Audit Sampling
Concepts
Importance of Sampling
• Auditor does not look at everything
– How does this affect the opinion?
• Auditor CANNOT look at everything
– Why?
Sampling-2
Purpose of Sampling
• The auditor examines only a portion of the
population in order to estimate
• How much is a portion?
Sampling-3
When to Do Sampling
When:
1.
The nature and materiality of the balance or class of
transactions does not demand a 100% audit
2.
A decision must be made about the balance or class of
transactions.
3.
The time and cost to audit 100% of the population would
be too great
Sampling-4
When is Sampling Used?
To conduct:
1. Walk through tests
2.
For tests of controls
3.
Tests of details
Sampling-5
Representative Sampling
• Having a representative sample is important
• What does representative mean?
Sampling-6
• Non-sampling risk:
• Sampling risk:
Sampling-7
Statistical Sampling
• Uses the laws of probability for selecting
and evaluating a sample from a
population
• Selected at random
• Statistical calculations are used
Sampling-8
Statistical vs. Non-Statistical
Similarities
• Both require a
structured process
Differences
• Sampling risk cannot be
quantified
• The use of stratification
Sampling-9
Non-Probabilistic Sample Selection
Methods
• Directed sample selection
– When used?
• Auditor often able to identify items likely to contain errors
• Items containing selected characteristics
• Large dollar item coverage
Sampling-10
• Block sample selection
• A selection of several items in a sequence
• Reasonable number of blocks must be chosen
• Haphazard sample selection
• Auditor goes through the population and haphazardly selects items
Sampling-11
Probabilistic Sample Selection
Methods
• Sampling risk requires
• Simple random sample selection
• Every member of the population has an equal chance of being
selected
• Systematic sample selection
– Auditor calculates an interval and use the interval to select sample
Sampling-12
– Major problem with systematic sampling is bias
• Once the first item is chosen
• No problem if
• But some characteristics
Sampling-13
Probability Proportionate-to-Size Sampling Methodology
• A key statistical methodology
– also known as
– the sampling unit is
– MUS allows the result to be stated
Sampling-14
Attribute Sampling Methodology
• Another key statistical methodology
– very useful for tests of controls
– The main question to be answered is
– If the auditor can allow 5% deviations
Sampling-15
Advantages of Statistical Sampling
Provides:
• for quantitative evaluation of the sample results
• a more defensible expression of the test results
• It is more objective
Sampling-16
Disadvantages of 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
Sampling-17
Advantages of non-statistical sampling
• Allows the auditor to inject his or her subjective
judgment in determining the sample size
• May be designed so that it is equally effective and
efficient as statistical sampling while being less costly
Sampling-18
Disadvantages of non-statistical sampling
• Cannot draw objectively valid statistical
inferences from the sample results
• Cannot quantitatively measure and express
sampling risk.
Sampling-19
The Main Phases of the Sampling
Process
Both statistical and non-statistical methods
1. Planning the sample
2. Selecting the sample
3. Performing the tests
4. Evaluating the results
Sampling-20
Sampling Process
• Fourteen steps in the sampling process.
• Look at tests of controls versus tests of details
Sampling-21
1. State the Objectives of the Test
Test of control:
• Are the controls working as
specified?
• 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
Sampling-22
2. Decide if Audit Sampling Applies
• Test of control:
• some controls can be
sampled
• others cannot be
• Test of detail:
• sampling test of details
depends on the nature
of the population
• high volume can be
Sampling-23
3. Define attributes and exception or error conditions
Planning term:
Test of control
Test of detail
Define the item of
interest
Identify the characteristic
or attribute of interest
Individual dollars
Define exceptions
or errors
Define the control
deviation or exception
Normally, any
monetary difference
or error
Sampling-24
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, what is the population?
• In testing details in accounts receivable it is the recorded dollar
population
• Most populations can be stratified, if needed.
Sampling-25
5. Define the sampling unit
Tests of controls:
Test of detail:
• Usually a physical unit
• If MUS
• If non-statistical sampling
Sampling-26
6. Specify tolerable exception rate (TER) or specify
materiality
• Test of control
• TER`
• Test of detail
• Materiality is used
• As TER increases
• These decisions require the
use of
Sampling-27
7. Specify ARACR or ARIA
• Test of control
• What is ARACR?
• Acceptable Risk of Assessing
Control Risk Too Low
• Test of detail
• What is ARIA?
• Acceptable Risk of Incorrect
Acceptance
Sampling-28
• Test of control
• Assume
– TER 6%
• Test of detail
• If ARIA changes from
10% to 5%
– Since assurance required
increases
– ARACR 10%
– When controls are good
– But unknown to the
auditor the true error rate
is 8%
Sampling-29
8. Estimate population exception rate or
misstatements
• Test of control
• Test of detail
• Estimated population error rate
(EPER)
• Provide an advance estimate
of the total dollar error, i.e.
misstatements, in the
population
• The lower the EPER, the smaller
the sample size
Sampling-30
9. Determine the initial sample size
• For non-statistical or 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
Sampling-31
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, i.e.
statistical, methods must be used
Sampling-32
11. Perform the audit procedures
• For test of controls, examine each item for the attribute defined in Step
#3, recording all exceptions found
• For test of details, apply the audit procedures designed in the audit
program
Sampling-33
12. Generalize from the sample to the population
• Test of controls sample error rate (SER)
• But that is not necessarily equal to the actual population rate
• In practice, auditors tend to test controls when they expect no
exceptions
• But ultimately, the method of generalization depends on the
sampling methodology used
Sampling-34
• When generalizing tests of details, auditors deal with
• Misstatements found are projected from the sample
results to the population
• Auditor must calculate a point estimate
Sampling-35
• To calculate the point estimate:
–
(Client Misstatement / Recorded Value of Sample) x Recorded Book Value of the Population
– Thus for a misstatement of $500 in A/R with a sample value of $10,000
and a total book value of $25,000
– Note that if the population is divided into strata
– The total point estimate may not be an adequate result for the
population
– The auditor must consider this fact
Sampling-36
Calculating Point Estimate for a population
Example of Errors Found
Dollars Audited
Stratum
Sample
Size
Book Value
of Stratum
Recorded
Value
Audited
Value
Client
Misstatement
1
3
$88,955
$88,955
$91,695
$(2,740)
2
6
71,235
43,995
43,024
971
3
6
47,105
13,105
10,947
2,158
Total
15
$207,295
$146,055
$145,666
$389
Example of Point Estimate Calculation
Stratum
Client Misstatement /
Recorded Value from
Sample
1
$(2,740)/$88,955
2
3
Total
x
Recorded Book
Value for
Stratum
=
Point Estimate of
Misstatement
$88,955
$(2,470)
971/43,995
71,235
1,572
2,158/13,105
47,105
7,757
$6,589
Sampling-37
13. Analyze exceptions or misstatements
• Test of control
• Test of detail
• What breakdown in internal
controls caused the
exceptions?
• Were the misstatements
caused by control
exceptions?
• Should additional
substantive testing be
conducted because of these
results?
• Is additional substantive
testing required?
Sampling-38
14. Decide the acceptability of the population
• Test of control
• If TER is sufficiently
larger than SER
• If TER – SER is too small
• Test of detail
• Compare the difference
between the projection
to the population
• If projection is greater
than materiality level
Sampling-39
• 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)
– 2. Expand the sample size.
– 3. Revise assessed control risk.
– 4. Report weaknesses in management letter.
Sampling-40
Problem 11-22, p. 357
•
•
For the examination of the financial statements of Scotia Inc., Rosa Schellenberg, a public accountant, has
decided to apply non-statistical audit sampling in the tests of sales transactions. Based on her knowledge of
Scotia’s operations in the area of sales, she decides that the estimated population deviation rate is likely to be 3
percent and that she is willing to accept a 5 percent risk the true population rate is not greater than 6 percent.
Given this information, Rosa selects a random sample of 150 sales invoices from the 5,000 prepared during the
year and examines them for exceptions. She notes the following exceptions in her working papers. There is no
other documentation.
REQUIRED
a. Which of the invoices in the table should be defined as an exception?
b. Explain why it is inappropriate to set a single acceptable TER and EPER for the combined exceptions.
c. State the appropriate analysis of exceptions for each of the exceptions in the sample.
Invoice
No:
Comment
5028
Sales invoice had incorrect price, but a subsequent credit not was sent out as a correction.
6791
Voided sales invoice examined by auditor.
6810
Shipping document for a sale of merchandise could not be located.
7364
Sales invoice for $2,875 has not been collected and is six months past due.
7625
Client unable to locate the printed duplicate copy of the sales invoice.
8431
Invoice was dated three days later than the date of the shipping document.
8528
Customer purchase order is not attached to the duplicate sales invoice.
8566
Billing is for $100 less than it should be due to a pricing error.
8780
Client unable to locate the printed duplicate copy of the sales invoice.
9169
Credit is not authorized, but the sale was only for $7.65.
Sampling-41
Problem 11-25, page 358
You have just completed the accounts receivable confirmation process in the audit of Danforth paper
Company Ltd., a paper supplier to retail shops and commercial users.
Following are the data related to the process:
Accounts receivable recorded balance
Number of accounts
$2,760,000
7,320
A non-statistical sample was taken as follows:
All accounts over $10,000 (23 accounts)
$465,000
77 accounts under $10,000
$81,500
Materiality
$100,000
Inherent and control risk are both high
No relevant analytical procedures were performed.
The table below gives the results of the confirmation procedures
REQUIRED
Evaluate the results of the non-statistical sample. Consider both the direct implications of the
misstatements found and the effect of using a sample.
Sampling-42
Recorded
Value
Items over $10,000
Audited
Value
$465,000
$432,000
81,500
77,150
Item 12
5,120
4,820
Item 19
485
385
Item 33
1,250
250
Item 35
3,975
3,875
Item 51
1,850
1,825
Item 59
4,200
3,780
Item 74
2,405
0
19,285
14,935
Items under $10,000
Individual misstatements
for items under $10,000
Sampling-43
Problem 11-23 (p.357)
You have been asked to do planning for statistical testing of the audit of cash receipts. Following is a
partial audit program for the audit of cash receipts.
1. Review the cash receipts journal for large and unusual transactions.
2. Trace entries from the prelisting of cash receipts to the cash receipts journal to determine
whether each is recorded.
3. Compare customer name, date, and amount on the prelisting with the cash receipts journal.
4. Examine the related remittance advice for entries selected from the prelisting to determine
whether cash discounts were approved.
5. Trace entries from the prelisting to the deposit slip to determine whether each has been
deposited.
REQUIRED
a. Identify which audit procedures can be tested using attribute sampling. Justify your response.
b. State the appropriate sampling unit for each of the tests in part (a).
c. Define the attributes that you would test for each of the tests in part (a). State the audit object associated
with each of the attributes.
d. Define exception conditions for each of the attributes that you have described in part (c).
e. Which of the exceptions would be indicative of potential fraud? Justify your response.
Sampling-44
Problem 12-24, page 404
Lenter Supply Corp. is a medium sized distributor of wholesale
hardware supplies in southern Manitoba. It has been a client of yours for
several years and has instituted excellent internal control for the control of
sales, at your recommendation.
In providing control over shipments, the client has prenumbered
“warehouse removal slips” that are used for every sale. It is company policy
never to remove goods from the warehouse without an authorized warehouse
removal slip. After shipment, two copies of the warehouse removal slip are sent
to billing for the computerized preparation of a sales invoice. One copy is
stapled to the duplicate copy of the prenumbered sales invoice, and the other
copy is filed numerically. In some cases more than one warehouse removal slip
is used for billing one sales invoice. The smallest warehouse removal slip
number for the year is 14682 and the largest is 37521. The smallest invoice
number is 47821 and the largest is 68507.
In the audit of sales, one of the major concerns is the effectiveness of
the control in making sure all shipments are billed. The auditor has decided to
use attribute sampling in testing internal control.
Sampling-45
(a)
State an effective audit procedure for testing whether shipments
have been billed. What is the sampling unit for the audit
procedure?
(b)
Assuming the auditor expects no deviations in the sample but is
willing to accept a TDR of 3%, at a 10% ARACR, what is the
appropriate sample size?
Sampling-46
EXPECTED
POPULATION
DEVIATION RATE (IN
PERCENTAGE)
2
TOLERABLE DEVIATION RATE
(IN PERCENTAGE)
4
5
6
7
8
9 10 15
3
20
5 PERCENT RISK OF OVER RELIANCE (ARACR)
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
5.00
6.00
7.00
149
236
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
99
157
157
208
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
74
117
117
117
156
156
192
227
.
.
.
.
.
.
.
.
.
.
.
.
59
93
93
93
93
124
124
153
181
208
.
.
.
.
.
.
.
.
.
.
49
78
78
78
78
78
103
103
127
127
150
173
195
.
.
.
.
.
.
.
42
66
66
66
66
66
66
88
88
88
109
109
129
148
167
185
.
.
.
.
36
58
58
58
58
58
58
77
77
77
77
95
95
112
112
129
146
.
.
.
32
51
51
51
51
51
51
51
68
68
68
68
84
84
84
100
100
158
.
.
29
46
46
46
46
46
46
46
46
61
61
61
61
61
76
76
89
116
179
.
19
30
30
30
30
30
30
30
30
30
30
30
30
30
40
40
40
40
50
68
14
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
30
30
37
Sampling-47
EPDR
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.50
5.00
5.50
6.00
7.00
7.50
8.00
8.50
2
3
4
5
6
7
8
9
10
15
20
10 PERCENT RISK OF OVER RELIANCE (ARACR)
114
194
194
265
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
76
129
129
129
176
221
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
57
96
96
96
96
132
132
166
198
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
45
77
77
77
77
77
105
105
132
132
158
209
.
.
.
.
.
.
.
.
.
.
.
.
.
38
64
64
64
64
64
64
88
88
88
110
132
132
153
194
.
.
.
.
.
.
.
.
.
.
32
55
55
55
55
55
55
55
75
75
75
94
94
113
113
131
149
218
.
.
.
.
.
.
.
28
48
48
48
48
48
48
48
48
65
65
65
65
82
82
98
98
130
160
.
.
.
.
.
.
25
42
42
42
42
42
42
42
42
42
58
58
58
58
73
73
73
87
115
142
182
.
.
.
.
22
38
38
38
38
38
38
38
38
38
38
52
52
52
52
52
65
65
78
103
116
199
.
.
.
15
11
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
34
18
34
18
34
18
45
25
52
25
52
25
60
25
68 Sampling-48
32
Effect of population size
-Initial sample size only
-Possible to make adjustment to initial sample size based on
overall population size
-Finite correction factor
n
=
n’
1 + n’/N
n = revised sample size
n’ = initial sample size
N = population size
Sampling-49
From the problem 12-24
Population is
n’ =
Thus revised sample size is
Sampling-50
c) Use of a random number table
– A one-to-one correspondence between
warehouse removal slip
– How is this correspondence achieved?
Sampling-51
Random Stab
Random
Number
Table
37039
97547
64673
31546
99314
66854
97855
25145
98433
97965
78049
50203
84834
54725
68548
67830
25658
23009
18864
81545
14624
91478
51584
65866
82933
17563
08509
66754
76918
93545
25697
23308
77785
78825
85959
07734
48130
52357
58210
63282
48243
65047
40059
84350
30954
86723
50188
67825
67241
51637
36464
22554
18934
54031
91500
98305
86160
64998
34535
48722
08009
92250
49807
04093
60988
00666
14021
71126
35062
60029
29255
65859
77818
58163
60873
18514
16237
50014
66023
04458
57510
43373
00463
21428
61862
36314
58939
13906
14742
63119
30452
95848
35936
94874
09541
09712
28288
71761
23308
01715
37714
60341
95755
58533
87901
95482
52174
87002
26507
91260
30507
11879
61500
78938
64257
56864
35314
12763
71312
93218
21554
29631
64433
99705
35793
70445
06937
02268
71546
43671
24841
54545
57905
42274
64055
04779
04470
72347
23915
88729
56774
75463
49498
38405
11168
96129
77112
40704
07318
94550
34348
92277
48823
44623
23299
81191
57115
65963
02843
45557
21027
50789
39359
33299
07923
77087
68111
12717
59872
75126
10909
75305
56201
86774
00808
03676
53289
22811
06926
01312
97723
39751
56093
16623
50848
48006
56640
58302
17849
93982
58200
27890
52236
96701
66451
58367
28825
65756
94971
32143
66577
96509
50273
94758
05441
68583
21363
61566
08845
10399
21108
53657
61962
32260
17775
41361
60119
Population of
Warehouse
Removal Slips
14,682 – 37,521
Sampling-52
Computed Upper Exception Rate
•
•
•
•
Sample size =
TER =
ARACR =
Number of deviations =
• Using the following tables:
• CUER =
• Are the controls working?
Sampling-53
Table 14-10
ACTUAL NUMBER OF DEVIATIONS FOUND
SAMPLE SIZE
0
25
30
35
40
45
50
55
60
65
70
75
80
90
100
125
150
200
11.3
9.5
8.2
7.2
6.4
5.8
5.3
4.9
4.5
4.2
3.9
3.7
3.3
3.0
2.4
2.0
1.5
1
17.6
14.9
12.9
11.3
10.1
9.1
8.3
7.7
7.1
6.6
6.2
5.8
5.2
4.7
3.7
3.1
2.3
2
3
4
5
6
7
8
9
5 PERCENT RISK OF OVER RELIANCE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
19.5
.
.
.
.
.
.
.
16.9
.
.
.
.
.
.
14.9 18.3
.
.
.
.
.
13.3 16.3 19.2
.
.
.
.
12.1 14.8 17.4 19.9
.
.
.
.
11.0 13.5 15.9 18.1
.
.
.
10.1 12.4 14.6 16.7 18.8
.
.
9.4 11.5 13.5 15.5 17.4 19.3
.
8.7 10.7 12.6 14.4 16.2 18.0 19.7
8.2
7.7
6.8
6.2
4.9
4.1
3.1
10.0
9.4
8.4
7.6
6.1
5.1
3.8
11.8
11.1
9.9
8.9
7.2
6.0
4.5
13.5
12.7
11.3
10.2
8.2
6.9
5.2
15.2
14.3
12.7
11.5
9.3
7.7
5.8
16.9
15.8
14.1
12.7
10.3
8.6
6.5
18.4
17.3
15.5
14.0
11.3
9.4
7.1
20.0
18.8
16.8
15.2
12.2
10.2
7.7
10
.
.
.
.
.
.
.
.
.
.
.
.
18.1
16.4
13.2
11.0
8.3
Sampling-54
Sample size
ACTUAL NUMBER OF DEVIATIONS FOUND
0
1
2
3
4
5
6
7
8
9
10
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
17.9
15.7
14.0
12.7
10.6
8.0
6.4
19.5
17.2
15.3
13.8
11.6
8.7
7.0
.
.
.
.
.
.
.
.
.
.
10 PERCENT RISK OF OVER RELIANCE
20
25
30
35
40
45
50
55
60
70
80
90
100
120
160
200
10.9
8.8
7.4
6.4
5.6
5.0
4.5
4.1
3.8
3.2
2.8
2.5
2.3
1.9
1.4
1.1
18.1
14.7
12.4
10.7
9.4
8.4
7.6
6.9
6.3
5.4
4.8
4.3
3.8
3.2
2.4
1.9
.
19.9
16.8
14.5
12.8
11.4
10.3
9.4
8.6
7.4
6.5
5.8
5.2
4.4
3.3
2.6
.
.
.
18.1
15.9
14.2
12.9
11.7
10.8
9.3
8.3
7.3
6.6
5.5
4.1
3.3
.
.
.
.
19.0
17.0
15.4
14.0
12.9
11.1
9.7
8.7
7.8
6.6
4.9
4.0
.
.
.
.
.
19.6
17.8
16.2
14.9
12.8
11.3
10.1
9.1
7.6
5.7
4.6
.
.
.
.
.
.
.
18.4
16.9
14.6
12.8
11.4
10.3
8.6
6.5
5.2
.
.
.
.
.
.
.
.
18.8
16.2
14.3
12.7
11.5
9.6
7.2
5.8
18.6
16.6
15.0
12.5
9.5
7.6
Sampling-55