The Use of Audit Sampling

1
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 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

• 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
• Population?

24

• 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?

25

• 6. Specify Tolerable Deviation Rate
• What does this mean?
• E.g. With time cards, auditor decides that 5 is
  the TDR. This means?

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

• Illustrative Guidelines for TDR and ARO

Control Risk ARO Significance of T/As TDR
Low 5 Highly significant 4
Medium 10 Significant 5
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
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.
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
EXPECTED POPULATION DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE) TOLERABLE DEVIATION RATE (IN PERCENTAGE)
EXPECTED POPULATION DEVIATION RATE (IN PERCENTAGE) 2 3 4 5 6 7 8 9 10 15 20
5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 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 . 157 117 93 78 66 58 51 46 30 22
0.75 . 208 117 93 78 66 58 51 46 30 22
1.00 . . 156 93 78 66 58 51 46 30 22
1.25 . . 156 124 78 66 58 51 46 30 22
1.50 . . 192 124 103 66 58 51 46 30 22
1.75 . . 227 153 103 88 77 51 46 30 22
2.00 . . . 181 127 88 77 68 46 30 22
2.25 . . . 208 127 88 77 68 61 30 22
2.50 . . . . 150 109 77 68 61 30 22
2.75 . . . . 173 109 95 68 61 30 22
3.00 . . . . 195 129 95 84 61 30 22
3.25 . . . . . 148 112 84 61 30 22
3.50 . . . . . 167 112 84 76 40 22
3.75 . . . . . 185 129 100 76 40 22
4.00 . . . . . . 146 100 89 40 22
5.00 . . . . . . . 158 116 40 30
6.00 . . . . . . . . 179 50 30
7.00 . . . . . . . . . 68 37

33
2 3 4 5 6 7 8 9 10 15 20
10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE
0.00 114 76 57 45 38 32 28 25 22 15 11
0.25 194 129 96 77 64 55 48 42 38 25 18
0.50 194 129 96 77 64 55 48 42 38 25 18
0.75 265 129 96 77 64 55 48 42 38 25 18
1.00 . 176 96 77 64 55 48 42 38 25 18
1.25 . 221 132 77 64 55 48 42 38 25 18
1.50 . . 132 105 64 55 48 42 38 25 18
1.75 . . 166 105 88 55 48 42 38 25 18
2.00 . . 198 132 88 75 48 42 38 25 18
2.25 . . . 132 88 75 65 42 38 25 18
2.50 . . . 158 110 75 65 58 38 25 18
2.75 . . . 209 132 94 65 58 52 25 18
3.00 . . . . 132 94 65 58 52 25 18
3.25 . . . . 153 113 82 58 52 25 18
3.50 . . . . 194 113 82 73 52 25 18
3.75 . . . . . 131 98 73 52 25 18
4.00 . . . . . 149 98 73 65 25 18
4.50 . . . . . 218 130 87 65 34 18
5.00 . . . . . . 160 115 78 34 18
5.50 . . . . . . . 142 103 34 18
6.00 . . . . . . . 182 116 45 25
7.00 . . . . . . . . 199 52 25
7.50 . . . . . . . . . 52 25
8.00 . . . . . . . . . 60 25
8.50 . . . . . . . . . 68 32
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
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
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 23308 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 Number Table
38

• 11. Perform the audit procedures
• Requirement a of 12-32 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

• Assume in problem 12-32 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
SAMPLE SIZE ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND ACTUAL NUMBER OF DEVIATIONS FOUND
SAMPLE SIZE 0 1 2 3 4 5 6 7 8 9 10
5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 5 PERCENT RISK OF OVER RELIANCE 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 11.3 14.9 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 10.1 12.4 14.6 16.7 18.8 . . . .
65 4.5 7.1 9.4 11.5 13.5 15.5 17.4 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 8.2 10.0 11.8 13.5 15.2 16.9 18.4 20.0 .
80 3.7 5.8 7.7 9.4 11.1 12.7 14.3 15.8 17.3 18.8 .
90 3.3 5.2 6.8 8.4 9.9 11.3 12.7 14.1 15.5 16.8 18.1
100 3.0 4.7 6.2 7.6 8.9 10.2 11.5 12.7 14.0 15.2 16.4
125 2.4 3.7 4.9 6.1 7.2 8.2 9.3 10.3 11.3 12.2 13.2
150 2.0 3.1 4.1 5.1 6.0 6.9 7.7 8.6 9.4 10.2 11.0
200 1.5 2.3 3.1 3.8 4.5 5.2 5.8 6.5 7.1 7.7 8.3

43
10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE 10 PERCENT RISK OF OVER RELIANCE
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 18.1 . . . . . . .
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 9.4 11.7 14.0 16.2 18.4 . . . .
60 3.8 6.3 8.6 10.8 12.9 14.9 16.9 18.8 . . .
70 3.2 5.4 7.4 9.3 11.1 12.8 14.6 16.2 17.9 19.5 .
80 2.8 4.8 6.5 8.3 9.7 11.3 12.8 14.3 15.7 17.2 18.6
90 2.5 4.3 5.8 7.3 8.7 10.1 11.4 12.7 14.0 15.3 16.6
100 2.3 3.8 5.2 6.6 7.8 9.1 10.3 11.5 12.7 13.8 15.0
120 1.9 3.2 4.4 5.5 6.6 7.6 8.6 9.6 10.6 11.6 12.5
160 1.4 2.4 3.3 4.1 4.9 5.7 6.5 7.2 8.0 8.7 9.5
200 1.1 1.9 2.6 3.3 4.0 4.6 5.2 5.8 6.4 7.0 7.6

. Over 20 percent
44

• This measure of CUDR means
• But true deviation rate is not 5.1
• Revised CUDR

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 12.32 TDR 3 and CUDR 5.1

47

• Four courses of action can now be followed

• Revise TDR or ARO

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 2. 12-34 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 5 5 5 10 10 5
TER (in percentage) 6 6 5 6 20 20 2
EPER (in percentage) 2 2 2 2 8 2 0
Population size 1,000 100,000 6,000 1,000 500 500 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 auditors 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 1 50 0
2 10 8 2 50 1
3 10 8 3 70 3
4 5 8 4 150 1
5 5 10 2 50 2
6 5 10 1 50 1
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. 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 Companys 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 2971. 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. 3118 (indicated
  on the invoice) could not be located. The
  accounts receivable record indicates that the
  customer paid for the quantity listed on the
  customers 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. 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..
• Invoice 5-422 Bill of lading No. 5892 indicated
  that the customer order number was LO5992, but
  the attached order number was PO6884..
• 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.
• Invoice 7-012 Invoice 7-012 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
  companys internal control?