arens_C11e_PPT_ch13

Auditing: The Art and Science of Assurance Engagements

Chapter 13: Audit Sampling Concepts

Copyright © 2011 Pearson Canada Inc.

Auditing, Canadian Eleventh Edition

Chapter 13 Learning Objectives

1. Define sampling. State when an auditor would use statistical rather than non-statistical sampling.

2. Explain the three different ways that an auditor can select a statistical sample.

3. Describe the 14 steps in planning and selecting a sample, performing the tests, and evaluating the sample.

13-2Copyright © 2011 Pearson Canada Inc.


Importance of Sampling to Auditors

• The auditor doesn’t look at everything… just pieces.• The auditor CANNOT look at everything.



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.



Use of Sampling

• The nature and materiality of the balance or class of transactions does not demand a 100% audit.

• A decision must be made about the balance or class of transactions.

• The time and cost to audit 100% of the population would be too great.



Sampling is Used to Conduct

• Walk through tests (to understand internal controls)• Tests of controls• Tests of details



Representative Sampling

• Definition: The characteristics in the sample of audit interest are approximately the same as those of the population.

(Continued)



Representative Sampling (Continued)

• Non-representativeness can occur due to:-Non-sampling risk: Audit test do not uncover the exceptions in the sample due to failure to recognize them, or due to ineffective procedures-Sampling risk: Results from testing less than the entire population



Statistical Sampling

• Sampling that uses the laws of probability for selecting and evaluating a sample from a population for the purposes of reaching a conclusion about the population– selected at random– statistical calculations are used to measure and

express the results



Statistical vs. Non-Statistical

Similarities• Both require a

structured process involving planning, selection, conducting, evaluating

• Any type can be stratified

Differences• Sampling risk can be

quantified in statistical sampling using mathematical formulae



Non-Probabilistic (Judgmental) Sample Selection Methods

• Directed sample selection, useful for:– Items likely to contain errors– Items containing selected characteristics (e.g. old amounts– Large dollar item coverage

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



Probabilistic Sample Selection Methods

• Simple random sample selection• Systematic sample selection• Probability proportionate-to-size sample selection

(also known as MUS monetary unit sampling)



Advantages of Statistical Sampling

• Provides for quantitative evaluation of the sample results.

• Provides a more defensible expression of the test results.

• Provides for more objective recommendations for management.



Disadvantagesof Statistical Sampling

• 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.



Advantages of Non-statistical Sampling

• Allows the auditor to inject his or her subjective judgment in determining the sample size and selection process to audit items of greatest value and highest risk.

• May be designed so that it is equally effective and efficient as statistical sampling while being less costly.



Disadvantages of Non-Statistical Sampling

Disadvantages• Cannot draw objectively valid statistical inferences

from the sample results.• Cannot quantitatively measure and express sampling

risk.



Professional Judgment Problem 13-25, p. 440

• Making decisions about sampling• Does the implementation method matter?



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



Steps in Sampling Process

• We are going to look at the fourteen steps in the sampling process, comparing the process for tests of controls versus tests of details.



1. State the Objectives of the Test

Test of controls:• Are the controls

applied?• Are there monetary

errors or fraud or other irregularities

Test of detail:• Auditor wants to

determine the maximum amount of overstatement and understatement that could exist based on the sample



2. Decide if Audit Sampling Applies

• Some controls can be sampled (e.g. is a shipping document attached?) while others cannot be (e.g. separation of duties)

• Ability to sample for test of details depends on the nature of the population (e.g. capital assets may not be sampled, depending upon volume, while A/R confirmations will be



3. Define Attributes and Exception or Error Conditions

Term related to planning:

Test of control (e.g. attribute sample)

Test of detail (e.g. for MUS sample)

Define the item of interest

Identify the characteristic or attribute of interest

Individual dollars

Define exceptions or errors

Define the control deviation (an exception)

Normally, any monetary difference (error)



3. Define Attributes and Exception or Error Conditions- Sales and A/R

Term related to planning:

Test of controls (e.g. attribute sample) Sales

Test of details (e.g. for MUS sample) Accounts Rec’bl

Define the item of interest

Are sales approved for credit?

Individual dollars

Define exceptions or errors

Sale made that causes customer balance to exceed credit limit

Confirmed amount different from amount in customer account



4. Define the Population

• Population can be defined in a way to suit the audit

tests.

• Must sample from the entire population as defined.

• In testing controls over sales population is likely

recorded sales invoices.

• In testing details in accounts receivable it is the

recorded dollar population.

• Most populations can be stratified, if needed.



5. Define the Sampling Unit

Test of controls:• Usually a physical unit,

e.g. invoice, shipping document, purchase order

Test of details:• If MUS, would be the

individual dollar• For non-statistical

sampling, it is likely the unit making up the balance, e.g. an unpaid invoice



6. Specify Tolerable Exception Rate (TER) or Specify Materiality

Test of controls• TER is the exception

rate the auditor will permit in the population and still be willing to use the assessed control risk

• As TER increases, the sample size decreases

Test of details• Materiality is used to

determine the tolerable misstatement amount for the audit of each account

These decisions require the use of professional judgment.



7. Specify ARACR or ARIA

Test of controls• Acceptable Risk of

Assessing Control Risk Too Low (ARACR) is the risk that the auditor will take of accepting controls as effective when population error rates are actually greater

Test of details• Acceptable Risk of

Incorrect Acceptance (ARIA) is the risk the auditor will take of accepting a balance as correct when the true misstatement is greater than materiality

(Continued)



7. Specify ARACR or ARIA (Continued)

Test of controls• Assumes TER 6%,

ARACR 10%, true error rate 8%

• True error rate exceeds TER, so population is NOT acceptable, but auditor does not know!

Test of details• If ARIA changes from

10% to 5%, sample size increases, since assurance required increases

• When controls are good (control risk is low), ARIA can be increased



8. Estimate Population Exception Rate or Misstatements

Test of controls• Estimated population

error rate (EPER) is an advance estimate of the percentage of exceptions in the population

• The lower the EPER, the smaller the sample size

Test of details• Provide an advance

estimate of the total dollar error (misstatements) in the population

• Use prior year data and professional judgment.



9. Determine the Initial Sample Size

• For non-statistical (also called judgmental) sampling,

professional judgment is used to calculate the sample

size.

• For statistical sampling, mathematical formulae are

used, either in specially prepared tables or using

software designed for audit sampling.

• For stratified sampling, the sample is allocated

among the strata.



10. Select the Sample

• Using the number of items determined in Step #9,

choose the items from the population using the

sampling unit defined in Step #5.

• Use probabilistic or non-probabilistic methods.

• To enable quantification of sampling risk, probabilistic

(statistical) methods must be used.



11. Perform the Audit Procedures

• For test of controls, examine each item for the attribute defined in Step #3, recording all exceptions found (e.g. all sales approved for credit).

• For test of details, apply the audit procedures to each item to determine whether it is correct or contains a misstatement (e.g. send and reconcile confirmations, conduct alternative procedures).



12. Generalize from the Sample to the Population

• For test of controls the sample error rate (SER) equals actual number of exceptions divided by actual sample size– But that is not necessarily equal to the actual

population rate: a potential range must be calculated

• In practice, auditors tend to test controls when they expect no exceptions

• Method of generalization depends on the sampling methodology used

(Continued)



12. Generalize from the Sample to the Population (Continued)

• When generalizing tests of details, auditors deal with

dollar amounts rather than with exceptions

• Misstatements found are projected from the sample

results to the population

• Need to consider sampling error and sampling risk

(ARIA)



13. Analyze Exceptions or Misstatements

Test of controls• What breakdown in

internal controls caused the exceptions? (does it affect control risk?)

• Should additional substantive testing be conducted because of these results?

Test of details• Were the misstatements

caused by control exceptions? (need to reassess control risk?

• Is additional substantive testing required?



14. Decide the Acceptability of the Population

Test of controls• If TER (Tolerable Error

Rate) is sufficiently larger than SER (sample error rate) will normally accept the population

Test of details• Compare the difference

between the projection to the population and materiality

• Use decision rule for statistical sampling

(Continued)



14. Decide the Acceptability of the Population (Continued)

What if the auditor decides the population is NOT acceptable? What to do?– 1. Revise TER (tolerable error rate), ARACR, or

ARIA (the risks of accepting incorrect populations) - not easily defensible

– 2. Expand the sample size. Will decrease the sampling error OR you could end up with

the same result.– 3. Revise assessed control risk. This will likely

mean an increase in tests of detail.– 4. Report weaknesses in management letter.


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