Chapter 9
SAMPLING IN SUBSTANTIVE TESTING
Planning: 1. Determine objectives 2. Define population 3. Sampling unit 4. Choose sampling technique (We will use MUS or PPS) 5. Determine sample size Consider variation within the population Determine acceptable risk of incorrect acceptance Determine tolerable misstatement Determine expected amount of misstatement Consider population size Performance: 6. Determine method of selecting sample items 7. Perform audit procedures Evaluation: 8. Calculate sample results 9. Perform error analysis 10. Draw final conclusions
SAMPLING PLAN - PROBABILITY PROPORTIONAL TO SIZE
I. Objective - Test for overstatement. For example, test existence and rights of account balance - Accounts Receivable (by confirming). II. Population and sampling unit A. Sampling unit is the individual dollar but the "logical sampling unit" is the location (document) containing the "dollar" 1. Possible - All balances, Debit, Credit, or Zero 2. Problems with zero and negative balances - these have no chance of selection B. For example assume the following: 1. Population is A/R with debit balances 2. Sampling unit is each of the $600,000 aggregate amount 3. Auditor concludes that $30,000 is a material misstatement 4. The auditor anticipates error of $6,000 5. Customer account is logical sampling unit 6. Risk of incorrect acceptance is 5% III. Sample size
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BV = Book value of population (sampling units) RF = Reliability Factor (From Table 9-4 - based on beta risk) TM = Tolerable misstatement AM = Anticipated misstatement EF = Expansion factor (From Table 9-5 - based on beta risk) Thus for our example
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IV. Sample selection method A. Systematic
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B. For our example
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Random start of $5,000 (assume) then every $6,818 dollar
SYSTEMATIC SELECTION PROCESS
Customer Number |
Book Value |
Cumulative Balance |
Dollar Unit Selected |
Book Value of Sample Item |
01001 |
$1,200 |
$ 1,200 |
|
|
01025 |
6,043 |
7,243 |
5,000 |
$6,043 |
01075 |
2,190 |
9,433 |
|
|
01140 |
3,275 |
12,708 |
11,818 |
3,275 |
01219 |
980 |
13,688 |
|
|
01365 |
1,647 |
15,335 |
|
|
01431 |
4,260 |
19,595 |
18,636 |
4,260 |
10592 |
480 |
20,075 |
|
|
01667 |
7,150 |
27,225 |
25,454 |
7,150 |
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Total |
600,000 |
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V. Execute plan - audit the items VI. Evaluate results A. Steps 1. Projected misstatement from sample to population 2. Determine allowance for sampling risk 3. Calculate the upper misstatement limit B. Considerations 1. The above steps are analogous to the sample occurrence rate, allowance for sampling risk and upper occurrence limit for attribute sampling 2. Upper misstatement limit = projected misstatement + allowance for sampling risk UML = PM + ASR ASR = BP + IA 3. Evaluation process depends on whether any errors are found in the sample. C. If no errors 1. Projected misstatement to population = $0 (That is PM = 0) 2. Thus, the allowance for sampling risk = upper misstatement limit And since IA = 0 for no errors, ASR = BP BP = RF x SI BP = "Basic precision" or allowance for sampling risk RF = Reliability factor as used from Table 9-4 SI = Sampling interval 3. For our example BP = 3.0 x $6,818 BP = $20,454 What statement can be made? D. If some errors 1. Project sample results to population a. For each logical unit with BV less than SI calculate tainting percentage:
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Projected misstatement = SI X Tainting % b. Each logical unit equal to or greater than SI, use actual errors. c. Sum errors for projected population misstatement
Calculation of Projected Misstatement
Book Value |
Audit Value |
Tainting %
|
Sampling Interval |
Projected Misstatement |
950 |
855 |
10 |
6,818 |
682 |
2,500 |
1,250 |
50 |
6,818 |
3,409 |
7,650 |
6,885 |
N/A |
N/A |
765 |
5,300 |
5,035 |
5 |
6,818 |
341 |
8,000 |
0 |
N/A |
N/A |
8,000 |
24,400 |
14,025 |
|
|
13,197 |
2. Calculate allowance for sampling risk and determine upper misstatement limit (UML) a. Two components - Sum of basic precision (BP) and incremental allowance for misstatements (IA) b. BP is same as with no errors - SI x RF c. Determine IA 1. Use errors related to logical units less than SI 2. Use Incremental change factors from Table 9-4 3. Rank errors by size 4. Extend factors times errors 5. Sum IA and BP
Ranked PM |
Factor |
IA |
3,409 |
.75 |
2,557 |
682 |
.55 |
375 |
341 |
.46 |
157 |
|
|
|
3,089 |
Ranked logical units less than SI d. Add projected misstatements and allowance for sampling risk to get upper misstatement limit (UML) UML = PM + ASR BP IA 36,740 = 13,197 + 20,454 + 3,089 VII. Review Advantages and Disadvantages - Page 340-341