1. Audit Sampling Concepts

2. Importance of Sampling
Auditor does not look at everything
How does this affect the opinion?
Auditor CANNOT look at everything
Why?

3. Introduction to Audit Sampling
Audit sampling is:
The application of an audit procedure to less than 100 percent of the items within an account balance population or class of transactions.
For the purpose of evaluating some characteristic of the balance or class.
Audit procedure
Account balance
Class of transactions

4. Purpose of Sampling
The auditor examines only a portion of the population in order to estimate
How much is a portion?

5. Risk and Materiality
Risk and materiality form the basis for determining the extent of procedures to be undertaken.
Extent
Materiality is related to sampling precision
Risk is related to confidence from sampling

7. When to Do Sampling When?
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

8. When is Sampling Used? To conduct: For tests of controls
Tests of details

9. Inclusions and Exclusions Related to Audit Sampling
Sampling involves looking at part of a population in order to reach a conclusion on the entire population.
Sampling would not include:
100% audit
a walk-through

10. Representative Sampling
Having a representative sample is important
What does representative mean?

11. Sampling and Non-Sampling Risk
The probability that an auditor’s conclusion based on a sample might be different from the conclusion based on an audit of the entire population.
Beta risk or risk of incorrect acceptance (RIA)
Alpha risk or risk of incorrect rejection (RIR).
Auditors are primarily concerned with Beta risk.

12. Non-sampling risk:
The risk of auditor error that arises from the possibility that the auditor
Failure to detect a misstatement

13. Statistical Sampling
Uses the laws of probability for selecting and evaluating a sample from a population
Selected at random
Random sample:
Statistical calculations are used

14. Nonstatistical (Judgmental) Sampling
Non-statistical sampling is audit sampling in which auditors do not utilize statistical calculations to express the results.

15. Statistical vs. Non-Statistical
Similarities
Both require a structured process
The use of stratification
Differences
Sampling risk cannot be quantified

16. 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

17. 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

18. 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 or systematic sampling
Auditor calculates an interval and use the interval to select sample

19. Major problem with systematic sampling is bias
Once the first item is chosen
No problem if
But some characteristics

20. Attribute Sampling Methodology
Another key statistical methodology
very useful for tests of controls
look in the population for a particular attribute or characteristic
The main question to be answered is
If the auditor can allow 5% deviations

21. Probability Proportionate-to-Size Sampling Methodology
A key statistical methodology
Also known as
The sampling unit is
MUS allows the result to be stated

22. Advantages of Statistical Sampling
Provides:
for quantitative evaluation of the sample results
a more defensible expression of the test results
It is more objective

23. 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

24. 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

25. Disadvantages of non-statistical sampling
Cannot draw objectively valid statistical inferences from the sample results
Cannot quantitatively measure and express sampling risk.

26. The Main Phases of the Sampling Process
Both statistical and non-statistical methods
Planning the sample
Selecting the sample
Performing the tests
Evaluating the results

27. Sampling Process Fourteen steps in the sampling process.
Look at tests of controls versus tests of details

28. 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

29. 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

30. 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

31. 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.

32. 5. Define the sampling unit
Tests of control:
Usually a physical unit
Test of detail:
If MUS
If non-statistical sampling

33. 6. Specify tolerable deviation rate (TDR) or specify materiality
Test of control:
TDR (Also TER)
As TDR increases
Test of detail:
Materiality is used
These decisions require the use of

34. 7. Specify RIA Test of control:
What is RIA? Also called RACR or ARACR.
Risk of Assessing Control Risk Too Low
Test of detail:
What is RIA (ARIA)?
Risk of Incorrect Acceptance

35. If RIA changes from 10% to 5%
Test of control:
Assume
TDR 6%
RIA 10%
But unknown to the auditor the true error rate is 8%
Test of detail:
If RIA changes from 10% to 5%
since assurance required increases
When controls are good

36. 8. Estimate population exception rate or misstatements
Test of control:
Estimated population deviation rate (EPDR or EPER)
The lower the EPDR, the smaller the sample size
Test of detail:
Provide an advance estimate of the total dollar error, i.e. misstatements, in the population

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. Example of Point Estimate Calculation x =
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
$91,695
$(2,740) 2 6
71,235
43,995
43,024
971
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 x
Recorded Book Value for Stratum =
Point Estimate of Misstatement 1
$(2,740)/$88,955
$88,955
$(2,470) 2
971/43,995
71,235
1,572 3
2,158/13,105
47,105
7,757
Total
$6,589

44. 13. Analyze exceptions or misstatements
Test of control
What breakdown in internal controls caused the exceptions?
Should additional substantive testing be conducted because of these results?
Test of detail
Were the misstatements caused by control exceptions?
Is additional substantive testing required?

45. 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

46. What if the auditor decides the population is NOT acceptable
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.

47. Problem 1
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
Which of the invoices in the table should be defined as an exception?
Explain why it is inappropriate to set a single acceptable TER and EPER for the combined exceptions.
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 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
9169
Credit is not authorized, but the sale was only for $7.65.

48. Problem 2
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.
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 whether each is recorded.
Compare customer name, date, and amount on the prelisting with the cash receipts journal.
Examine the related remittance advice for entries selected from the prelisting to determine whether cash discounts were approved.
Trace entries from the prelisting to the deposit slip to determine whether each has been deposited.
REQUIRED
Identify which audit procedures can be tested using attribute sampling. Justify your response.
State the appropriate sampling unit for each of the tests in part (a).
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.
Define exception conditions for each of the attributes that you have described in part (c).
Which of the exceptions would be indicative of potential fraud? Justify your response.

49. Problem 3 – Attribute Sampling
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 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.

50. 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% RIA, what is the appropriate sample size?

51. Calculating Sample Size – CAS 530
R = nP
R is the PPS Factor determiner from a PPS table.
n is the sample size
P is the precision or Tolerable Deviation Rate
The auditor also needs to know the Expected Population Deviation Rate (EPDR)
Usually obtained from last years audit sampling results
Use an EPDR of 0. i.e. the auditor expects no deviations

52. R Value Table Number of Errors R @ 90% R @ 95% R @ 97.5% 2.31 3.00
2.31
3.00
3.69 1
3.89
4.75
5.58 2
5.33
6.30
7.23 3
6.69
7.76
8.77 4
8.00
9.16
10.25 5
9.28
10.52
11.67 6
10.54
11.85
13.06 7
11.78
13.15
14.43 8
13.00
14.44
15.77 9
14.21
15.71
17.09 10
15.41
16.97
18.40

53. Given a confidence level of 90% and TDR of 3%
With and EPDR of 0, R = 2.31
Thus n = R/P = 2.31/0.03 = 77.

54. The following table is from the text, Appendix 10A.
TABLE FOR DETERMINING SAMPLE SIZE FOR TEST OF CONTROL USING THE MUS APPROACH TOLERABLE RATE OF DEVIATIONS FOR ERRORS
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.15
0.20
Beta Risk = 0.05
300
150
100 75 60 50 43 38 34 30 20 15
Beta Risk = 0.10
231
116 77 58 47 39 33 29 26 24 16 12
Beta risk or risk of incorrect acceptance. The risk of accepting an account as materially accurate when it is in fact materially misstated. More audit work would actually be needed and it is not performed.
Alpha risk or risk of incorrect rejection. The risk of rejecting an account as materially accurate when it is in fact not materially misstated. This would require more audit work when it is really not needed.

55. 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 % Risk of Incorrect Acceptance(RIA or Beta Risk)
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

56. 10 % Risk of Incorrect Acceptance (RIA or Beta Risk)2 3 4 5 6 7 8 9 10 15 20
10 % Risk of Incorrect Acceptance (RIA or Beta Risk)
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
EPDR

57. 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

58. From the problem 12-24
Population is
n’ =
Thus revised sample size is

59. Use of a random number table
A one-to-one correspondence between warehouse removal slip
How is this correspondence achieved?

60. Random Number Table Random Stab 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
Random Stab
Random Number Table

61. Upper Exception Limit (UEL)
Sample size =
TER =
RIA =
Number of deviations =
Using the following tables:
UEL =
Are the controls working?

62. 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 % Risk of Incorrect Acceptance( RIA or Beta Risk) 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

63. 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
10 % Risk of Incorrect Acceptance (RIA or Beta Risk) 20
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