Matakuliah
Tahun
: A0294/Audit SI Lanjutan
: 2009
Audit Sampling
Pertemuan 15-16
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Memahami teknik penentuan ukuran sample
• Memahami teknik pengambilan sample
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Attribute sampling
• It is a statistical method used to estimate the proportion of a characteristic in a
population (absence or presence of a control)
• The auditor is normally attempting to determine the operating effectiveness of a
control procedure in terms of deviations from the prescribed control
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Attribute sampling
• Planning
–
–
–
–
–
–
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1st - Determine the objective(s) of the test
2nd - Define the control deviation conditions.
3rd - Define the population
4rd - Define the period covered by the test
5th - Define the sampling unit.
6th –Define the technical parameters to determine the sample size
4
Attribute sampling
• Sample size
– It could be determined using:
• Mathematic formulas
• Statistic tables
• software (CAAT: ACL or IDEA)
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Attribute sampling
• Select the sample, perform the tests and evaluate the results
– Selection using:
• Tables of random numbers
• software (CAATS: ACL or IDEA or EXCEL)
– Evaluation of results using:
• Satistic tables
• Software (CAATS: ACL or IDEA or EXCEL)
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Attribute sampling
• Key concepts
–
–
–
–
–
–
–
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Confidence level, say 90%(complement of risk of incorrect acceptance: 10%)
Expected deviation rate (EDR)
Maximum Tolerable deviation rate (MTDR)
Precision of the test (P<=MTDR-ER)
Confidence interval
Sample size
Results evaluation
7
Attribute sampling
Confidence level (CL) or reliability level (RL)
It is a probability of the auditor being correct in his/her evaluation of the risk of
control (genneraly varies from 90 to 99%)
CL is 100% if all the items in the population are examined
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Attribute sampling
• Risk (2 types of sampling risks):
– Risk of assessing control risk too low (complement of reliability or confidence level)- is the
probability that the sample supports the conclusion that the controls are operating effectively
when they are not (we fail to recognise unreliable controls and setting CL for operations at a
lower level)
– Risk of assessing control risk too high- is the probability that the sample supports the
conclusion that the controls are not operating effectively when this is not the case (this
situation causes setting of CL for audit on operations at a higher level and more unnecessary
audit work)
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Attribute sampling
Expected deviation rate (EDR)
• Maximum expected of deviations in the population based on last year audit or a pilot
test
• EDR allows to define an interval of confidence for the sample identifying its precision
(precision<=MTDR-EDR)
• The bigger EDR (more per cent or number of errors) the larger is the sample size
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Attribute sampling
3,00%
C onfidence level: 95%
MTDR
4,00%
5,00%
6,00%
7,00%
8,00%
9,00%
10,00%
99 (0)
74 (0)
59 (0)
49 (0)
42 (0)
36 (0)
32
(0)
29
(0)
0,25% 236 (1) 157 (1) 117 (1)
93 (1)
78 (1)
66 (1)
58 (1)
51
(1)
46
(1)
0,50%
157 (1) 117 (1)
93 (1)
78 (1)
66 (1)
58 (1)
51
(1)
46
(1)
0,75%
208 (2) 117 (1)
93 (1)
78 (1)
66 (1)
58 (1)
51
(1)
46
(1)
1,00%
156 (2)
93 (1)
78 (1)
66 (1)
58 (1)
51
(1)
46
(1)
1,25%
156 (2) 124 (2)
78 (1)
66 (1)
58 (1)
51
(1)
46
(1)
1,50%
192 (3) 124 (2) 103 (2)
66 (1)
58 (1)
51
(1)
46
(1)
1,75%
227 (4) 153 (3) 103 (2)
88 (2)
77 (2)
51
(1)
46
(1)
2,00%
181 (4) 127 (3)
88 (2)
77 (2)
68
(1)
46
(1)
2,25%
208 (5) 127 (3)
88 (2)
77 (2)
68
(1)
61
(2)
2,50%
150 (4) 109 (3)
77 (2)
68
(2)
61
(2)
2,75%
173 (5) 109 (3)
95 (3)
68
(2)
61
(2)
3,00%
195 (6) 129 (4)
95 (3)
84
(3)
61
(2)
3,25%
148 (5) 112 (4)
84
(3)
61
(2)
3,50%
167 (6) 112 (4)
84
(3)
76
(3)
3,75%
185 (7) 129 (5)
100
(4)
76
(3)
4,00%
146 (6)
100
(4)
89
(4)
158
(8) 116
(6)
EDR
2,00%
0,00% 149 (0)
5,00%
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Attribute sampling
Upper error limit rate confidence level: 95%
Sample
Number of errors found
size
25
30
35
40
45
50
55
60
65
70
75
80
90
100
125
150
200
0
11,3
9,5
8,3
7,3
6,5
5,9
5,4
4,9
4,6
4,2
4,0
3,7
3,3
3,0
2,4
2,0
1,5
1
17,6
14,9
12,9
11,4
10,5
9,2
8,4
7,7
7,1
6,6
6,2
5,8
5,2
4,7
3,8
3,2
2,4
2
3
4
5
19,6
17,0
15,0
13,4
12,1
11,1
10,2
9,4
8,8
8,2
7,7
6,9
6,2
5,0
4,2
3,2
18,3
16,4
14,8
13,5
12,5
11,5
10,8
10,1
9,5
8,4
7,6
6,1
5,1
3,9
19,2
17,4
15,9
14,7
13,6
12,6
11,8
11,1
9,9
9,0
7,2
6,0
4,6
19,9
18,2
16,8
15,5
14,5
13,6
12,7
11,4
10,3
8,3
6,9
5,2
Fonte: Guy, D.M., Audit Sampling: na introduction , 5
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Variables sampling
Auditor problem:
• Is there the possibility of overstatement in value of some item of the population
which could result in a qualified opinion?
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Variables sampling statistical methods
• Sampling proporcionate to size (PPS/MUS)
• Classical variables sampling:
– Direct projection (stratification required);
– Ratio or difference estimation (when errors are fairly frequent)
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Monetary Unit Sampling (MUS)
The classical variables sampling can fail in the detection of the material mistake
because:
–
–
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The methods of selection are random and based on physical registers (we maynot choose a
document that contains a mistake)
There is a possibility not to project this mistake for the population, so there is the possibility not
to detect one material mistake
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Monetary Unit Sampling (MUS)
• Auditor precautions:
– examine all the big transactions that individually can contain a material mistake
– apply a method of sampling for the remaining items on basis of a stratified selection
(nevertheless the stratification does not remove totally the problem of the possibility not to
select a group of items that totalizes a material mistake)
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Monetary Unit Sampling (MUS)
• Another approach:
– as bigger values are the most relevant items for the auditor the suggested new approach
makes a selection based on the weight of monetary value, generically designated by
probability-proportional-to-size (PPS) or monetary unit sampling (MUS)
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Monetary Unit Sampling (MUS)
• Evaluation of results
– The Poisson distribution is used for the evaluation of results:
– Tables
– Audit Software (ACL, IDEA, Etc…)
– Specific programmes
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Monetary Unit Sampling (MUS)
• Opinion formulation
– The auditor, based on the evidence of the sample, declares, with a CL of y %,
an upper error limit in the population (where the amount depends on the
results of the sample, for a sample size of n and for a number x errors found in
the sample).
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Monetary Unit Sampling (MUS)
–
–
–
–
–
–
–
–
Risk
Monetary precision (MP)
Expected error
Tolerable error (materiality threshold)
Sample size
Confidence factor R (Poisson)
Expansion factors for expected error
Upper error limit
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Monetary Unit Sampling (MUS)
• Risk (2 types of sampling risks):
– Risk of incorrect acceptance- is the probability that the sample supports the
conclusion that the book value is not materially misstated when it is (not
identified qualified opinion)
– Risk of incorrect rejection- is the probability that the sample supports the
conclusion that the book value is materially misstated when it is not (this
situation cause more audit work)
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Monetary Unit Sampling (MUS)
Monetary precision (MP)
It is a basic threshold to determine the sample size that means, the
auditor expects a maximum amount of overstatement in the population
equivalent to the MP even if there are no misstatements in the sample, for
a certain confidence level (auditor judgement)
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Monetary Unit Sampling (MUS)
Expected error (EE)
– Based on last year experience and inherent risk evaluation, considering the results
of tests of controls and other procedures, expected error is the amount of
overstatement the auditor expects to find in the population
– It is used to control the risk of incorrect rejection due to a small sample size
(increases the initial sample size)
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Monetary Unit Sampling (MUS)
–
–
–
Tolerable error (TE)
It is the maximum overstatement error for a population of accounts or group of
transactions that can be accepted by the auditor without causing material error in
the financial demonstrations (judgement of the auditor)
It is compared against the results of the sample in order to decide whether the
auditor accepts the population as free of material errors or alternatively qualifies
the opinion
Commission stated in Annex IV CR 1828 that the maximum materiality threshold
is 2%
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Nature and Cause of Errors
• The auditor should consider:
– The nature
– The cause
In order to evaluate the sample results this means that he have to classify the errors
before the extrapolation:
• anomalous error
• Systematic error
• Random error
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Errors Evaluation
Population
Sample
Systemic error
Known
Random error
unknown
Random error
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Errors Evaluation
• anomalous error
– The error arises from an isolated event that has not occurred other than on specifically
identifiable occasions and is therefore not representative of similar errors in the population
the auditor has to have a high degree of certainty that such error is not
representative of the population
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Errors Evaluation
• Systematic error
– is a non-random exception that is likely to have occurred more than once on
positively identifiable occasions.
– The auditor obtains the effect of each systematic error on the total population
by performing additional audit in order to make a qualitative evaluation of
how, why, when and where the systematic error occurred
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Using Microsoft Excel for Sampling
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The End
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