Module G
Variables Sampling
Accounting 408 Module G 1

1. Introduction
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Variables sampling
 variable - a measure possessed by every member of the population (dollar)
Monetary method
Used in substantive testing
Used to substantiate an account balance or estimate an account balance
Accounting 408 Module G 2

1. Introduction (continued)
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Types
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PPS Sampling
Classical methods (omit pages 811-820)
 mean per unit
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 difference estimation ratio estimation
Accounting 408 Module G 3

2. PPS Sampling
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Introduction
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 called various names relatively new method developed specifically for auditing
Sampling unit
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 each dollar in the population number of physical items is irrelevant example of selecting a sample
Accounting 408 Module G 4

2. PPS Sampling (continued)
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Characteristics of PPS
 advantages
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 automatically accomplishes stratification (greater chance of including larger dollar amount items) with low error rates, requires smaller sample sizes than classical methods (research suggests that error rates are lower since passage of SOX) generally easier to use than classical methods no need to measure the standard deviation of the population
Accounting 408 Module G 5

2. PPS Sampling (continued)
 disadvantages
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 provides conservative (higher) estimate of misstatement zero or negative items have no chance of being selected and require special consideration less useful for understated account balances or omission errors less useful for high expected error rates requires a book value for each item
Accounting 408 Module G 6

2. PPS Sampling (continued)
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Works best when searching for overstatements with a low expected error rate
Assumptions
 low expected error rate (< 10%)
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 population contains > 2,000 items the amount of any error cannot be more than the reported BV of the item
Accounting 408 Module G 7

2. PPS Sampling (continued)
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Statistical conclusion:
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I am X% confident that the dollar amount of error in the account does not exceed $Y.
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Where: X = confidence level
Y = sample result (UL)
Accounting 408 Module G 8

2. PPS Sampling (continued)
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Evaluation of results
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 if UL ≤ tolerable misstatement—accept balance
 investigate causes of misstatements.
if UL > tolerable misstatement—cannot accept balance
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 increase sample size (usually not recommended) or adjust balance for difference
Example - handout
Accounting 408 Module G 9

2. PPS Sampling (continued)
A/R Balance:
Risk of Incorrect
$650,000
Acceptance: 5.0%
Expected Error:
Case A:
Case B:
Tolerable Error: $19,500
$ 0
$ 6,500
Accounting 408 Module G 10

Expansion Factor Table
Expansion Factors for Risk of Incorrect Acceptance
Factor
1%
1.9
5%
1.6
10%
Risk of Incorrect Acceptance
15% 20% 25%
1.5
1.4
1.3
1.25
30%
1.2
50%
1.1
Accounting 408 Module G 11

3. Nonstatistical Methods
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Does not measure auditor’s exposure to sampling risk
Permitted under GAAS
Differences
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 does not consider sampling risk in determining sample size or evaluating sample results may use nonprobabilistic selection technique
Accounting 408 Module G 12

4. Classical Methods
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Introduction
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 based on normal distribution theory requires an estimate of the population’s standard deviation sampling unit - physical items in population
Accounting 408 Module G 13

4. Classical Methods (cont)
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Mean per Unit
Difference Estimation
Ratio Estimation
Example
Accounting 408 Module G 14

Review Questions for Discussion
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Chapter 2
G.1
G.3
G.4
G.6
G.7
G.11
G.12
G.14
G.16
G.20
Accounting 408 Module G 15