on the financial statements 
taken as a whole.

Steps a. and b. are usually done with software such as IDEA in 
consultation with the Statistician.

.40: 
The effects of any misstatements detected in a sample should be 
projected to the population. In doing so, the auditor should ask the 
auditee to determine the cause of any misstatement found. The auditor 
should project all misstatements unless he or she has obtained highly 
persuasive evidence that the misstatement is not representative of the 
entire population. If the evidence is highly persuasive that a 
misstatement is not representative of the population, the auditor 
should (1) perform procedures to test that the same type of 
misstatement does not exist elsewhere in the population, (2) evaluate 
the misstatement that is not representative, (3) evaluate the sample, 
excluding the misstatement that is not representative, and (4) obtain 
the approval of the Audit Director that the evidence is highly 
persuasive. The projected misstatement amount should be included in the 
Summary of Possible Adjustments as a likely misstatement, the 
evaluation of which is discussed in section 540.

.41: 
At the conclusion of the test, the auditor also should consider whether 
the assessment of combined risk remains appropriate, particularly in 
light of any misstatements identified. If the preliminary combined risk 
assessment was not appropriate, the auditor should consult with the 
Reviewer to determine whether the extent of substantive procedures is 
adequate.

.42: 
When understated amounts are detected in any sample designed primarily 
to test the existence assertion (i.e., designed to test primarily for 
overstatement), the auditor should consult with the Statistician in 
evaluating the sample results.

Calculating the projected misstatement for DUS:

.43: 
If the auditor does not use software to evaluate sample results, he or 
she may calculate projected misstatement as follows. For a misstatement 
detected in which the item equals or exceeds the amount of the sampling 
interval (each of which is selected for testing), the projected 
misstatement is the amount of the misstatement detected. For any other 
misstatement detected, the projected misstatement is computed as 
follows: (1) divide the amount of misstatement by the recorded amount 
of the sample item and (2) multiply the result by the amount of the 
sampling interval. The sum of all projected misstatements represents 
the aggregate projected misstatement for the sample. For example, 
assume the following two misstatements are detected in a sample for 
which the sampling interval is $300,000: (1) a $50,000 misstatement 
detected in a $500,000 item (which exceeds the amount of the sampling 
interval) results in a projected misstatement of $50,000, and (2) a 
$100 misstatement in a $1,000 sample item represents a 10 percent 
misstatement, which results in a projected misstatement of $30,000 (10 
percent of the $300,000 sampling interval). In this case, the aggregate 
projected misstatement is $80,000.

Converting a DUS to a Classical PPS sample:

.44: 
If a dollar-unit sample results in a large number of misstatements, it 
is likely that the evaluation calculated using the method illustrated 
above would indicate that the upper limit of misstatement in the 
population exceeds materiality (IDEA indicates the number of 
misstatements that would yield acceptable results). However, if there 
are a large number of misstatements,[Footnote 15] the auditor, in 
consultation with the Statistician, should evaluate the sample using 
classical PPS. This evaluation is complex and cannot be done directly 
using IDEA.

Evaluating the results of a classical variables estimation sample:

.45: 
The auditor should consult with the Statistician in evaluating the 
results of a classical variables estimation sample.

Evaluating the results of other samples:

.46: 
When misstatements are detected in a sample for which guidance on 
evaluation is not described above, the auditor should consult with the 
Statistician.

EFFECTS OF MISSTATEMENTS ON THE FINANCIAL STATEMENTS:

.47: 
The quantitative and qualitative effects of all misstatements detected 
in the audit --both known and likely --must be evaluated in relation to 
the financial statements as a whole. Section 540 provides guidance on 
this evaluation.

[End of section]

490 - DOCUMENTATION: 

.01: 
The auditor should document the nature, timing, and extent of tests 
performed during this phase of the audit, as well as the conclusions 
reached. The auditor should specifically identify the procedures used 
to obtain substantive assurance for an account balance. This 
identification is particularly important if detail tests are relied on 
for complete substantive assurance and supplemental analytical 
procedures are performed to increase the auditor's understanding of the 
account balances and transactions.

.02: 
For example, assume an entity incurs and accounts for operating 
expenses at 50 locations. After considering the guidance in section 295 
C regarding multiple-location audits, the auditor decides to obtain all 
the required substantive assurance from detail tests. The auditor 
subjects all operating expenses to a statistical sample and visits only 
the locations for which selections were made. Assume that the auditor 
decides to obtain additional knowledge of the current-year operations, 
particularly for locations not visited, through supplemental analytical 
procedures at all locations. These procedures consist of comparing 
current-year operating expenses with prior-year audited information by 
location and between locations.

.03: 
In the above situation, the auditor is obtaining the entire required 
amount of substantive assurance from detail tests. The comparison of 
the current-and prior-year amounts is considered a supplemental 
analytical procedure and does not provide substantive audit assurance 
that the auditor may use to reduce the detail tests. During this 
supplemental analytical procedure, the auditor may detect misstatements 
that were not detected during the detail tests. The auditor must 
consider the implications of these misstatements to determine if the 
original assessment of combined risk was appropriate and if the amount 
of substantive testing performed (the detail tests) was adequate. Even 
though misstatements may be detected during supplemental analytical 
procedures, these procedures cannot be relied on for substantive 
assurance.

.04: 
In the audit program, the auditor generally should explain the 
objectives of audit procedures. Also, written guidance either within or 
accompanying the audit program to explain possible exceptions, their 
nature, and why they might be important, may help auditors focus on key 
matters, more readily determine which exceptions are important, and 
identify significant exceptions.

.05: 
The auditor also should document, usually in the audit program, whether 
a selection is intended to be a representative selection (a sample 
projectable to the population) or a nonrepresentative selection (not 
projectable to the population). If it is a nonrepresentative selection, 
the auditor also should document the basis for concluding that enough 
work has been done to obtain sufficient assurance that the items not 
tested are free from aggregate material misstatement.

.06: 
As the audit work is performed, the auditors may become aware of 
possible reportable conditions or other matters that should be 
communicated to the auditee. The auditor generally should document and 
communicate these as described in paragraph 290.02.

.07: 
Documentation of this phase should specifically include (see section 
495 E for example workpapers):

For tests involving sampling:

** the sampling method used and any key factors regarding selection;

** the sample size and the method of determining it;

** the audit procedures performed; and:

** the results of tests, including evaluations of sample results, and 
conclusions.

For substantive analytical procedures:

** the model used to develop the expectation and the basis for the 
model;

** the data used and the data sources;

** the auditor's assessment of the reliability of the data used and 
procedures performed to establish or increase the amount of 
reliability, if applicable;

** the amount of the limit and the criteria for establishing the limit;

** explanations for fluctuations considered significant, sources of 
these explanations, and corroborating evidence obtained;

** the additional procedures performed and related conclusions if 
misstatements are detected or if the initial procedures are not 
considered adequate; and:

** conclusions regarding findings, including proper treatment of any 
misstatements detected and assessment of any other effects of these 
misstatements.

Interim testing procedures (see section 495 C for documentation 
guidance).

Any misstatements detected (which also should be referenced to their 
posting on the Summary of Possible Adjustments (see section 540) where 
they will be considered further).

[End of section]

495 A - DETERMINING WHETHER SUBSTANTIVE ANALYTICAL PROCEDURES WILL BE 
EFFICIENT AND EFFECTIVE: 

.01: 
The following factors should be considered when determining whether 
analytical procedures will be effective and efficient as a substantive 
test:

* nature of the account balance, the specific audit objective 
(including the assertions being tested), and any identified inherent 
or control risks;

* expected availability and reliability of explanations for fluctuations 
and related corroborating evidence;

* plausibility and predictability of the relationship;

* availability and reliability of data; and:

* preciseness of the expectation.

NATURE OF THE ACCOUNT BALANCE, THE SPECIFIC AUDIT OBJECTIVE, AND ANY 
IDENTIFIED INHERENT OR CONTROL RISKS:

.02: 
Analytical procedures are usually more effective for testing net cost 
statement amounts than balance sheet amounts. Balance sheet amounts are 
more difficult to predict because they are as of a specific point in 
time. Additionally, net cost statement amounts generally have 
relationships with various types of other data, such as cost of sales 
as a percentage of sales, interest expense as a function of the debt 
balance and interest rates, or sales revenue as a function of the 
number of units shipped and the average sales price. Analytical 
procedures are usually less effective for testing amounts that are 
subject to management discretion or are unpredictable, such as repairs 
or miscellaneous expenses.

.03: 
The auditor should consider the specific audit objective, including the 
assertions being tested, and any identified inherent and control risks 
to determine whether substantive analytical procedures will be 
effective and efficient in achieving the audit objective and level of 
assurance. The procedures need to be more effective if fraud, inherent, 
and control risks have been identified. The auditor can obtain three 
levels of substantive assurance from analytical procedures--complete, 
partial, or none. The effectiveness and the amount of assurance 
provided by an individual procedure are matters of the auditor's 
judgment and are difficult to measure.

.04: 
As discussed, the auditor may choose to rely completely on analytical 
procedures when the level of combined risk has been assessed as high. 
In these cases, the analytical procedures should be extremely effective 
and persuasive to serve as the sole source of audit evidence for 
achieving the audit objective. This level of effectiveness is very 
difficult to achieve when combined risk is assessed as high; therefore, 
complete reliance on analytical procedures for substantive assurance in 
these situations is rare, particularly for balance sheet accounts.

EXPECTED AVAILABILITY AND RELIABILITY OF EXPLANATIONS FOR FLUCTUATIONS 
AND RELATED CORROBORATING EVIDENCE:

.05: 
Explanations for fluctuations and related, reliable corroborating 
evidence may not always be readily available. This audit evidence is 
essential to using analytical procedures as a substantive test. The 
relative ease of obtaining explanations for significant differences and 
relevant, reliable corroborating evidence should be considered when 
determining whether analytical procedures will be the most efficient 
and effective substantive test.

PLAUSIBILITY AND PREDICTABILITY OF THE RELATIONSHIP:

.06: 
Relationships between the amount being tested (the recorded amount) and 
other data are an essential component of substantive analytical 
procedures. The relationships identified and used for these procedures 
should be good indicators of the account balance of the item being 
tested. To be considered a good indicator of the recorded balance, the 
relationship between the recorded amount and the other data should be 
plausible and predictable.

Plausibility:

.07: 
If one set of data provides a reasonable basis for predicting another 
set of data, the relationship between the two sets of data is 
considered to be plausible. As the plausibility of the relationship 
increases, so does the effectiveness of analytical procedures as a 
substantive test.

.08: 
For example, there is a plausible relationship between payroll expense, 
the average number of employees, and the average pay rate. This 
relationship generally is effective for estimating payroll expense for 
salaried employees. Alternatively, there is not usually a plausible 
relationship between revenue and interest expense; therefore, this 
relationship would not be used for testing.

Predictability:

.09:
The more predictable the relationship is, the more effective the 
substantive analytical procedure will be. Relationships are more 
predictable in a stable environment. As relationships become more 
complex as a result of increases in the number and type of contributing 
factors, related amounts become more difficult to effectively and 
efficiently predict.

.10: 
For example, payroll expense generally is very predictable if there is 
little employee turnover during the period, if all employees receive 
the same percentage raise at the same time, and if all employees are 
salaried. Payroll expense becomes more difficult to predict if any of 
these factors changes (e.g., high turnover resulting in a different mix 
of employee pay, a wide range of raises awarded at different times, or 
a mix of hourly and salaried employees). Therefore, to effectively 
estimate payroll expense, the auditor may need to use a more complex 
relationship that considers these factors.

.11: 
The relationships identified may be between the recorded amount and 
either prior-year or current-year data, using financial or nonfinancial 
data, including underlying business factors. For example, the auditor 
may estimate current-year (1) interest expense using current-year 
audited, long-term debt amounts and interest rate information or (2) 
sales revenue based on the auditor's estimate of the expected gross 
margin percentage applied to the audited cost of sales amounts. When 
using current-year relationships, the data used to estimate the 
recorded amount must be audited by a method other than a substantive 
analytical procedure that uses a relationship with the recorded amount.

.12: 
The auditor should exercise caution when using prior-year amounts as 
the basis for the expectation of the current-year recorded amount. The 
workpapers must document why, in the auditor's judgment, the prior-year 
amount, and any adjustments to that amount, have a plausible and 
predictable relationship with the current-year recorded amount. Any 
adjustments to the prior amount, such as for the effects of inflation, 
must be supported by reliable data and must be corroborated. 
Additionally, the prior-year amount must meet the criteria discussed 
below for reliable data. The easiest way to meet these criteria is if 
the prior-year amount is audited.

.13: 
As an example of prior-year relationship, assume that the payroll 
raises for the year were authorized at 5 percent and that the number 
and salary mix of employees have remained relatively stable. In this 
example, the auditor might reasonably expect current-year payroll 
expense to be 5 percent higher than the prior-year's payroll expense. 
However, the auditor would need to test the reliability of the 
percentage pay increase and the assumptions regarding the number and 
mix of employees.

AVAILABILITY AND RELIABILITY OF DATA:

Availability of Data:

.14: 
Data needed to perform analytical procedures as a substantive test may 
not always be readily available. The relative ease of obtaining 
relevant, reliable data should be considered when determining whether 
analytical procedures will be the most efficient and effective 
substantive test.

Reliability of Data:

.15: 
The reliability of the data used is important in determining the 
effectiveness of the substantive analytical procedures. The more 
reliable the data are, the more effective these procedures will be as a 
substantive test. In assessing the reliability of data, which is a 
matter of auditor judgment, the auditor should consider the following:

* the source of the data, including whether the data are audited or 
unaudited;

* conditions under which the data were gathered, including related 
internal controls; and:

* other knowledge the auditor may have about the data.

Sources of Data:

.16: 
Data obtained from an independent source outside the entity are 
generally more reliable than data obtained from inside the entity; 
however, the auditor should determine if the outside information is 
comparable to the item being tested. This issue of comparability is 
particularly important if the auditor is using industry statistics.

.17: 
Data obtained from entity sources are considered more reliable if the 
sources are independent of the accounting function and if the data are 
not subject to manipulation by personnel in the accounting function. If 
multiple data sources are used, the reliability of all sources should 
be considered.

Audited versus unaudited data:

.18: 
The auditor should consider whether the data are audited or unaudited 
because audited data are considered more reliable than unaudited data. 
If data are audited by the entity's IG office, they may be as reliable 
as data audited by independent auditors if the IG's work is considered 
adequate. (See FAM section 650.):

.19: 
Unaudited data are not considered reliable unless procedures are 
followed to establish their reliability. These procedures could consist 
of either tests of controls over data production or tests of the data. 
The extent of such procedures is left to the auditor's judgment. For 
example, interest rates from an entity's loan register may be used to 
estimate interest income. The reliability of this information may be 
established by including the interest rate on loan confirmations that 
are sent to the borrowers or by reviewing original loan documents.

Conditions under which the data were gathered:

.20: 
Another consideration of internal data is whether the data were 
developed under a reliable system with adequate financial reporting or 
operations controls. In some instances, testing operations controls may 
be appropriate to assess the reliability of the data used for 
substantive analytical procedures. The extent of this testing is a 
matter of the auditor's judgment.

.21: 
If the system used to develop internal data is computerized rather than 
manual, the auditor must perform additional procedures before relying 
on the data. The auditor must test either (1) the general controls and 
the specific application controls over the IS system that generated the 
report or (2) the data in the report.

.22: 
An auditor might choose to test operations controls when using entity-
prepared statistics for a substantive analytical procedure. For 
example, the auditor might choose to use Air Force statistics to test 
the reasonableness of its Airlift Services aircraft operating costs. 
The auditor might compare the per hour fuel and maintenance costs for 
Airlift Services cargo and passenger aircraft with the "block hour" 
costs incurred by major airlines for similar aircraft as published by 
Aviation Week and Space Technology. The auditor should first determine 
if the industry statistics are comparable, e.g., if the statistics are 
for the same or similar types of aircraft and if the types of items 
included in maintenance costs are similar. If appropriate, the auditor 
should identify and test the internal controls over the production of 
these operating statistics.

PRECISENESS OF THE EXPECTATION:

.23: 
The expectation, the auditor's estimate of the account balance, should 
be precise enough to provide the desired level of substantive 
assurance. When determining how precise the expectation should be, the 
auditor should determine the proper balance between effectiveness and 
efficiency. Any work to make the expectation more precise than the 
desired level of assurance is unnecessary and inefficient.

.24: 
To maximize efficiency, the auditor should conduct procedures at the 
minimum level of effort that can reasonably be expected to provide the 
assurance needed. If the audit objective cannot be achieved with the 
original expectation, the auditor may be able to perform additional 
procedures to make the expectation more precise. The preciseness of the 
expectation and changes in this preciseness are difficult to measure in 
quantifiable terms, unless the auditor uses regression analysis for the 
analytical procedures. If the auditor uses regression analysis, he or 
she should consult with the Statistician.

.25: 
Factors that influence the expectation's preciseness follow:

* The identification and use of key factors when building the model 
based on the relationships identified by the auditor: The expectation 
generally becomes more precise as additional key factors are 
identified.

* The reliability of the data used to develop the expectation: The 
expectation becomes more precise as the reliability of the data 
increases.

* The degree of disaggregation of the data: The expectation becomes 
more precise as the disaggregation of the data increases.

[End of section]

495 B - EXAMPLE PROCEDURES FOR TESTS OF BUDGET INFORMATION: 

.01: 
This section includes example procedures auditors may perform in 
testing budget information for the statements of budgetary resources 
and financing.

.02: 
In addition, if budget controls are ineffective and quantitative 
provisions of budget-related laws and regulations are considered 
significant, the auditor should perform audit procedures sufficient to 
detect the types of budget information misstatements listed in 
paragraph 460.04. Following is an example of procedures for testing 
obligation and expended authority transactions for these misstatements. 
(Test materiality for determination of sample sizes is discussed in 
paragraph 460.03.):

* Validity, cutoff, recording, and classification: Select obligations 
recorded as of the end of the audit period and expended authority 
transaction recorded during the audit period. Determine if each 
selected item is a valid obligation or expended authority transaction 
based on the criteria set forth in section 395 F and if each is 
recorded in the appropriate period. If the obligation or expended 
authority transaction is not recorded or is recorded in the incorrect 
period, determine the effects of this misstatement on budget amounts 
and consider whether the auditor's evaluation of budget controls is 
affected.

Also determine if each selected item is:

** recorded at the proper amount and:

** classified in the proper appropriation or fund account (also by 
program and by object, if applicable), including the proper 
appropriation year.

* Completeness and cutoff: First, select obligations and expended 
authority transactions recorded during the period following the balance 
sheet date. Second, examine open purchase orders, unpaid invoices, and 
contracts as of the report date. Third, select items representing 
payments by Treasury or cash disbursements by the entity during the 
audit period. (Substantive detail test selections of expenses and 
additions to inventory, property, and prepaid accounts may be used for 
this purpose if the populations from which they are selected are 
complete.) For each selection, determine whether the obligation or 
expended authority transaction is recorded in the proper period. If it 
is not recorded or is recorded in the incorrect period, determine the 
effects of this misstatement on budget amounts and consider any impact 
on the evaluation of budget controls.

If the selected obligation or expended authority transaction relates to 
the audit period and is recorded in that period, determine if it is:

** recorded at the proper amount and:

** classified in the proper appropriation or fund account (also by 
program and by object, if applicable), including the proper 
appropriation year.

* Summarization: Test the footing of the detail of the obligation 
account balance recorded as of the end of the audit period and expended 
authority accounts recorded during the audit period. Then reconcile the 
total of these details to the recorded totals for obligation and 
expended authority accounts as of the end of the audit period. (Audit 
software is often an effective tool for footing the transactions 
recorded in the accounts and for simultaneously selecting items for 
this test.):

.03: 
The audit procedures discussed above for testing expended authority 
transactions should be coordinated with the audit of the other 
financial statement amounts. For example, if appropriate, the tests of 
accounts payable for completeness may be coordinated with the selection 
of subsequent obligations and expended authority transactions described 
above.

.04: 
Following is an example of procedures for testing outlay transactions. 
These audit procedures also should be coordinated with the audit of the 
other financial statement amounts, chiefly cash disbursements.

* Validity and classification: Select outlays recorded during the audit 
period. Determine if an invoice and receiving report supports each 
selected outlay and determine the obligation that was liquidated by the 
outlay. Examine the support for the obligation and determine if the 
invoice billed for goods or services is related to (or properly 
"matches") the obligation (and, in turn, the appropriation). Obtain the 
accounting data of the matched obligation to include appropriation and 
year. Match these data to the type of services paid for of the selected 
outlay. Determine if the related appropriation authorizes payment for 
the services billed and paid.

.05: 
The auditor also generally should audit upward and downward adjustments 
of prior year obligations. If any of these adjustments relate to closed 
accounts, the auditor generally should determine whether the 
adjustments are in compliance with the requirements of the National 
Defense Authorization Act for fiscal year 1991, section 1405(a), 
Closing Appropriation Accounts, 31 U.S.C. 1551-1558.

[End of section]

495 C - MISSTATEMENTS IN INTERIM TESTING: 

MISSTATEMENTS IN INTERIM BALANCES:

.01: 
The auditor should use judgment to determine whether any misstatements 
detected in interim tests (see section 295 D for a discussion of 
factors to consider in deciding whether to use interim substantive 
testing of balance sheet accounts) warrant a revision of (1) the 
auditor's combined risk assessment and (2) the nature, timing, and 
extent of planned audit procedures. In determining the effects of such 
misstatements, the auditor should consider all relevant factors, 
including:

* the nature and cause of the misstatement,

* the estimated effects on the overall line item/account balance,

* whether the entity has subsequently corrected the misstatement, and

* the impact of the misstatement on other parts of the audit.

.02: 
Any financial statement misstatements detected should be discussed with 
entity management. Based on the nature and cause of the misstatements 
detected, the auditor should determine, and obtain supporting evidence 
on, whether the misstatements are isolated or are likely to occur in 
the remainder of the line item/account balance at the interim testing 
date and at the year's end. (See paragraph 480.40 for a discussion of 
the need to project all misstatements unless evidence is highly 
persuasive that a misstatement is isolated and the Audit Director 
approves.) The auditor should encourage management to correct any such 
misstatements in the population. Based on the following guidance, the 
auditor should use judgment to determine the extent, if any, that 
interim testing can be relied on, in conjunction with substantive tests 
of the rollforward period, to provide evidence on the year-end line 
item/account balance:

* If the misstatements are not material when projected to the entire 
population and are expected to be representative of the misstatements 
of the year-end balance, the auditor may rely on the results of the 
interim testing.

* If the auditor has obtained highly persuasive evidence that the 
misstatements are isolated (generally by nature, cause, or extent), the 
auditor may be able to rely on unaffected parts of the interim testing 
and apply procedures at the year's end to test only those financial 
statement assertions associated with the misstatements. For example, in 
interim testing of inventory, the auditor might determine that the 
misstatements concern only the costing of inventory; accordingly, 
reliance could be placed on other parts of the interim testing, such as 
those for the accuracy of the physical count, and only cost testing and 
related procedures would be required at the year's end.

* If the misstatements are material or pervasive, it might be necessary 
to place no reliance on the interim testing and to perform extensive 
substantive testing of the line item/account balance as of the balance 
sheet date.

.03: 
For any misstatements found during interim testing, the auditor should 
use judgment to evaluate, in a manner appropriate for the 
circumstances, the effects on the year-end balance.

TESTING THE ROLLFORWARD PERIOD:

.04: 
Because the auditor reports on the financial statements as of the 
year's end, not the interim test date, additional procedures must be 
performed to extend the interim conclusions to the year's end. The 
auditor should perform substantive tests of the rollforward period 
activity or the year-end balance. For example, after interim testing of 
the accounts receivable balance, the auditor might examine supporting 
documents for selected debits and credits to the balance during the 
rollforward period and/or might apply analytical procedures to compare 
the amount of rollforward activity, on a month-by-month basis, with 
that of preceding months or similar periods of preceding years.

.05: 
The auditor should determine the extent of the required substantive 
procedures based on the assessment of combined risk and test 
materiality, in substantially the same manner as for other substantive 
tests. In some instances, the auditor may determine that specific 
combined risk warrants additional substantive procedures at the year's 
end (such as cutoff tests). If control risk is moderate or low, the 
auditor should determine whether the internal controls as of the 
interim testing date were in place and were functioning effectively 
during the rollforward period (generally by reference to the results of 
tests of financial reporting controls which generally cover the entire 
year under audit for significant systems).

DOCUMENTATION:

.06: 
The auditor should document:

* the line items/accounts (and assertions, where applicable) to which 
interim testing is applied;

* the factors considered when determining whether to use interim 
testing;

* the audit procedures used to test interim balances and the rollforward 
period (including tests of controls, findings, and conclusions); and:

* the effects of any misstatements found during interim testing.

The following table illustrates the correlation between combined risk 
and the substantive assurance obtained from substantive analytical 
procedures and detail test. This example is based on 95 percent audit 
assurance.[Footnote 16] The table also provides the statistical risk 
factors to be used when the auditor manually computes sample size using 
DUS (see paragraph 480.17).

[End of section]

495 D - EXAMPLE OF AUDIT MATRIX WITH STATISTICAL RISK FACTORS: 

Figure 495 D.1: Example Audit Matrix:

Assessed combined risk level: Low; Substantive assurance: 63%; 
Substantive assurance from analytical procedures[A]: Complete; Minimum
confidence level for detail tests: 0%; Statistical risk factor[B]: 
N/A[C]; Substantive assurance from analytical procedures[A]: Partial; 
Minimum confidence level for detail tests: 50%; Statistical risk 
factor[B]: 0.7; Substantive assurance from analytical 
procedures[A]: None; Minimum confidence level for detail tests: 
63%; Statistical risk factor[B]: 1.0.

Assessed combined risk level: Moderate; Substantive assurance: 86%; 
Substantive assurance from analytical procedures[A]: Complete; Minimum
confidence level for detail tests: 0%; Statistical risk factor[B]: 
N/A; Substantive assurance from analytical procedures[A]: Partial; 
Minimum confidence level for detail tests: 77%; Statistical risk 
factor[B]: 1.5; Substantive assurance from analytical 
procedures[A]: None; Minimum confidence level for detail tests: 
86%; Statistical risk factor[B]: 2.0.

Assessed combined risk level: High; Substantive assurance: 95%; 
Substantive assurance from analytical procedures[A]: Complete; Minimum
confidence level for detail tests: 0%; Statistical risk factor[B]: 
N/A; Substantive assurance from analytical procedures[A]: Partial; 
Minimum confidence level for detail tests: 92%; Statistical risk 
factor[B]: 2.5; Substantive assurance from analytical procedures[A]: 
None; Minimum confidence level for detail tests: 95%; Statistical risk 
factor[B]: 3.0.

[A] Complete assurance from analytical procedures requires procedures 
that are extremely effective and persuasive to serve as the sole source 
of audit evidence for achieving the audit objective. This level of 
effectiveness or persuasiveness is very difficult to achieve when 
combined risk is assessed as high. Therefore, complete reliance on 
analytical procedures for substantive assurance in these situations is 
rare, particularly for balance sheet accounts.

[B] Based on the Poisson distribution; used if sample size computed 
manually.

[C] Not applicable.

[End of table]

[End of section]

495 E - SAMPLING: 

SAMPLING FLOWCHARTS AND EXAMPLE WORKPAPERS:

.01: 
This section contains sampling flowcharts (pages 495 E-2 through 495 E-
6) and example workpapers for sampling (pages 495 E-7 through 495 E-
19).

.02: 
Flowchart 1 (page 495 E-2) is to assist the auditor in deciding 
selection method: nonrepresentative selections versus sampling 
(statistical or nonstatistical). Flowchart 2 (page 495 E-3) is to help 
the auditor determine which type of sampling to use in various 
situations. The second, third, and fourth pages of this flowchart are 
to assist the auditor in performing attribute, dollar unit, and 
classical variables estimation sampling.

.03: 
Example workpapers for documenting sampling are given for attribute 
sampling (pages 495 E-7 through 495 E-10), for dollar unit sampling 
(pages 495 E-11 through 495 E-15), and for classical variables sampling 
(pages 495 E-16 through 495 E-19).

[See PDF for images]

[End of figures]

[End of section]

495 F - MANUALLY SELECTING A DOLLAR UNIT SAMPLE: 

.01: 
Even though auditors usually use software (such as IDEA) to select a 
dollar-unit sample, it is helpful to understand the process for 
manually selecting a dollar-unit sample. To select a dollar-unit sample 
manually, the following steps should be performed:

a. Determine the sampling interval using the following formula:

sampling interval = test materiality ¸ statistical risk factor:

b. Clear the calculator:

c. Select and document a random start and enter as a negative number in 
the calculator. The random start should be a number between 1 and the 
sampling interval.

d. Enter the positive amounts in the test population (items) until the 
calculator's running subtotal becomes positive. The item that caused 
the subtotal to become positive is the item selected for testing.

[See page 495 F-3. Note that the calculator subtotals were positive for 
invoices #3, 10, 17, 19, and 24.]

Do not enter into the calculator any items in the population with zero 
or credit balances. These items should be accumulated separately and 
tested in conjunction with tests of completeness of the account balance 
or class of transactions if they are expected to be significant.

e. After each selection, subtract the sampling interval until the 
subtotal is negative. Even if the last item in the population is 
selected, the sampling interval should be subtracted until the 
subtotal is negative.

[See page 495 F-3. For invoice #19, the auditor had to subtract the 
sampling interval twice to get a negative subtotal.]

f. Repeat steps d. and e. until all items in the test population have 
been entered into the calculator and the ending subtotal is negative.

g. To test the footing of the population, reconcile the sample to the 
recorded amount of the test population as follows:

Add:

(a) Random start:

(b) Sampling interval multiplied by the number of times the sampling 
interval was subtracted during selection of the sample:

(c) The remaining subtotal on the calculator.

The total should equal the test population amount.

If the total on the reconciliation is not equal to the population 
amount, there is either an error in the total population amount or 
there was an error in entering the population items into the adding 
machine.

The auditor should consider the amount of any difference when 
determining whether investigation of the difference is necessary. 
Immaterial amounts generally do not require investigation.

[See page 495 F-4 for an example reconciliation to test the footing.]

[PAGE 495 F-3]: Example of Systematic Selection for DUS: 

[See PDF for image]

[End of table]

PAGE 495 F-4: 

Reconciliation of book amounts footed to test population:

Random start: $6,000:

+ Sampling interval x number of times subtracted: 300,000:

($50,000 x 6):

+ Remaining subtotal: (14,400):

Population total: $291,600:

[End of section]

FOOTNOTES

[1] The FAM generally uses the same terminology as the Audit Guide.

[2] Many factors influence efficiency in addition to number of sampling 
applications, such as sample size, number of locations it is necessary 
to visit to achieve audit objectives, nature of the audit procedures, 
extent of review required, whether rework can be avoided by designing 
easy-to-follow procedures.

[3] Tables I and II assume a large population (generally over 5,000 
items). If the population is small, the auditor may ask the 
Statistician to calculate a reduced sample size and to evaluate the 
results. Generally, the effect is small unless the sample size per the 
table is more than 10 percent of the population.

[4] Using the AICPA guidance, the auditor computes the deviation rate 
and the upper limit at the desired confidence level (usually the same 
confidence level used to determine sample size). If the upper limit of 
deviations is less than the tolerable rate, the results support the 
control risk assessment. If not, the control risk should be increased 
in designing substantive tests.

[5] Tolerable rate of 5 percent, expected population deviation rate of 
0, and a large population (see footnote on page 450-3). If the 
population is small, the auditor may ask the Statistician to compute a 
reduced sample size and to evaluate the results.

[6] The proprietary accounting system supports the accrual basis of 
accounting.

[7] If the data are disaggregated, the limit is still applied on an 
annual basis.

[8] IDEA is the primary software GAO uses. It is distributed by 
Audimation Services, Inc., Houston, Texas.

[9] Usually the auditor applying nonstatistical sampling will select a 
"haphazard sample." A haphazard sample is a sample consisting of 
sampling units selected without conscious bias, that is, without any 
special reason for including or excluding items from the sample. It 
does not consist of sampling units selected in a careless manner; 
rather it is selected in a way the auditor expects to be representative 
of the population.

Since a haphazard sample is not the same as a statistical sample, the 
auditor using a haphazard sample cannot calculate precision at a given 
confidence level. However, AICPA guidance indicates that the auditor 
may use the haphazard sample to make a judgment of what a statistical 
sample might have shown. For example, he or she might use the haphazard 
sample to make a judgment as to the likely misstatement in areas that 
are not very significant. Even though the judgment will not be a 
statistical projection, it may assist the auditor in determining 
whether the possible misstatement could be material. Thus, the auditor 
should not avoid making the judgment.

Professional standards and the FAM do not use the term "judgment 
sample." All selections (including statistical selections) require 
judgment. The term "judgment sample" is often used to refer to 
nonrepresentative selections, although it sometimes refers to 
nonstatistical samples.

[10] See Dollar Unit Sampling, by Leslie, Teitlebaum, and Anderson 
(Copp Clark Pitman, 1979), for a more technical discussion of DUS.

[11] This expectation affects the efficiency of the sample, not its 
effectiveness. GAO auditors who use IDEA to calculate sample size 
(based on the binomial distribution) generally use classical variables 
estimation sampling when they expect that more than 30 percent of the 
sampling units contain misstatements (no matter what the size of the 
misstatement). When GAO auditors expect that 10 percent or fewer of the 
sampling units contain misstatements, GAO auditors generally use 
dollar-unit sampling. When GAO auditors expect between 10 and 30 
percent of the sampling units contain misstatements, GAO auditors 
consult with the Statistician. If a large misstatement rate is found, 
the auditor, in consultation with the Statistician, should consider 
whether to use classical PPS to evaluate the sample to obtain a smaller 
precision. Other auditors, in consultation with their Statisticians, 
may use different rules of thumb in deciding when to use DUS versus 
classical variables estimation sampling.

[12] This means, for example, that an item that has a selected amount 
of $1,000 cannot be misstated by more than $1,000. This is usually not 
an issue in testing existence or valuation (overstatement). However, it 
might be an issue in testing completeness (understatement). Thus, if 
understatements larger than the selected amount are expected, classical 
variables estimation sampling generally should be used.

[13] IDEA offers two methods of selecting a dollar-unit sample. The 
auditor generally should use the cell method rather than the fixed 
interval method. In the cell method, the program divides the population 
into cells such that each cell is equal in size to an interval. Then 
the program selects a random dollar in each cell. The random dollar 
selected identifies the transaction, account, or line item to be tested 
(sometimes called the logical unit).

[14] The 25 percent is a rough estimate that is used because there is 
no way to calculate the correct sample size.

[15] As a general rule, this means 10 misstatements if the sample size 
is between 75 and 100, 10 percent if the sample size is between 100 and 
300, and 30 if the sample size is over 300. Minimum sample size for 
classical PPS is 75.

[16] Audit assurance is not the same as statistical confidence level. 
Assurance is a combination of quantitative measurement and auditor 
judgment.

[End of section]