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APIPA 2009 1
STATISTICAL SAMPLING
FOR AUDITORS
Jeanne H.
Yamamura
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APIPA 2009 2
OBJECTIVES Review of sampling concepts
Types of sampling Attribute sampling
Steps
Nonstatistical attribute sampling
Compliance auditing
Monetary unit sampling Steps
Nonstatistical monetary unit sampling Classical sampling
Ratio estimation
Difference estimation
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APIPA 2009 3
AUDIT SAMPLING Application of an audit procedure to less
than 100% of the items in a population
Account balance Class of transactions
Examination on a test basis
Key: Sample is intended to berepresentative of the population.
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APIPA 2009 4
SAMPLING RISK Possibility that the sample is NOT
representative of the population
As a result, auditor will reach WRONGconclusion
Decision errors
Type I Risk of incorrect rejection Type II Risk of incorrect acceptance
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APIPA 2009 5
TYPE I RISK OFINCORRECT REJECTION
Internal control: Risk that samplesupports conclusion that control is NOT
operating effectively when it really isAKA Risk of underreliance, risk of
assessing control risk too high
Substantive testing: Risk that samplesupports conclusion that balance is NOTproperly stated when it really is
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APIPA 2009 7
WHICH RISK POSES THEGREATER DANGER TO ANAUDITOR?
Risk of incorrect rejection
Efficiency
Risk of incorrect acceptance Effectiveness
Auditor focus on Type II
Also provides coverage for Type I
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APIPA 2009 8
NONSAMPLING RISK Risk of auditor error
Sample wrong population
Fail to detect a misstatement when applying auditprocedure
Misinterpret audit result
Controlled through
Adequate training Proper planning
Effective supervision
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APIPA 2009 9
SAMPLE SIZE FACTORS Desired level of assurance
(confidence level)
Acceptable defect rate (tolerableerror)
Historical defect rate (expectederror)
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APIPA 2009 10
CONFIDENCE LEVEL Complement of sampling risk
5% sampling risk, 95% confidence level
How much reliance will be placed on testresults
The greater the reliance and the more severethe consequences of Type II error, the higherthe confidence level needed
Sample size increases with confidence level(decreases with sampling risk)
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APIPA 2009 11
TOLERABLE ERROR ANDEXPECTED ERROR
Precision the gap between tolerableerror and expected error
AKA Allowance for sampling risk Sample size increases as precision
decreases
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APIPA 2009 12
WHEN DO YOU SAMPLE? Inspection of tangible assets, e.g.,
inventory observation
Inspection of records or documents, e.g.,internal control testing
Reperformance, e.g., internal controltesting
Confirmation, e.g., verification of ARbalances
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APIPA 2009 13
WHEN IS SAMPLINGINAPPROPRIATE?
Selection of all items with a particularcharacteristic, e.g., all disbursements >$100,000
Testing only one or a few items, e.g.,automated IT controls, walk throughs
Analytical procedures
Scanning Inquiry
Observation
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APIPA 2009 14
WALKTHROUGHS Designed to provide evidence regarding the
design and implementation of controls Can provide some assurance of operating
effectiveness BUT Depends on nature of control (automated or
manual) Depends on nature of auditors procedures to test
control (also includes inquiry and observation
combined with strong control environment andadequate monitoring)
Walkthough = sample of 1
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APIPA 2009 15
STATISTICAL VSNONSTATISTICAL SAMPLING
Statistical sampling Statistical computation of sample size
Statistical evaluation of results
Nonstatistical sampling
Sample sizes should be approximately thesame (AU 350.22)
Sample sizes must be sufficient to supportreliance on controls and assertions beingtested
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APIPA 2009 16
WHEN IS SAMPLINGNONSTATISTICAL?
If sample size determined judgmentally
If sample selected haphazardly
If sample results evaluated judgmentally
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APIPA 2009 17
TYPES OF SAMPLING Attribute sampling
Monetary unit sampling
Classical variables sampling
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APIPA 2009 18
ATTRIBUTE SAMPLING Used to estimate proportion of a
population that possesses a specific
characteristic Most commonly used for T of C
Can also be used for dual purpose
testing (T of C and Substantive T of T)
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APIPA 2009 19
MONETARY-UNITSAMPLING
AKA probability proportional to size(PPS) sampling, cumulative monetary
unit sampling Used to estimate dollar amount of
misstatement
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APIPA 2009 20
CLASSICAL VARIABLESSAMPLING
Uses normal distribution theory to identifyamount of misstatement
Useful when large number of differencesexpected Smaller sample size than MUS
Effective for both overstatements andunderstatements
Can easily incorporate zero balances
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APIPA 2009 21
IN-CLASS EXERCISENO. 1
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APIPA 2009 22
IN-CLASS EXERCISENO. 1
Test Involves
Sampling?
Attribute / Variable / MUS / NA
1 Yes Attribute (ST of T)
2 No NA
3 Yes Attribute (T of C)
4 No NA
5 No NA (Could be MUS if largepopulation)
6 No NA
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APIPA 2009 23
IN-CLASS EXERCISENO. 1
Test Involves
Sampling?
Attribute / Variable / MUS / NA
7 Yes Attribute (T of C)
8 Yes MUS
9 No NA
10 Yes Attribute (T of C/ST of T)
11 No NA
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APIPA 2009 24
STEPS IN STATISTICALATTRIBUTE SAMPLINGAPPLICATION
Planning1. Determine the test objectives2. Define the population characteristics
3. Determine the sample size Performance
4. Select sample items5. Perform the auditing procedures
Evaluation6. Calculate the results7. Draw conclusions
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APIPA 2009 25
STEP 1: DETERMINE THETEST OBJECTIVES
Objective for T of C: To determine theoperating effectiveness of the internal
control Support control risk assessment below
maximum
Identify controls to be tested andunderstand why they are to be tested
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APIPA 2009 26
TESTS OF CONTROLS Concerned primarily with
Were the necessary controls performed?
How were they performed? By whom were they performed?
Appropriate when documentary evidence
of performance exists
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APIPA 2009 27
STEP 2: DEFINE THEPOPULATIONCHARACTERISTICS
Define the sampling population
Assertion
Completeness Define the sampling unit
Determined by available records
Define the control deviation conditions
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APIPA 2009 28
STEP 3: DETERMINE THESAMPLE SIZE
Determine factors Desired confidence level (direct)
Tolerable deviation rate (inverse) Expected population deviation rate (direct)
Desired confidence level If planning to rely on controls, would be 90 to
95% Significance of account and importance of
assertion affected by control being tested
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APIPA 2009 29
STEP 3: DETERMINE THESAMPLE SIZE
Tolerable deviation rate
Maximum deviation rate that auditor willing toaccept and still consider control effective Control would be relied upon
Why any errors acceptable? Control deviation = Misstatement
Assessed importance of control Tolerabledeviation rate
Highly important 3-5%
Moderately important 6-10%
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APIPA 2009 30
STEP 3: DETERMINE THESAMPLE SIZE
Expected population deviation rate
Rate expected to exist in population
Based on prior years results or pilot sample If expected population deviation rate >
tolerable rate, DO NOT TEST
SAMPLE SIZE TABLES
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APIPA 2009 31
STEP 3: DETERMINE THESAMPLE SIZE
Testing multiple attributes on the samesample
Select largest sample size and audit all ofthem for all attributes
Result is some overauditing BUT may takeless time than trying to remember whichsample items need to be tested for whichattribute
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APIPA 2009 32
FINITE POPULATIONCORRECTION FACTOR
When population size < 500
Apply finite population correction factor
1-(n/N) Where n = sample size from table and N =
number of units in population
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APIPA 2009 33
STEP 4: SELECT THESAMPLE ITEMS
Sample must be selected to berepresentative of the population
Each item must have an equalopportunity of being selected
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APIPA 2009 34
STEP 4: SELECT THESAMPLE ITEMS
Random number selection
Unrestricted random sampling without
replacement (once selected cannot beselected again)
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APIPA 2009 35
STEP 4: SELECT THESAMPLE ITEMS
Random number table
Need to document
Correspondence: relationship betweenpopulation and random number table
Route: selection path, e.g., up or down columns,and right to left (must be consistent)
Starting point: starting row, column, digit
Stopping point: to enable adding more sampleitems if needed
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APIPA 2009 36
RANDOM NUMBER TABLEILLUSTRATION
Select a sample of 4 items from prenumberedcanceled checks numbered from 1 to 500.Start at row 5, column 1, digit starting position1. Select three-digit numbers. Items selected
are: 145 (sample item #1) 516 (discard because checks numbers do not
exceed 500)
032 (sample item #2) 246 (sample item #3) 840 (discard)181 (sample item #4)
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APIPA 2009 37
RANDOM NUMBER TABLEILLUSTRATION
To minimize discards, table numbers > 500 canbe reduced by 500 to produce a sample itemwithin the population boundary of 1 to 500. The
four sample items selected are: 145 (sample item #1)
016 (sample item #2 = 516 500 = 016)
032 (sample item #2)
246 (sample item #3)
340 (sample item #4 = 840 500 = 340)
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APIPA 2009 39
STEP 4: SELECT THESAMPLE ITEMS - EXCEL
Excel
Select Tools
Select Data Analysis Select Sampling
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APIPA 2009 40
STEP 4: SELECT THESAMPLE ITEMS - EXCEL
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APIPA 2009 41
STEP 4: SELECT THESAMPLE ITEMS
Input Range
Enter the references for the range of data that contains the population ofvalues you want to sample. Microsoft Excel draws samples from the firstcolumn, then the second column, and so on.
Labels
Select if the first row or column of your input range contains labels. Clearif your input range has no labels; Excel generates appropriate data labelsfor the output table.
Sampling Method
Click Periodic orRandom to indicate the sampling interval you want. Period
Enter the periodic interval at which you want sampling to take place. Theperiod-th value in the input range and every period-th value thereafter iscopied to the output column. Sampling stops when the end of the inputrange is reached.
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APIPA 2009 42
STEP 4: SELECT THESAMPLE ITEMS
Number of Samples
Enter the number of random values you want in theoutput column. Each value is drawn from a randomposition in the input range, and any number can be
selected more than once. Output Range
Enter the reference for the upper-left cell of the outputtable. Data is written in a single column below the cell.If you select Periodic, the number of values in the
output table is equal to the number of values in theinput range, divided by the sampling rate. If you selectRandom, the number of values in the output table isequal to the number of samples.
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APIPA 2009 43
STEP 4: SELECT THESAMPLE ITEMS
Systematic selection Determine sampling interval = Population / Sample
Size Ensure population is in random order Select random starting number (within first interval)
Better to use multiple random starting points to reduce riskof missing systematic deviations
Select every nth item Continue sample selection until population is
exhausted (Last sample selected + sampling interval) > Last item in
population In other words, dont stop when desired sample size
reached
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APIPA 2009 44
STEP 5: PERFORM THEAUDITING PROCEDURES
Conduct planned audit procedures
What if?
Voided documents - if properly voided, not adeviation; replace with new sample item
Unused or inapplicable documents replacewith new sample item
Inability to examine sample item deviation Stopping test before completion large
number of deviations detected
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APIPA 2009 45
STEP 5: PERFORM THEAUDITING PROCEDURES
Deviations observed
Investigate nature, cause, and consequence
of every exception Unintentional error? Or fraud?
Monetary misstatement resulted?
Cause misunderstanding of instructions?
Carelessness? Effect on other areas?
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APIPA 2009 46
STEP 6: CALCULATERESULTS
Summarize deviations for each control
Calculate sample deviation rate and
computed upper deviation rate Sample deviation rate + Allowance for
sampling risk = Computed upper deviationrate
Statistical sampling results evaluation tables
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APIPA 2009 47
STEP 7: DRAWCONCLUSIONS
If Computed Upper Deviation Rate >Tolerable Rate, control is ineffective and
cannot be relied upon. If Computed Upper Deviation Rate expected
population deviation rate, control noteffective
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APIPA 2009 70
COMPLIANCE AUDITING Performance of auditing procedures to
determine whether an entity is complying withspecific requirements of laws, regulations, or
agreements
Governmental entities and other recipients ofgovernmental financial assistance
Compliance with laws and regulations thatmaterially affect each major federal assistanceprogram
COMPLIANCE AUDITING OF
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APIPA 2009 71
FEDERAL ASSISTANCEPROGRAMS
Definition of population for testing of aninternal control procedure that applies to
more than one program Define items from each major program as a
separate population, OR
Define all items to which control is applicable
as a single population
Second choice usually more efficient
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APIPA 2009 72
COMPLIANCE AUDITING -EXAMPLE
Federal financial assistance for IslandCity
Three major federal financial assistanceprograms
Four nonmajor programs
Control: Transaction review to ensurethat only legally allowable costs arecharged to each program
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APIPA 2009 73
COMPLIANCE AUDITING -EXAMPLE
More efficient to select one sample frompopulation of all transactions (major andnonmajor programs)
Confidence level = 95%
Tolerable deviation rate = 9%
Expected population deviation rate = 1%
Sample size: 51
1 allowable deviation
SMALL POPULATIONS AND
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APIPA 2009 74
INFREQUENTLY OPERATINGCONTROLS
Small Population Sample Size Table
Control Frequency and
Popu lat ion Size
Samp le Size
Quarterly (4) 2
Monthly (12) 2-4
Semimonthly (24) 3-8Weekly (52) 5-9
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APIPA 2009 75
IN-CLASS EXERCISENO. 4
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APIPA 2009 76
IN-CLASS EXERCISENO. 4
Selected Payroll T of C
1. Examine the time cardfor approval of a
supervisor
Moderately criticalaffects E/O of S& W
2. Account for asequence of payrollchecks in the payroll
journal
Very critical affects E/Oof S&W
3. Recompute hours onthe time card
Moderately criticalaffects V of S&W
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APIPA 2009 77
IN-CLASS EXERCISENO. 4
4. Compare theemployee name in thepayroll journal to
personnel records
Very critical affectsE/O - affects E/O of S&W; also an area subject
to fraud
5. Review OT chargesfor approval of a
supervisor
Moderately criticalaffects E/O and V of
S&W
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APIPA 2009 78
IN-CLASS EXERCISENO. 4
Selected Cash Disbursement T of C
6. Examine voucher for
supporting invoices,receiving reports, etc.
Very critical affects
E/O of purchasetransactions
7. Examine supportingdocuments for evidence
of cancellation (paid)
Moderately criticalaffects validity of
purchase transactionsand relates to doublepayment
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APIPA 2009 79
IN-CLASS EXERCISENO. 4
Selected Cash Disbursement T of C
8. Ascertain whether
cash discounts weretaken
Least critical affects V
of purchasetransactions; amountsusually minor
9. Review voucher for
clerical accuracy
Moderately critical
affects V of purchasetransactions
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APIPA 2009 80
IN-CLASS EXERCISENO. 4
Selected Cash Disbursement T of C
10. Agree purchase
order price to invoice
Moderately critical
affects V of purchasetransactions
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APIPA 2009 81
MONETARY UNITSAMPLING
Uses attribute sampling theory to expressconclusions in dollar amounts
Estimates the percentage of monetary units in a
population that might be misstated Multiples the percentage by an estimate of how
much the dollars are misstated
Developed by auditors
Assumes little or no misstatements
Designed primarily to test for overstatements
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APIPA 2009 82
ADVANTAGES When no misstatements expected,
results in smaller (more efficient) sample
size than classical variables sampling No need to compute/identify standard
deviation
Automatically stratifies sample
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APIPA 2009 83
DISADVANTAGES Zero or negative balances must be tested
separately
Assumes audited amount of sampleitems is not in error by more than 100%
When more than 1 or 2 misstatementsfound, allowance for sampling risk may
be overstatedAuditor more likely to reject balance and
overaudit
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APIPA 2009 84
STEPS IN MONETARY UNITSAMPLING APPLICATION
Planning1. Determine the test objectives2. Define the population characteristics
3. Determine the sample size Performance
4. Select sample items5. Perform the auditing procedures
Evaluation6. Calculate the results7. Draw conclusions
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APIPA 2009 85
STEP 1: DETERMINE THETEST OBJECTIVES
Substantive testing: To test thereasonableness of an amount, i.e., that
an amount is fairly stated To test the assertion that no material
misstatements exist in an accountbalance, class of transactions, ordisclosure component of the financialstatements
STEP 2: DEFINE THE
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APIPA 2009 86
POPULATIONCHARACTERISTICS
Define the sampling population Monetary value of an account balance
Verify completeness of population
Define the sampling unit - Each individualdollar
Define the logical unit - The account ortransaction that contains the sampling units
Define a misstatement The differencebetween the book value and the audited value
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APIPA 2009 87
STEP 3: DETERMINE THESAMPLE SIZE
Determine factors (effect on sample size)
Desired confidence level (direct)
To increase confidence, more work is required!(larger sample size)
Tolerable misstatement (inverse)
Expected misstatement (direct)
Population size (direct)
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APIPA 2009 88
STEP 3: DETERMINE THESAMPLE SIZE
Computing sample sizes using theattribute sampling tables Select desired confidence level
Compute tolerable misstatement aspercentage of book value
Compute expected misstatement as
percentage of book value Look up sample size in attribute sampling
table
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APIPA 2009 90
STEP 5: PERFORM THEAUDITING PROCEDURES
Conduct planned audit procedures onlogical units
What if? Missing document consider to be a
misstatement
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APIPA 2009 91
STEP 6: CALCULATERESULTS
Projected misstatement: Projection ofthe errors to the population
Upper limit on misstatement: Adds anallowance for sampling risk to theprojected misstatement
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APIPA 2009 92
STEP 6: CALCULATERESULTS
Sort misstatements into two groups Group 1: Logical unit equal to or greater
than the sampling interval
Group 2: Logical unit less than the samplinginterval
For Group 2, compute the tainting factor
for each misstatement Tainting factor = Book value Audit value
Book value
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APIPA 2009 93
STEP 6: CALCULATERESULTS
Place the Group 2 items in rank order bytainting factor (from largest to smallest)
Compute the projected misstatement
Calculate the upper limit increments (using theMonetary Un it Samp ling Conf idenceFacto rs for Sample Evaluat iontable)
Calculate upper misstatement for each Group2 item
Add differences for Group 1 Total = Upper misstatement limit
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APIPA 2009 94
STEP 6: CALCULATERESULTS - EXAMPLE
Book value = $3,100,000
Tolerable misstatement = $150,000
Expected misstatement = $25,000 Desired confidence level = 95%
Tolerable misstatement rate =4.8%,round to 5%
Expected misstatement rate = .8%, roundto 1%
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APIPA 2009 95
STEP 6: CALCULATERESULTS - EXAMPLE
Sample size = 93
Sampling interval = $33,333
Expected misstatement = $25,000
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APIPA 2009 96
STEP 6: CALCULATERESULTS - EXAMPLE
Item Book Value Audited Value Difference
Item 1 12,000 3,120 8,880
Item 2 35,000 32,000 3,000
Item 3 1,400 0 1,400
Item 4 45,200 41,000 4,200Item 5 740 555 185
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STEP 6: CALCULATE
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APIPA 2009 98
RESULTS - EXAMPLEItem Difference Book Value Tainting Factor
Group 2: BV < SI (33,333)
Item 1 8,880 12,000 .74
Item 3 1,400 1,400 1.0
Item 5 185 740 .25
STEP 6: CALCULATE
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APIPA 2009 99
RESULTS - EXAMPLEItem Tainting Factor Sampling
Interval
Projected
Misstatement
(Tainting
Factor * SI)
Item 3 1.0 33,333 33,333
Item 1 .74 33,333 24,666
Item 5 .25 33,333 8,333
STEP 6: CALCULATE
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APIPA 2009 100
RESULTS - EXAMPLEItem Projected
Misstatement
95% Upper
Limit
Increment
Upper
Misstatement
Item 3 33,333 3.0 99,999
Item 1 24,666 1.7 41,932
Item 5 8,333 1.5 12,500
154,431
STEP 6: CALCULATE
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APIPA 2009 101
RESULTS - EXAMPLEItem Projected
Misstatement
95% Upper
Limit
Increment
Upper
Misstatement
Group 2 154,431
Group 1 7,200
Upper Misstatement Limit 161,631
STEP 7: DRAW
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APIPA 2009 102
CONCLUSIONS If Upper Misstatement Limit > Tolerable
Misstatement, balance is materiallymisstated.
If Upper Misstatement Limit > TolerableMisstatement, balance is not materiallymisstated
IN-CLASS EXERCISES
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APIPA 2009 103
NO. 5 TO NO. 6
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IN-CLASS EXERCISE
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APIPA 2009 105
NO. 52. Sampling items always included:
The loans > the sampling intervalLoan #1 141,100
Loan #26 131,200
IN-CLASS EXERCISE
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APIPA 2009 106
NO. 6Recorded amount of accounts receivable =
$400,000
Tolerable misstatement: $20,000; 20,000 /
400,000 = 5% Risk of incorrect acceptance: 5%
Expected misstatements: 0
Sample size = 59
Sampling interval = 400,000 / 59 = 6,780
IN-CLASS EXERCISE
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APIPA 2009 107
NO. 6Error Recorded
Amount
Audit
Amount
Difference Tainting
%
1 400 320 80 20%
2 500 0 500 100%
3 7,000 6,500 500 NA
IN-CLASS EXERCISE
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APIPA 2009 108
NO. 6Error Tainting % Sampling
Interval
Projected
Misstate-
ment
Upper
Limit
Increment
Upper
Limit
Misstate-
ment
Logical unit BV < Sampling Interval
2 100 6,780 6,780 1.7 11,526
1 20 6,780 1,356 1.5 2,034
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IN-CLASS EXERCISE
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APIPA 2009 110
NO. 6Error Tainting % Sampling
Interval
Projected
Misstate-
ment
Upper
Limit
Increment
Upper
Limit
Misstate-
ment
Logical unit BV < Sampling Interval 13,560Logical unit BV > Sampling Interval 500
Basic Precision 20,340
Upper Misstatement Limit 34,400Conclusion: The account is materially misstated. The upper misstatement
limit of 34,400 exceeds the tolerable misstatement of 20,000.
NONSTATISTICAL SAMPLING
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APIPA 2009 111
BALANCE TESTING Differences in
Identifying individually significant items
Determining sample size Selecting sample items
Calculating sample results
IDENTIFYING INDIVIDUALLY
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APIPA 2009 112
SIGNIFICANT ITEMS Selected due to large size
Tested 100%
Results similar to PPS selection
For example, selecting all items >$100,000
DETERMINING SAMPLE
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APIPA 2009 113
SIZE Sample size =
Sampling Population BV * Assurance
(Tolerable Expected FactorMisstatement)
where Sampling Population BV excludesindividually significant items
DETERMINING SAMPLE
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APIPA 2009 114
SIZEAssessment
of RMM
Desired Level of Confidence Assurance Factors
Maximum Slightly below
maximum
Moderate Low
Maximum
3.0 2.7 2.3 2.0Slightly below
maximum2.7 2.4 2.0 1.6
Moderate 2.3 2.1 1.6 1.2
Low 2.0 1.6 1.2 1.0
DETERMINING SAMPLE
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APIPA 2009 115
SIZE - EXAMPLE Book value = $3,100,000 Individually significant items = $1,500,000 Tolerable misstatement = $150,000
Expected misstatement = $25,000 Desired confidence level = Maximum Risk of MM = Maximum Sample size = 1,600,000 * 3.0
(150,000 25,000)= 38.4, round to 39
SELECTING SAMPLE
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ITEMS Random selection
Systematic selection
Haphazard selection
CALCULATING SAMPLE
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RESULTS Sample misstatement MUST be
projected to population
Two acceptable methodsApply sample misstatement ratio to
population (ratio estimation)
Apply average misstatement $ of each item
in sample to all items in population(difference estimation)
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CLASSICAL SAMPLING Ratio estimation
Difference estimation
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DIFFERENCE ESTIMATION Sample misstatements = $19,000
# of sample items with misstatements = 5
Average misstatement per sample item =
$3,800 # items in population = 256
Projected misstatement = $3,800 * 256 =$972,800
Compare projected misstatement to tolerablemisstatement
IN-CLASS EXERCISE
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NO. 7
IN-CLASS EXERCISE
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NO. 7Nons tat ist ical Samp le Results : Errors in accounts > $10,000 33,000 Errors in accounts < $10,000: Total errors $ 4,350 Sample BV $81,500 Error rate 5.34% Applied to population: 2,760,000 (465,000) 2,295,000 * 5.34% 122,553 Total estimated error 155,553 Tolerable misstatement 81,500 Conclusion: Account materially misstated
IN-CLASS EXERCISE
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NO. 7 - PPSPPS Sample Results:
Accounts receivable recorded
balance: $2,760,000
Accounts > $10,000 (tested
separately) (465,000)
Accounts receivable population
PPS $2,295,000
Tolerable misstatement $ 81,500
IN-CLASS EXERCISE
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NO. 7 - PPSSample and sampling interval:
Tolerable rate: 81,500 / 2,295,000 = 3.55%,round to 4%
Expected rate: 0
5% risk of overreliance (since IR and CR areboth high)
Sample size: 74Sampling interval: 2,295,000 / 74 = 31,014
IN-CLASS EXERCISE
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NO. 7 - PPSRecorded
ValueAudited
ValueDifference Tainting %
Item 12 5,120 4,820 300 5.85
Item 19 485 385 100 20.6Item 33 1,250 250 1,000 80
Item 35 3,975 3,875 100 25.2
Item 51 1,850 1,825 25 1.4
Item 59 4,200 3,780 420 10
Item 74 2,405 0 2,405 100
IN-CLASS EXERCISE
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NO. 7 - PPS# of Overstatement
Misstatements5% Upper Limit Increment
0 3.00
1 4.75 1.75
2 6.30 1.55
3 7.76 1.46
4
9.16
1.40
5 10.52 1.36
6 11.85 1.33
7 13.15 1.30
IN-CLASS EXERCISE
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NO. 7 - PPSTainting
%Sampling
IntervalProjected
MisstatementUpper Limit
FactorUpper
Misstatement
Item 74 100 31,014 31,014 1.75 54,275
Item 33 80 31,014 24,811 1.55 38,457
Item 35 25.2 31,014 7,816 1.46 11,411
Item 19 20.6 31,014 6,389 1.40 8,944
Item 59 10 31,014 3,101 1.36 4,218
Item 12 5.85 31,014 1,814 1.33 2,413
Item 51 1.4 31,014 434 1.30 564
120,282
IN-CLASS EXERCISE
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NO. 7 - PPS Items < Sampling Interval: 120,282
Items > Sampling Interval: None
Basic precision: 3.0 * 31,014 = 93,042
Upper misstatement limit = 213,324
Conclusion: Account is materially misstated.Upper misstatement limit 213,324 > tolerable
misstatement 81,500
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RESOURCES Audit Sampling: An Introduction, 3rd
Edition, Guy, Carmichael & Whittington
Audit Guide: Audit Sampling, New Edition
as of May 1, 2008, AICPA Auditing & Assurance Services, 6th
Edition, Messier, Glover, & Prawitt
Auditing & Assurance Services, 12thEdition, Arens, Elder & Beasley
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THE END!
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