The Use of Audit Sampling
Attribute Sampling

• The application of an audit procedure to less than 100% of the items within an account balance or class of transactions for the purpose of evaluating some characteristic of the balance or class.
• Extrapolation

• Representative sample
• Sample projection
• Aggregate all projected misstatements

• Determine minimum sample need to control audit risk
• How does this relate to sampling?

Defining the Population
• First step
• Restricted to items in the balance or class of transactions

Sampling risk
• When an audit test is restricted to a sample
• For testing controls or account balances this means
• Sampling risk inversely related to sample size

Nonsampling risk
• Covers all risks that are not specifically the result of sampling
• i.e. any factor other than sample size

• Three factors
– Acceptable level of sampling risk
– How much deviation can be accepted
– How much deviation there might be in the population

Acceptable Level of Sampling Risk
• Must consider evidence from other procedures
• Example 1: Low control risk
• Example 2: High control risk

Tolerable Deviation Rate/Tolerable Misstatement
• Rate of deviation from a prescribed control that can be found to exist, without causing a revision in the assessed level of control risk
• Tolerable misstatement amount

• Cannot be larger than the smaller of :
– The materiality amount for the individual item or
– The F/S taken as a whole
• As tolerable rate or misstatement increases

• Suggested range of TDR
• No such guidelines for substantive testing
• Usually done judgmentally based on:
• Overall materiality
• Account balance materiality
• Type and amount of individual item in the account balance

• Designing a sample with high tolerable rate or misstatement
• A large sample vs. a small sample
• Highly material accounts or accounts with high likelihood of misstatement

Expected Deviation Rate/ Misstatement Amount
• Impact on sample size
• Commonly use prior years tests of controls

• Estimate need not be exact
• Unless deviation rate is low for tests of controls, what is the alternative?

• Attribute Sampling
– Used to estimate the rate of occurrence of a specific quality or attribute in a population
– Primarily used for

• E.g. Estimating the percentage of shipments not billed
• Thus testing to see if the item was processed correctly or incorrectly
• What about dollar value?

• For Attribute Sampling there is no CICA pronouncement
•
Three areas to look at:
1. Planning the sample
2. Selecting the sample and performing the tests
3. Evaluating the results

• Three sections a) Plan the sample b) Select the sample and perform audit procedures c) Evaluate the results

(a) Planning the Sample
• 9 steps involved
1. State the objectives of the test
• Consider the Revenue Cycle

2. Decide if audit sampling applies
•
Is the population appropriate?
•
Sampling applies when?

3. Define attributes and error conditions
– Specific statement of what contributes an attribute must be made in advance
– E.g.1 A copy of a shipping document is attached to a duplicate sales invoice
– E.g.2 A foreman initials the hourly payroll time cards

4.
Define the population
– Must be defined in advance
– E.g.1 A copy of a shipping document is attached to a duplicate sales invoice
• Population?
– E.g.2 A foreman initials the hourly payroll time cards
• Population?

5.
Define the sampling unit
– What dictates the sampling unit?
– E.g.1 Valid sales
• Sampling unit?
– E.g.2 Valid time cards
• Sampling unit?

6. Specify Tolerable Deviation Rate
– What does this mean?
– E.g. With time cards, auditor decides that 5% is the TDR. This means?
- As TDR Sample size?

7.
Specify the acceptable risk of over reliance
(ARO)
– Over reliance on what?
– The ARO is the risk the auditor is willing to take of:
 accepting the control procedure as effective
 when the true population deviation rate
 is greater than the TDR
– An alternative understanding

Illustrative Guidelines for TDR and ARO
Control Risk ARO
Significance of T/A’s
TDR
Low
Medium
High
5% Highly significant
10% Significant
20% Less significant
4%
5%
6%
•Thus what does it mean if control risk is high?

8.
Estimate the expected population deviation rate
(EPDR)
– An advanced estimate
– What is typically used?
– If this estimate is not available?

9. Determine the initial sample size
– Why look at the initial sample size?
– Will look at an illustrative example.

12-32. Lentner Supply Corp.
Lentner 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.

(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% risk of over reliance, what is the appropriate sample size?
1.
TDR = 3%
2.
ARO = 10%
3.
EPDR = ?

0.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
5.00
6.00
7.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
EXPECTED
POPULATION
DEVIATION RATE (IN
PERCENTAGE)
TOLERABLE DEVIATION RATE
(IN PERCENTAGE)
2 3 4 5 6 7 8 9 10 15 20
5 PERCENT RISK OF OVER RELIANCE
149 99 74 59 49 42 36 32 29 19 14
236 157 117 93 78 66 58 51 46 30 22
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
157 117 93 78 66 58 51 46 30 22
.
208 117 93 78 66 58 51 46 30 22
.
.
156
156
93
124
78
78
66
66
58
58
51
51
46
46
30
30
22
22
.
.
.
.
192
227
.
.
124
153
181
208
103
103
127
127
66
88
88
88
58
77
77
77
51
51
68
68
46
46
46
61
30
30
30
30
22
22
22
22
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
.
150 109 77 68 61 30 22
.
173 109 95 68 61 30 22
.
.
195 129 95 84 61 30 22
.
148 112 84 61 30 22
.
.
.
.
.
167 112 84 76 40 22
.
185 129 100 76 40 22
.
.
.
.
146
.
.
.
100
158
.
.
89
116
179
.
40
40
50
68
22
30
30
37

0.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
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
114 76 57 45 38 32 28 25 22 15 11
194 129 96 77 64 55 48 42 38 25 18
194 129 96 77 64 55 48 42 38 25 18
265 129 96 77 64 55 48 42 38 25 18
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
176 96 77 64 55 48 42 38 25 18
.
221 132 77 64 55 48 42 38 25 18
.
.
132
166
105
105
64
88
55
55
48
48
42
42
38
38
25
25
18
18
.
.
.
.
198
.
132
132
88
88
75
75
48
65
42
42
38
38
25
25
18
18
.
158 110 75 65 58 38 25 18
.
209 132 94 65 58 52 25 18
.
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.
.
132 94 65 58 52 25 18
.
153 113 82 58 52 25 18
.
.
194 113 82 73 52 25 18
.
131 98 73 52 25 18
.
.
.
.
.
.
.
.
.
149
218
.
.
.
.
.
.
.
98
130
160
.
.
.
.
.
73
87
115
142
65
65
78
103
25
34
34
34
18
18
18
18
.
182 116 45 25
.
.
.
.
199
.
52
52
25
25
.
60 25
.
68 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

From the problem 12-32
Population is n =
Thus revised sample size is ?

(b) Select sample and perform audit procedures
• Two Steps involved
10. Randomly select the sample
(Requirement c of 12-32)
• Use of a random number table
• A one-to-one correspondence between warehouse removal slip
• How is this correspondence achieved?

Random Stab
Random Number
Table
37039
25145
98433
97965
78049
50203
40059
84350
30954
86723
50188
50014
66023
04458
57510
43373
61500
78938
64257
56864
35314
40704
07318
94550
34348
92277
56093
16623
50848
48006
56640
31546
51584
65866
82933
17563
08509
64998
34535
48722
08009
92250
35936
94874
09541
09712
28288
02268
71546
43671
24841
54545
39359
33299
07923
77087
68111
65756
94971
32143
66577
96509
64673
23009
18864
81545
14624
91478
18934
54031
91500
98305
86160
13906
14742
63119
30452
95848
64433
99705
35793
70445
06937
65963
02843
45557
21027
50789
52236
96701
66451
58367
28825
97547
84834
54725
68548
67830
25658
67825
67241
51637
36464
22554
00463
21428
61862
36314
58939
12763
71312
93218
21554
29631
48823
44623
23299
81191
57115
58302
17849
93982
58200
27890
66854
77785
78825
85959
07734
48130
71126
35062
60029
29255
65859
95755
58533
87901
95482
52174
72347
23915
88729
56774
75463
56201
86774
00808
03676
53289
61566
08845
10399
21108
53657
99314
66754
76918
93545
25697
23308
49807
04093
60988
00666
14021
71761
23308
01715
37714
60341
57905
42274
64055
04779
04470
12717
59872
75126
10909
75305
50273
94758
05441
68583
21363
97855
52357
58210
63282
48243
65047
77818
58163
60873
18514
16237
87002
26507
91260
30507
11879
49498
38405
11168
96129
77112
22811
06926
01312
97723
39751
61962
32260
17775
41361
60119
Population of
Warehouse Removal
Slips 14,682 – 37,521

11. Perform the audit procedures
• Requirement a of 12-32 already done
• Requirement d of 12-32
– Other audit procedures

(c) Evaluating the results
• Three steps involved
– Generalize from the sample to the population
(12)
– Analyze deviations (13); and
– Decide the acceptability of the population
(14)

12. Generalize from the sample to the population
• Need to calculate the sample deviation rate
• SDR = Actual number of deviation
Sample size
• Assume in problem 12-32 that there was 1 deviation in the sample of 76

• Sampling risk prevent auditor from
• Note: ARO was 10%, and n = 76
• Calculation of CUDR

SAMPLE SIZE
25
80
90
100
125
150
200
60
65
70
75
30
35
40
45
50
55
ACTUAL NUMBER OF DEVIATIONS FOUND
0 1 2 3 4 5 6 7 8 9 10
5 PERCENT RISK OF OVER RELIANCE
11.3
17.6
.
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.
.
.
.
.
.
9.5
14.9
19.5
8.2
12.9
16.9
.
.
7.2
11.3
14.9
18.3
.
.
.
6.4
10.1
13.3
16.3
19.2
.
.
.
.
5.8
9.1
12.1
14.8
17.4
19.9
5.3
8.3
11.0
13.5
15.9
18.1
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.
.
.
.
.
4.9
7.7
10.1
12.4
14.6
16.7
18.8
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.
.
4.5
7.1
9.4
11.5
13.5
15.5
17.4
19.3
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.
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.
.
.
.
.
4.2
6.6
8.7
10.7
12.6
14.4
16.2
18.0
19.7
.
.
.
.
.
.
.
.
.
3.9
6.2
8.2
10.0
11.8
13.5
15.2
16.9
18.4
20.0
3.7
5.8
7.7
9.4
11.1
12.7
14.3
15.8
17.3
18.8
.
.
.
.
.
.
.
.
.
.
.
3.3
5.2
6.8
8.4
9.9
11.3
12.7
14.1
15.5
16.8
18.1
3.0
4.7
6.2
7.6
8.9
10.2
11.5
12.7
14.0
15.2
16.4
2.4
3.7
4.9
6.1
7.2
8.2
9.3
10.3
11.3
12.2
13.2
2.0
3.1
4.1
5.1
6.0
6.9
7.7
8.6
9.4
10.2
11.0
1.5
2.3
3.1
3.8
4.5
5.2
5.8
6.5
7.1
7.7
8.3

20
70
80
90
100
120
160
200
45
50
55
60
25
30
35
40
. Over 20 percent
10 PERCENT RISK OF OVER RELIANCE
10.9
18.1
.
8.8
14.7
19.9
7.4
12.4
16.8
.
.
.
6.4
10.7
14.5
18.1
.
.
.
.
5.6
9.4
12.8
15.9
19.0
.
.
.
.
.
5.0
8.4
11.4
14.2
17.0
19.6
4.5
7.6
10.3
12.9
15.4
17.8
.
.
.
.
.
.
.
4.1
6.9
9.4
11.7
14.0
16.2
18.4
.
.
.
.
.
.
.
.
3.8
6.3
8.6
10.8
12.9
14.9
16.9
18.8
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.
.
.
.
.
.
.
.
.
.
.
.
.
3.2
5.4
7.4
9.3
11.1
12.8
14.6
16.2
17.9
19.5
2.8
4.8
6.5
8.3
9.7
11.3
12.8
14.3
15.7
17.2
18.6
2.5
4.3
5.8
7.3
8.7
10.1
11.4
12.7
14.0
15.3
16.6
2.3
3.8
5.2
6.6
7.8
9.1
10.3
11.5
12.7
13.8
15.0
1.9
3.2
4.4
5.5
6.6
7.6
8.6
9.6
10.6
11.6
12.5
1.4
2.4
3.3
4.1
4.9
5.7
6.5
7.2
8.0
8.7
9.5
1.1
1.9
2.6
3.3
4.0
4.6
5.2
5.8
6.4
7.0
7.6
.
.
.
.
.
.
.
.
.
.

• This measure of CUDR means:
• But true deviation rate is not 5.1
• Revised CUDR =
(CUDR-SDR) x N – n
N
+ SDR

13. Analyze deviations or errors
• Why?
• What could have caused the deviation?

14. Decide the acceptability of the population
• When can the population be considered acceptable?
• From 12.32 TDR = 3% and CUDR = 5.1%

Four courses of action can now be followed
1. Revise TDR or ARO
2. Expand sample size
1. If n CUDR

3. Revise assessed control risk
4. Write a letter to management

Problem 1. 12-33: The 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 if each is recorded.
3.
Compare customer name, date, and amount on the prelisting with the cash receipts journal.
4.
Examine the related remittance advices for entries selected from the prelisting to determine if cash discounts were approved.
5.
Trace entries from the prelisting to the deposit slip to determine if each has been deposited.
Required: a.
Identify which audit procedures could be tested using attribute sampling.
b.
What is the appropriate sampling unit for the tests in part (a)?
c.
List the attributes for testing in part (a).
d.
Assume an ARACR of 5 percent and a TER of 8 percent for tests of controls. The estimated population deviation rate for tests of controls is 2 percent. What is the initial sample size for each attribute?

Problem 2. 12-34 The following questions concern the determination of the proper sample size in attributes sampling using the following table:
ARACR (in percentage)
1
10
6 TER (in percentage)
EPER (in percentage)
2
2
5
6
2
3
5
5
2
4
5
6
2
5
10
20
8
6
10
20
2
7
5
2
0
Population size
1,000 100,000 6,000 1,000 500 500 1,000,000

Required: a.
For each of the columns numbered 1 through 7, decide the initial sample size using nonstatistical methods.
b.
For each of the columns numbered 1 through 7, determine the initial sample size needed to satisfy the auditor’s requirements using attribute sampling from Table 12-
8.
c.
Using your understanding for the relationship between the following factors and sample size, state the effect on the initial sample size (increase or decrease) of changing each of the following factors while the other three are held constant.
1) An increase in ARACR.
2) An increase in the TER.
3) An increase in the EPER.
4) An increase in the population size.
d.
Explain why there is such a large difference in the column sizes for columns 3 and 6.
e.
Compare your answers in part (b) with the results in part (a). Which of the four factors appears to have the greatest effect on the initial sample size? Which appears to have the least effect?
f.
Why is the sample size referred to as the initial sample size?

Problem 3. Computed Upper Deviation Rate : The questions below relate to the upper deviation rate for the following six tests of controls using attribute sampling.
Control
1
4
5
2
3
6
ARO
10
5
5
10
10
5
TDR
8
8
10
8
8
10
1
4
2
2
3
1
EDR n
50
50
70
150
50
50
Deviations
Found
0
1
2
1
3
1
CUDR

Required: a.
For each control from 1 through 6, determine the computed upper deviation rate.
b.
For which controls does the result suggest that the control risk is higher than the auditor has assessed?
c.
Explain the effect on the CUDR of changing each of the following three factors while holding the other factors constant: a.
Decreasing the risk of assessing control risk too low.
b.
Increasing the deviations found in the sample.
c.
Increasing the sample size.

Problem 4. Attributes in Tests of Controls . In auditing the December 31, 200X, financial statements of the Henderson Company, Jenny Starr, CA, is applying attribute sampling in the tests of controls for sales transactions. Based on her knowledge of Henderson Company’s internal control, she estimated that the population deviation rate was 2 percent, and she was willing to accept a 5 percent risk of assessing control risk at a lower level than it actually is. She believes that if the maximum deviation rate is 6 percent, her assessment of control risk at less than maximum is appropriate. Jenny selected a random sample of 200 shipping documents from the 5,500 prepared during the year and audited them. She noted the following matters in the working papers.
1.
Invoice 1-422 : The signature that would indicate that the shipping clerk recounted the quantity of goods before making shipment was missing from sales order 2971.
The accounts receivable record indicates that the customer paid for the quantity listed on the sales order and sales invoice.
2.
Invoice 2-631 : Bill of lading No. 3118 (indicated on the invoice) could not be located. The accounts receivable record indicates that the customer paid for the quantity listed on the customer’s purchase order and sales invoice.
3.
Invoice 3-249 : The date that goods were shipped according to the attached bill of lading was four days earlier than the date indicated on the sales invoice and sales journal.

4.
Invoice 4-395 : The bill of lading No. 5113 indicated that six pairs of R327 flanges were shipped, and the sales invoice and sales journal indicated that only six R327 flanges were shipped. The flanges cost $2.02 each..
5.
Invoice 5-422 : Bill of lading No. 5892 indicated that the customer order number was LO5992, but the attached order number was PO6884..
6.
Invoice 6-837 : Bill of lading No. 8921 indicated that a dozen hammers were shipped. The sales journal and sales invoice indicated that 12 dozen hammers were shipped.
7.
Invoice 7-012 : Invoice 7-012 was voided.
8.
Invoice 8-318: A signature was not recorded on the invoice copy indicating that math had been checked before the invoice was mailed to the customer. A mathematical error was not made in calculating the total invoice price.
Required: a.
What attribute(s) did jenny test?
b.
Which items listed above should she treat as a deviation?
c.
Is it appropriate for Jenny to combine the results of her testing and make an overall statement about internal control?
d.
State the statistical conclusions Jenny should reach.
e.
What conclusions should Jenny reach about the company’s internal control?