1. The Use of Audit Sampling Attribute Sampling
Section 2
The Use of Audit Sampling
Attribute Sampling

2. Definition of Audit 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

3. Representative sample
Sample projection
Aggregate all projected misstatements

4. Audit Risk and Sampling
Determine minimum sample need to control audit risk
How does this relate to sampling?

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

6. 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

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

8. Determinants of Sample Size
Three factors
Acceptable level of sampling risk
How much deviation can be accepted
How much deviation there might be in the population

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

10. Tolerable misstatement amount
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

11. 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

12. 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

13. 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

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

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

16. Statistical Tests of Controls
Attribute Sampling
Used to estimate the rate of occurrence of a specific quality or attribute in a population
Primarily used for

17. 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?

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

19. Audit Sampling Steps Three sections Plan the sample
Select the sample and perform audit procedures
Evaluate the results

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

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

22. 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

23. 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

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

25. 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?

26. 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

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

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

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

30. 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 and the largest is The smallest invoice number is and the largest is
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.

31. State an effective audit procedure for testing whether shipments have been billed. What is the sampling unit for the audit procedure?
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?
TDR = 3%
ARO = 10%
EPDR = ?

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

33. 10 PERCENT RISK OF OVER RELIANCE2 3 4 5 6 7 8 9 10 15 20
10 PERCENT RISK OF OVER RELIANCE
0.00
114 76 57 45 38 32 28 25 22 11
0.25
194
129 96 77 64 55 48 42 18
0.50
0.75
265
1.00 .
176
1.25
221
132
1.50
105
1.75
166 88
2.00
198 75
2.25 65
2.50
158
110 58
2.75
209 94 52
3.00
3.25
153
113 82
3.50 73
3.75
131 98
4.00
149
4.50
218
130 87 34
5.00
160
115 78
5.50
142
103
6.00
182
116
7.00
199
7.50
8.00 60
8.50 68

34. 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 = revised sample size
n’ = initial sample size
N = population size
n = n’
1 + n’/N

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

36. (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?

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

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

39. (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)

40. 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 that there was 1 deviation in the sample of 76

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

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

43. 10 PERCENT RISK OF OVER RELIANCE20
10.9
18.1 . 25
8.8
14.7
19.9 30
7.4
12.4
16.8 35
6.4
10.7
14.5 40
5.6
9.4
12.8
15.9
19.0 45
5.0
8.4
11.4
14.2
17.0
19.6 50
4.5
7.6
10.3
12.9
15.4
17.8 55
4.1
6.9
11.7
14.0
16.2
18.4 60
3.8
6.3
8.6
10.8
14.9
16.9
18.8 70
3.2
5.4
9.3
11.1
14.6
17.9
19.5 80
2.8
4.8
6.5
8.3
9.7
11.3
14.3
15.7
17.2
18.6 90
2.5
4.3
5.8
7.3
8.7
10.1
12.7
15.3
16.6
100
2.3
5.2
6.6
7.8
9.1
11.5
13.8
15.0
120
1.9
4.4
5.5
9.6
10.6
11.6
12.5
160
1.4
2.4
3.3
4.9
5.7
7.2
8.0
9.5
200
1.1
2.6
4.0
4.6
7.0
. Over 20 percent

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

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

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

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

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

49. Problem 1. 12-33: The following is a partial audit program for the audit of cash receipts
Review the cash receipts journal for large and unusual transactions.
Trace entries from the prelisting of cash receipts to the cash receipts journal to determine if each is recorded.
Compare customer name, date, and amount on the prelisting with the cash receipts journal.
Examine the related remittance advices for entries selected from the prelisting to determine if cash discounts were approved.
Trace entries from the prelisting to the deposit slip to determine if each has been deposited.
Required:
Identify which audit procedures could be tested using attribute sampling.
What is the appropriate sampling unit for the tests in part (a)?
List the attributes for testing in part (a).
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?

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

51. Required:
For each of the columns numbered 1 through 7, decide the initial sample size using nonstatistical methods.
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.
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.
An increase in ARACR.
An increase in the TER.
An increase in the EPER.
An increase in the population size.
Explain why there is such a large difference in the column sizes for columns 3 and 6.
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?
Why is the sample size referred to as the initial sample size?

52. 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
ARO
TDR
EDR n
Deviations Found
CUDR 1 10 8 50 2 3 70 4 5
150 6

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

54. Problem 4. Attributes in Tests of Controls
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.
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 The accounts receivable record indicates that the customer paid for the quantity listed on the sales order and sales invoice.
Invoice 2-631: Bill of lading No (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.
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.

55. Invoice 4-395: The bill of lading No
Invoice 4-395: The bill of lading No 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..
Invoice 5-422: Bill of lading No indicated that the customer order number was LO5992, but the attached order number was PO6884..
Invoice 6-837: Bill of lading No indicated that a dozen hammers were shipped. The sales journal and sales invoice indicated that 12 dozen hammers were shipped.
Invoice 7-012: Invoice was voided.
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:
What attribute(s) did jenny test?
Which items listed above should she treat as a deviation?
Is it appropriate for Jenny to combine the results of her testing and make an overall statement about internal control?
State the statistical conclusions Jenny should reach.
What conclusions should Jenny reach about the company’s internal control?