Basic Sampling Concepts

8/3/2019 Basic Sampling Concepts

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Chapter 17:

Audit SamplingConcepts


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Purpose of Sampling

Sampling is a method of obtaining

information that will permit an estimate

of the value or quality of a population

by examining only a portion of the

population.


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PSA 530Audit Sampling as the application of a

compliance or substantive procedure to less

than 100% of the items within an accountbalance or class of transactions to enable the

auditor to obtain and evaluate evidence of

some characteristic of the balance or class

and to form or assist in forming a conclusion.


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Auditors sample whenThe nature and materiality of the balance

or class of transactions does not demand a

100% auditA decision must be made about thebalance or class of transactions

The time and cost to audit 100% of thepopulation would be too great


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Note:

Not all testing procedures performed by

auditors involve audit sampling.

The auditor may decide to apply audit

procedures only to those items which have

particular significance.


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Sampling Risk

Sampling risk refers to the possibility

that the auditors conclusion, based on a

sample maybe different from the

conclusion reached if the entire population

were subject to the same audit procedures.


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Types of Sampling Risk Alpha Riskis the risk the auditor will

conclude,

a. In the case oftest of control, that theinternal control is not reliable when in fact it

is effective.

b. In the case ofsubstantive test, that the

materialmisstatements exist in an accountbalance or transaction class when in fact

such misstatement does not exist.


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Beta Risk

a.T

est Control- internal control is reliablewhen in fact it is not effective and cannot be

relied upon.

b. Substantive Test- materialmisstatement

does not exist when in factmaterialmisstatement exist

Types of Sampling Risk


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Non-sampling Risk

Non-sampling Risk arises from factors

that cause the auditor to reach an erroneous

conclusion for any reason related to the size

of the sample.

Example: Use of inappropriate

procedures, misinterpretation of evidenceand failure to recognize an error.


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Controlling the Risks

Control Sampling Risk Increase the sample size

Using an appropriate sample selection method

Control Non-sampling Risk

Proper Planning

Adequate direction, review and supervision of the

audit team


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Approaches to Audit Sampling

Statistical Sampling

Non-Statistical Sampling


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Statistical Sampling is a

mathematically derived tool which

provides the auditor with an objectivebasis for expressing conclusions about

population characteristic based upon a

sample of items from the population.


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Statistical SamplingSampling that uses the laws of

probability for selecting and

evaluating a sample from a populationfor the purposes of reaching aconclusion about the population

selected at random

statistical calculations are used tomeasure and express the results


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Advantages Provides:

for quantitative evaluation of the sample

results.

a more defensible expression of the test results.

for more objective recommendations for

management.


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Disadvantages

Requires random sample selection which may

be more costly and time consuming.

Might require additional training costs for staff

members to use statistics or specialized

software.


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Non-Statistical Sampling is an approach

that purely uses auditors judgement in

estimating sampling risks, determining

sample size, and evaluating sample results.


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Directed sample selection, useful for:

Items likely to contain errors

Items containing selected characteristics (e.g. old

amounts

Large peso item coverage

Block sample selection (e.g. sequences) Haphazard sample selection



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Non-statistical Sampling

Advantages

Allows the auditor to inject his or her subjective

judgment in determining the sample size and selectionprocess to audit items of greatest value and highestrisk.

May be designed so that it is equally effective andefficient as statistical sampling while being lesscostly.


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Non-statistical Sampling

Disadvantages

Cannot draw objectively valid statisticalinferences from the sample results.

Cannot quantitatively measure and express

sampling risk.


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Statistical vs. Non-statistical

Similarities

Both require a

structured processinvolving planning,selection,conducting,evaluating

Any type can bestratified

Differences

Sampling risk can be

quantified instatistical samplingusing mathematicalformulae


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Sampling process

For both statistical and non-statistical

methods, the four main parts are:

1. Planning the sample

2. Selecting the sample

3. Performing the tests

4. Evaluating the results


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Attribute and VariablesSampling Techniques

Attribute estimation procedures measurequalitative characteristics

Variables estimation procedures measure

quantitative characteristics


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Design of the sample

Audit objectives

Population and its characteristics

Risk and Assurance

Tolerable error

Expected error in the population

Stratification


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Audit objectives

The auditor first considers the specific

objectives to be achieved and the combination

of audit procedures which is likely to best

achieve those objectives.


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Population

Population can be defined in a way to suit

the audit tests

It is important for the audit to ensure that

the population is:

a. Appropriate

b. Completeness


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Risk and Assurance

In planning the audit, the auditor uses

professional judgement to assess the level of audit

risk that is appropriate. Audit risks include: The risk that material errors will occur

The risk that the clients system of internal control

will not prevent or correct such errors

The risk that any remaining material errors will notbe detected by the auditor


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Tolerable Error

This is the maximum error in the

population that the auditor would be

willing to accept and still conclude that

the result from the sample has achieved

its audit objective.


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Expected Error in the PopulationThe following factors should be considered in determining the

Expected Error in the Population:

a. Error levels identified in previous audits

b. Changes in client procedures

c. Evidence available from his evaluation

of the system of internal control and from

results of analytical review procedures


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Stratification

Stratification is the process of dividing

a population into subpopulation, that is, a

group of sampling units which have

similar characteristics.


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Sample Selection Methods

Most commonly used selection methods

for Statistical and Non-statistical Sampling

are as follows..


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Sample Selection Methodsa. Random Sampling

sample that is selected in such a way that everyitem in a population has an equal chance of beingselected

accomplished by using a printed table of randomnumbers or computer software that generatesrandom numbers


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b. Systematic Samplingin using this method, the auditor counts

through the population and selects items on thebasis of a sampling interval which is

determined by dividing the number of physical

items in the population by the sample size.


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c. Stratified Random Samplingto stratify, the auditor groups the population into

subpopulation, or strata that are similar inamount

samples are then drawn from each stratum using

one of the random selection methods


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d. Sampling with Probability Proportional to

Sizemethod of sampling that emphasizes larger peso

items within an account balance

the probability of an item being selected in this

method is directly proportional to its pesoamount


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Sample Size-can be determined by the application of

statistically-based formula or through theexercise of professional judgment objectivelyapplied to the circumstances

-affected by the level of sampling risk thatthe auditor is willing to accept

-the lower the risk the auditor is willing to

accept, the greater sample size will need to be


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Examples of Factors Influencing Sample Size for Tests of

CONTROL

FACTOR EFFECT ONSAMPLE SIZE

1.An increase in the extent to which the auditors risk

assessment takes into account relevant controls

INCREASE

2. An increase in the tolerable rate of deviation DECREASE

3.An increase in the expected rate of deviation of the

population to be testedINCREASE

4.An increase in the auditors desired level of assurance

that the tolerable rate of deviation is not exceeded by theactual rate of deviation in the population. INCREASE

5.An increase in the number of sampling units in the

populationNEGLIGIBLE

EFFECT


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Examples of Factors Influencing Sample Size for Tests of

DETAILS

FACTOR EFFECT ON

SAMPLE SIZE

1.An increase in the auditors assessment of the risk of

material misstatement

INCREASE

2.An increase in the use of other substantive procedures

directed at the same assertionDECREASE

3.An increase in the auditors desired level of assurancethat tolerable misstatement is not exceeded by actual

misstatement in the population

INCREASE

4.An increase in tolerable misstatement DECREASE


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FACTOR EFFECT ON

SAMPLE SIZE

5.An increase in the amount of misstatement the

auditor expects to find in the populationINCREASE

6.Stratification of the population when

appropriateDECREASE

7.The number of sampling units in the population NEGLIGIBLE

EFFECT


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Performing the Audit Procedure

The auditor should perform audit

procedures appropriate to theparticular test objective on each item

selected


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Evaluation of Sample Results

Analyze any error detected in the

sample

Project the errors found in the sample

to the population

Assess the sampling risk


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Evaluation of Sample Results

Analysis of Errors in the Sample

- the auditor should consider the sample

results, the nature and cause of any errors

identified, and their possible effect on the

particular test objective and on other areas

of the audit


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Evaluation of Sample Results Projection of Errors

-for substantive procedures, the auditor should project

monetary errors found in the sample with the

population and should consider the effect of the projectederror on the particular test objective and on other areas of

the audit.

-when an error has been established as an anomalous error, it

may be excluded when projecting sample errors to the

population.

-for tests of control, no explicit projection of errors is

necessary.


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-the auditor should project the error results of

the sample to the population from which

the sample was selected

-when projecting error results, the auditor

should keep in mind the qualitative

aspects of the errors found


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Evaluation of Sample ResultsAssessing Sampling Risk

-the auditor should evaluate the sample

results to determine whether the preliminaryassessment of the relevant characteristic of the

population is confirmed or needs to be revised.

-auditor should consider whether errors in

the population might exceed the tolerable error.


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-as projected error approaches tolerable

error, the risk of incorrect acceptance or

over reliance increases. The auditor should

therefore reconsider the sampling risk and if

he determines that the risk is unacceptable,

he should consider extending his audit

procedures or performing alternative audit

procedures.


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Conclusion

Having evaluated the sampling result, theauditor should conclude as to the extent to whichhe has obtained sufficient appropriate auditevidence in support of the particular characteristic of the account balance or class oftransaction with which he is concerned.


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Detailed Audit Sampling PlanAudit Sampling

Attributes Sampling

in Tests of Control

Variable Sampling

In Substantive Tests

of Details

Statistical Non-statisticalStatistical Non-statistical

Regular or Classical

Discovery

Sequential or Stop

or Go

Classical

Probability Proportional

to Size

Mean per unit

Difference Estimation

Ratio Estimation

Regression


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Attributes Sampling Plan

used to test an entity's rate of deviation from

a prescribed control procedure

audit sampling in which auditors look for the

presence or absence of a control condition


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Variables Sampling Plan used to test whether recorded account

balances are fairly stated

might be used by an auditor to test

recorded peso amounts for receivables,

inventory and fixed asset additions


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Statistical Sampling Plan

sampling technique in which an auditor

uses the laws of probability to selectand evaluate a sample


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Non statistical Sampling Plan

rely exclusively on subjective judgment

to determine sample size and to

evaluate sample results


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Regular orClassical Statistical AttributesSampling

enables the auditor to estimate the

rate of occurrence of certaincharacteristics in the population


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Discovery Sampling

designed to locate at least one deviation

in the population

often used in situations in which the

auditors expect a very low rate of

occurrence of some critical deviation


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Sequential (Stop or Go) Sampling

sample is selected in several steps, with

the need to perform each step conditional

on the results of the previous steps


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Probability Proportional to Size

also referred to as peso-unit sampling

applies attributes sampling theory to

develop an estimate of the total peso

amount of misstatement in a population


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Classical Variables Sampling Models

use normal distribution theory to evaluate

selected characteristics of a population on

the basis of a sample of the itemsconstituting the population

provide the auditors with an estimate of anumerical quantity such as the peso

balances of an account


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Mean-per-unit Estimation

classical variables sampling plan

enabling the auditors to estimate theaverage peso value of items in a

population by determining the average

value of items in a sample


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Difference Estimation

uses the difference between the audited

values and book values of items in a

sample to calculate the estimated total

audited value of the population


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Ratio Estimation

uses the ratio of audited values to book

values of items in the sample to

calculate the estimated total audited

value of the population


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Regression

has the effect of using both the average

ratio and the average difference in

calculating an estimate of the total

amount for the population


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Presented by:

Casas, Lorenz Nicole

Mauhay, Ana Kristina

Basic Sampling Concepts

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