### Chapter 12

```Module G
Variables Sampling
Accounting 408
Module G
1
1. Introduction
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Variables sampling
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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
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2
1. Introduction (continued)
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Types
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PPS Sampling
Classical methods (omit pages 811-820)
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Accounting 408
mean per unit
difference estimation
ratio estimation
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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
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Accounting 408
automatically accomplishes stratification (greater
chance of including larger dollar amount items)
with low error rates, requires smaller sample sizes
than classical methods
generally easier to use than classical methods
no need to measure the standard deviation of the
population
Module G
5
2. PPS Sampling (continued)
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Accounting 408
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
Module G
6
2. PPS Sampling (continued)
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Works best when searching for overstatements
with a low expected error rate
Assumptions
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low expected error rate (< 10%)
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population contains > 2,000 items
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the amount of any error cannot be more than the
reported BV of the item
Accounting 408
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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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Accounting 408
Where: X = confidence level
Y = sample result (UL)
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8
2. PPS Sampling (continued)
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Evaluation of results
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if UL < tolerable misstatement—accept balance
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if UL > tolerable misstatement—cannot accept
balance
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investigate causes of misstatements.
increase sample size (usually not recommended) or
Example - handout
Accounting 408
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2. PPS Sampling (continued)
A/R Balance:
Risk of Incorrect
Acceptance:
Expected Error:
Case
Case
Tolerable Error:
Accounting 408
\$650,000
5.0%
A:
\$
0
B:
\$ 6,500
\$19,500
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10
Expansion Factor Table
Expansion Factors for Risk of Incorrect Acceptance
Factor
1%
1.9
Accounting 408
5%
1.6
Risk of Incorrect Acceptance
10%
15%
20%
25%
1.5
1.4
1.3
1.25
Module G
30%
1.2
50%
1.1
11
3. Nonstatistical Methods
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Does not measure auditor’s exposure to sampling
risk
Permitted under GAAS
Differences
 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
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14
```