Audit Sampling
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Transcript of Audit Sampling
Audit Sampling
Chapter 9
9-2
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
What is Audit Sampling?
Applying a procedure to less than 100% of a population
To estimate some characteristic of the population Qualitative Quantitative
9-3
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Advantages of Statistical Sampling
Design efficient samples Measure sufficiency of evidence Objectively evaluate sample results
9-4
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Selection of Random Sample
Random number tables Random number generators Systematic selection
9-5
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Random Number Table
9-6
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Types of Statistical Sampling Plans
Attributes sampling Discovery sampling Classical variables sampling Probability-proportional-to-size sampling
9-7
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Requirements of AuditSampling Plans
When planning the sample consider: The relationship of the sample to the relevant audit objective Materiality or the maximum tolerable misstatement or
deviation rate Allowable sampling risk Characteristics of the population
Select sample items in such a manner that they can be expected to be representative of the population
Sample results should be projected to the population Items that cannot be audited should be treated as
misstatements or deviations in evaluating the sample results Nature and cause of misstatements or deviations should be
evaluated
9-8
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True State of Population
Deviation Rate Deviation Rate Exceeds Is
Less ThanAuditors’ Conclusion Tolerable Rate Tolerable RateFrom the Sample Is:
Deviation Rate Exceeds Tolerable Rate
Deviation Rate Is Less Than Tolerable Rate
Sampling Risks--Tests of Controls
CorrectDecision
Incorrect Decision
(Risk of Assessing Control Risk
Too High)
IncorrectDecision
(Risk of AssessingControl Risk
Too Low)
Correct Decision
9-9
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Audit Sampling for Tests of Controls
Determine the objective of the test Define the attributes and deviation conditions Define the population to be sampled Choose an audit sampling technique Specify:
The risk of assessing control risk too low The tolerable deviation rate
Estimate the population deviation rate Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure
9-10
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Sampling Risks--Substantive Tests
True State of Population
Misstatement in Misstatement in Account Exceeds
Account Is Less Auditors’ Conclusion Tolerable Amount Than Tolerable From the Sample Is: Amount
Misstatement inAccount Exceeds Tolerable Amount
Misstatement inAccount Is LessThan TolerableAmount
CorrectDecision
Incorrect Decision
(Risk of Incorrect Rejection)
IncorrectDecision
(Risk of Incorrect Acceptance)
Correct Decision
9-11
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Audit Sampling for Substantive Tests
Determine the objective of the test Define the population and sampling
unit Choose an audit sampling technique Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure
9-12
McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Population Variability—Why it Matters
Item Population A Population B
1 2,100 8,000 2 2,100 25 3 2,100 2,000 4 2,100 400 5 2,100 75
Mean 2,100 2,100
Standarddeviation -0- 3,395
The variability determines how much information each of the items in the population tells you about the other items in the population.
9-13
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Factors Affecting Sample Size
9-14
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Determining Sample Size--MPU
Sample size =
risksamplingforallowancePlannedSDEstxcoefrejIncorrectxsizePop ....
9-15
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Determining Sample Size--MPU Sampling
Planned allowancefor sampling risk =
Tolerable misstatement______________________
1 + Incorrect acceptance coef. Incorrect rejection coef.
9-16
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Adjusted allowance for sampling risk =
Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.) misstatement Sample size
This formula “adjusts” the allowance for sampling risk to consider the standard deviation of the audited values in the sample. It holds the risk of incorrect acceptance at its planned level.
Variables Sampling Illustration--MPU
9-17
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Variables Sampling Illustration--MPU
Using the text example with a standard deviation of audited values of $16Adjusted allowance for sampling risk =
Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)
misstatement Sample size
= $364,000 _ ($100,000 * 1.64 * $16)
225
= $189,067
We would still “accept” the book balance because the $6,250,000 (book value) falls within this interval
Estimate of total + Adjusted allowanceaudited value for sampling risk $6,100,000 + $189,067 [$5,910,933 to $6,289,067]
9-18
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Acceptance Interval
9-19
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Nonstatistical Variables Sampling Illustration
Plan Sample: Population:
Size = 363 items Book value = $200,000
Tolerable misstatement = $10,000 Risk assessments:
Inherent and control risk = Slightly below maximum Other substantive tests = Moderate
9-20
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Nonstatistical Sampling--Determination of Sample Size
Sample size = Population book value X Reliability factor Tolerable misstatement
= $200,000 X 2.0 = 40 items $10,000
9-21
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Nonstatistical Sampling--Evaluation of Sample Results
Sample results: 40 accounts in sample $350 net overstatement $60,000 book value of sample items
Projected misstatement:
= [Sample net misstatement] X Book value of population [ Book value of sample ] = [ $350 ] X $200,000 [$60,000]
= $1,167
Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct.
9-22
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PPS Sampling Illustration
Population book value = $6,250,000 Other Information:
Tolerable misstatement = $364,000 Sampling risk--Incorrect acceptance = 5% Expected misstatement = $50,000
Use Figures 9-14 and 9-15 to obtain a “reliability factor” and an “expansion factor.”
9-23
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PPS Sample Size Computation
Sample size =
Recorded amount of population * Reliability factor
Tolerable misstatement - (Expected misstatement * Expansion factor)
= $6,250,000 * 3.0 = 66 $364,000 - ($50,000 * 1.6)
Sampling interval = Book value of the population Sample size
= $6,250,000 = $95,000 (approximately) 66
9-24
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PPS Evaluation of Results
Upper Limit on misstatement =
Projected misstatement
+ Basic precision (Rel. factor x interval)
+ Incremental allowance
9-25
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Calculation of Upper Limit on Misstatement