Audit Sampling

Chapter 09

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

9-2

What is Audit Sampling?

Applying a procedure to less than 100%

of a population

To estimate some characteristic of the

population

Qualitative

Quantitative

9-3

Risk

Sampling risk

risk that the auditors’ conclusions based on a

sample may be different from the conclusion

they would reach if they examined every item

in the population

Nonsampling risk

risk pertaining to nonsampling errors

Can be reduced to low levels through

effective planning and supervisions of audit

engagements

9-4

Nonstatistical Sampling

The auditor estimates sampling risk by

using professional judgment rather than

statistical techniques

Provides no means of quantifying

sampling risk

Sample may be larger than necessary or

auditors may unknowingly accept a higher

than acceptable degree of sampling risk

9-5

Advantages of Statistical Sampling

Allows auditors to measure and control

sampling risk which helps:

Design efficient samples

Measure sufficiency of evidence

Objectively evaluate sample results

9-6

Selection of Random Sample

Random sample results in a statistically

unbiased sample that may not be a

representative sample

Random sample techniques

Random number tables

Random number generators

Systematic selection

9-7

Random Number Table

9-8

Other Methods of

Sample Selection Other methods

Haphazard selection

• Select items on an arbitrary basis, but without any

conscious bias

Block selection

• Block sample consists of all items in a selected

time period, numerical sequence or alphabetical

sequence

Stratification

Technique of dividing population into relatively

homogeneous subgroups

9-9

An Illustration of Stratification

9-10

Types of Statistical Sampling Plans

Attributes sampling

Discovery sampling

Classical variables sampling

Mean-per-unit estimation

Ratio estimation

Difference estimation

Probability-proportional-to-size sampling

9-11

Dual Purpose Test

Tested used both as a test of control and

substantiating the dollar amount of an

account balance

Ex. Test to evaluate the effectiveness of a

control over recording sales transactions and

to estimate the total overstatement or

understatement of the sales account

9-12

Allowance for Sampling Risk

Amount used to create a range, set by + or

– limits from the sample results, within

which the true value of the population

characteristic being measured is likely to

lie

Precision

Wider the interval, more confident but less

precise conclusion

Can be used to construct a dollar interval

9-13

Sample Size

Significant effect on allowance for

sampling risk and sampling risk

Sample size increase -> sampling risk and

allowance for sampling risk decrease

Sample size affected by characteristics of

population

Generally as Population increases -> sample

size increase

9-14

Requirements of Audit

Sampling Plans

When planning the sample consider:

The relationship of the sample to the relevant audit objective

Materiality or the maximum tolerable misstatement or deviation rate

Allowable sampling risk

Characteristics of the population

Select sample items in such a manner that they can be expected to be representative of the population

Sample results should be projected to the population

Items that cannot be audited should be treated as misstatements or deviations in evaluating the sample results

Nature and cause of misstatements or deviations should be evaluated

9-15

Actual Extent of Operating Effectiveness

of the Control Procedure is

Adequate Inadequate

The Test of Controls Sample Indicates:

Extent of Operating Effectiveness is Adequate

Extent of Operating Effectiveness Inadequate

Sampling Risks--Tests of Controls

Correct

Decision

Incorrect

Decision (Risk of Assessing

Control Risk

Too Low)

Incorrect

Decision (Risk of Assessing

Control Risk

Too High)

Correct

Decision

9-16

Audit Sampling Steps for

Tests of Controls

Determine the objective of the test

Define the attributes and deviation conditions

Define the population to be sampled

Specify:

The risk of assessing control risk too low

The tolerable deviation rate

Estimate the population deviation rate

Determine the sample size

Select the sample

Test the sample items

Evaluate the sample results

Document the sampling procedure

9-17

Attributes Sampling: Relationship Between the

Planned Assessed Level of Control Risk and the

Tolerable Deviation Rate

9-18

Illustration of Attributes Sampling--

Determining Sample Size

Risk of Assessing Control Risk Too Low—

5 percent

Tolerable Deviation Rate—9 percent

Expected Population Deviation Rate—2

percent

9-19

Figure 9.4: Statistical Sample Sizes for Tests of Controls

at 5 Percent Risk of Assessing Control Risk Too Low

9-20

Sample Size

Sample size using Figure 9-4 (next slide)

=68 (2)

This means the auditor should select a

sample of 68 items. We will discuss the

(2) in a few slides.

9-21

Attributes Sampling Evaluation of

Results

2 possible approaches:

1. Use the bracketed number from Table

9.4. If you find that number or less

deviations, conclude that you have

accomplished your audit objective.

2. Use Table 9.5 for a more precise

conclusion.

9-22

Example A--No Deviations Identified (Evaluating

Attributes Sampling Results) Approach 1—You have met your audit objective (because the bracketed number was (2),

you meet objective when you identify 0, 1 or 2 deviations). What can you say?

―I believe that the deviation rate in the population is less than 9 percent.‖ You will be

wrong 5 percent of the time when the deviation is exactly 9 percent. If the deviation rate is in excess of 9 percent you will be wrong even less than 5 percent of the time. The planned assessed level of control risk is achieved.

Approach 2

You have tested 68 items, a number not on Table 9-5 (next slide

To be conservative go to next lowest number on table (65) and use it for your conclusions (we could, but won't interpolate for a more precise answer).

You have met your audit objective. Table 9-5 gives us an answer of 4.6 percent. What can you say?

"I believe that the deviation rate in the population is less than 4.6 percent.‖ You will be wrong 5 percent of the time when the deviation rate is exactly 4.6 percent. If the deviation rate is in excess of 4.6 percent you will be wrong even less than 5 percent of the time. The planned assessed level of control risk is achieved.

9-23

Figure 9.5 Statistical Sampling Results Evaluation Table for

Tests of Controls: Achieved Upper Deviation Rate at

5 Percent Risk of Assessing Control Risk Too Low

9-24

Example B--3 Deviations Identified

(Evaluating Attributes Sampling Results)

Approach 1—You have not met your audit objective. What can you say?

―The achieved upper deviation rate is higher than 9 percent.‖ The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.

Accordingly, you may not ―rely‖ on internal control to the extent planned. Thus, the auditor will need to increase the scope of substantive procedures (the nature, timing, and/or extent).

Approach 2—You have not met your audit objective. Table 9-5 provides us an answer of 11.5 percent

―I believe that the deviation rate in the population is less than 11.5 percent.‖ You will be wrong 5 percent of the time when the deviation rate is exactly 11.5 percent. But this is not good enough as you wanted 9 percent rather than 11.5 percent. The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.

As per Approach 1, an increase in the scope of substantive procedures is appropriate.

9-25

Other Statistical Attributes

Sampling Approaches Discovery sampling

Purpose is to detect at least one deviation,

with a predetermined risk of assessing

control risk too low if the deviation rate in

population is greater than specified tolerable

deviation rate

Useful in suspected fraud

Sequential (Stop-or-Go) Sampling

Audit sample taken in several stages

9-26

Sampling Risks--Substantive Tests

The Population Actually is

Not Materially Materially Misstated Misstated The Substantive Procedure Sample Indicates

Misstatement in Account Exceeds Tolerable Amount

Misstatement in Account Is Less Than Tolerable Amount

Correct

Decision

Incorrect

Decision (Risk of Incorrect

Rejection)

Incorrect

Decision (Risk of Incorrect

Acceptance)

Correct

Decision

9-27

Audit Sampling Steps for

Substantive Tests

Determine the objective of the test

Define the population and sampling unit

Choose an audit sampling technique

Determine the sample size

Select the sample

Test the sample items

Evaluate the sample results

Document the sampling procedure

9-28

Population Variability—Why it Matters

Item Population A Population B 1 2,100 8,000 2 2,100 25 3 2,100 2,000 4 2,100 400 5 2,100 75 Mean 2,100 2,100 Standard deviation -0- 3,395 The variability determines how much information each of the

items in the population tells you about the other items in the population.

9-29

Factors Affecting Sample Size

9-30

Mean Per Unit (MPU) Illustration

Population Size = 100,000 accounts

Book value = $6,250,000

Other information:

Tolerable misstatement = $364,000

Sampling risk

Incorrect Acceptance = 5%

Incorrect Rejection = 4.6 %

9-31

MPU Risk Coefficients

Acceptable

Level of Risk

(%)

Incorrect

Acceptance

Coefficient

Incorrect

Rejection

Coefficient

1.0 2.33 2.58

4.6 1.68 2.00

5.0 1.64 1.96

10.0 1.28 1.64

15.0 1.04 1.44

20.0 .84 1.28

25.0 .67 1.15

30.0 .52 1.04

40.0 .25 .84

50.0 .00 .67

9-32

Determining Sample Size--MPU

(1 of 2)

t)coefficien rejectionIncorrect t / coefficien acceptance (Incorrect + 1

ntmisstateme Tolerable = ASR Planned

000,00$2 = )00.2/64(1. + 1

000,364$ = ASR Planned

9-33

Determining Sample Size--MPU

(2 of 2)

2

risk samplingfor allowance Planned

dev. std. Est.*t coefficien rejectionIncorrect * size Population Size Sample

2

000,200$

$15 * 2.00 * 100,000Size Sample

= 225 Accounts

9-34

Adjusted allowance for sampling risk =

Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.) misstatement Sample size

This formula ―adjusts‖ the allowance for sampling risk to consider the standard

deviation of the audited values in the sample. It holds the risk of incorrect

acceptance at its planned level.

Variables Sampling Illustration--MPU

9-35

Variables Sampling Illustration--MPU

Using the text example with a standard deviation of audited values of $16

Adjusted allowance for sampling risk =

Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)

misstatement Sample size

= $364,000 _ ($100,000 * 1.64 * $16)

225

= $189,067

We would still “accept” the book balance because the $6,250,000 (book value) falls within this interval

Estimate of total + Adjusted allowance audited value for sampling risk $6,100,000 + $189,067

[$5,910,933 to $6,289,067]

9-36

Acceptance Interval

Figure 9-12

9-37

Difference Estimation

Difference

Use sample to estimate the avg. difference

between the audited value and book value of

items in population

Projected = Sample Net Misstatement * Pop. Items

Misstatement Sample items

Most appropriate when size of misstatements

does not vary significantly in comparison to

book value

9-38

Ratio Estimation

Use a sample to estimate the ratio of

misstatement in a sample to its book

value and project it to population

Projected = Sample Net Misstatement * Pop. Book Value

Misstatement Book Value of Sample

Preferred when the size of misstatements is nearly

proportional to the book values of the items

Large accounts have large misstatements

9-39

Nonstatistical Variables Sampling

Illustration

Plan Sample:

Population:

• Size = 363 items

• Book value = $200,000

Tolerable misstatement = $10,000

Risk assessments:

• Inherent and control risk = Slightly below maximum

• Other substantive tests = Moderate

9-40

Nonstatistical Sampling--

Determination of Sample Size

Sample size = Population book value X Reliability factor Tolerable misstatement = $200,000 X 2.0 = 40 items $10,000

9-41

Nonstatistical Sampling--Evaluation of Sample Results

Sample results:

40 accounts in sample

$350 net overstatement

$60,000 book value of sample items

Projected misstatement:

= [Sample net misstatement] X Book value of population [ Book value of sample ] = [ $350 ] X $200,000 [$60,000] = $1,167

Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct.

9-42

PPS Sampling Illustration

Population book value = $6,250,000

Other Information:

Tolerable misstatement = $364,000

Sampling risk--Incorrect acceptance = 5%

Expected misstatement = $50,000

Use Figures 9-14 and 9-15 to obtain a ―reliability factor‖ and an ―expansion factor‖--next slide

9-43

PPS Sampling Reliability and

Expansion Factors

9-44

PPS Sample Size Computation

Sample size =

Recorded amount of population * Reliability factor

Tolerable misstatement - (Expected misstatement * Expansion factor)

= $6,250,000 * 3.0 = 66 $364,000 - ($50,000 * 1.6) Sampling interval = Book value of the population Sample size = $6,250,000 = $95,000 (approximately) 66

9-45

Figure 9.16 PPS Sample

Selection Process

9-46

PPS Evaluation of Results

Upper Limit on misstatement =

Projected misstatement

+ Basic precision (Rel. factor x interval)

+ Incremental allowance

9-47

Calculation of Upper Limit on Misstatement

9-48

Comparison of statistical sampling

techniques for substantive procedures

9-49

Audit Risk

AR = IR x CR x DR

where AR=The allowable audit risk that a material misstatement might

remain undetected for the account balance and related assertions.

IR= Inherent risk, the risk of a material misstatement in an assertion,

assuming there were no related controls.

CR= Control risk, the risk that a material misstatement that could

occur in an assertion will not be prevented or detected on a timely

basis by internal control.

DR= Detection risk, the risk that the auditors’ procedures will fail to

detect a material misstatement if it exists.