STATISTICAL SAMPLING FOR AUDITORS

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STATISTICAL SAMPLING FOR AUDITORS
Jeanne H. Yamamura CPA, MIM, PHD
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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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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 be representative of
  the population.

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SAMPLING RISK

• Possibility that the sample is NOT representative
  of the population
• As a result, auditor will reach WRONG conclusion
• Decision errors
• Type I Risk of incorrect rejection
• Type II Risk of incorrect acceptance

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TYPE I RISK OF INCORRECT REJECTION

• Internal control Risk that sample supports
  conclusion that control is NOT operating
  effectively when it really is
• AKA Risk of underreliance, risk of assessing
  control risk too high
• Substantive testing Risk that sample supports
  conclusion that balance is NOT properly stated
  when it really is

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TYPE II RISK OF INCORRECT ACCEPTANCE

• Internal control Risk that sample supports
  conclusion that control is operating effectively
  when it really isnt
• AKA Risk of overreliance, risk of assessing
  control risk too low
• Substantive testing Risk that sample supports
  conclusion that balance is properly stated when
  it really isnt

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WHICH RISK POSES THE GREATER DANGER TO AN AUDITOR?

• 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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NONSAMPLING RISK

• Risk of auditor error
• Sample wrong population
• Fail to detect a misstatement when applying audit
  procedure
• Misinterpret audit result
• Controlled through
• Adequate training
• Proper planning
• Effective supervision

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SAMPLE SIZE FACTORS

• Desired level of assurance (confidence level)
• Acceptable defect rate (tolerable error)
• Historical defect rate (expected error)

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CONFIDENCE LEVEL

• Complement of sampling risk
• 5 sampling risk, 95 confidence level
• How much reliance will be placed on test results
• The greater the reliance and the more severe the
  consequences of Type II error, the higher the
  confidence level needed
• Sample size increases with confidence level
  (decreases with sampling risk)

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TOLERABLE ERROR AND EXPECTED ERROR

• Precision the gap between tolerable error and
  expected error
• AKA Allowance for sampling risk
• Sample size increases as precision decreases

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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 control testing
• Confirmation, e.g., verification of AR balances

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WHEN IS SAMPLING INAPPROPRIATE?

• Selection of all items with a particular
  characteristic, e.g., all disbursements gt
  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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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 and
  adequate monitoring)
• Walkthough sample of 1

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STATISTICAL VS NONSTATISTICAL SAMPLING

• Statistical sampling
• Statistical computation of sample size
• Statistical evaluation of results
• Nonstatistical sampling
• Sample sizes should be approximately the same (AU
  350.22)
• Sample sizes must be sufficient to support
  reliance on controls and assertions being tested

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WHEN IS SAMPLING NONSTATISTICAL?

• If sample size determined judgmentally
• If sample selected haphazardly
• If sample results evaluated judgmentally

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TYPES OF SAMPLING

• Attribute sampling
• Monetary unit sampling
• Classical variables sampling

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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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MONETARY-UNIT SAMPLING

• AKA probability proportional to size (PPS)
  sampling, cumulative monetary unit sampling
• Used to estimate dollar amount of misstatement

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CLASSICAL VARIABLES SAMPLING

• Uses normal distribution theory to identify
  amount of misstatement
• Useful when large number of differences expected
• Smaller sample size than MUS
• Effective for both overstatements and
  understatements
• Can easily incorporate zero balances

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IN-CLASS EXERCISE NO. 1
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IN-CLASS EXERCISE NO. 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 large population)
6 No NA
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IN-CLASS EXERCISE NO. 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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STEPS IN STATISTICAL ATTRIBUTE SAMPLING
APPLICATION

• Planning
• Determine the test objectives
• Define the population characteristics
• Determine the sample size
• Performance
• Select sample items
• Perform the auditing procedures
• Evaluation
• Calculate the results
• Draw conclusions

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STEP 1 DETERMINE THE TEST OBJECTIVES

• Objective for T of C To determine the operating
  effectiveness of the internal control
• Support control risk assessment below maximum
• Identify controls to be tested and understand why
  they are to be tested

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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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STEP 2 DEFINE THE POPULATION CHARACTERISTICS

• Define the sampling population
• Assertion
• Completeness
• Define the sampling unit
• Determined by available records
• Define the control deviation conditions

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STEP 3 DETERMINE THE SAMPLE 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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STEP 3 DETERMINE THE SAMPLE SIZE

• Tolerable deviation rate
• Maximum deviation rate that auditor willing to
  accept and still consider control effective
• Control would be relied upon
• Why any errors acceptable?
• Control deviation Misstatement

Assessed importance of control Tolerable deviation rate
Highly important 3-5
Moderately important 6-10
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STEP 3 DETERMINE THE SAMPLE SIZE

• Expected population deviation rate
• Rate expected to exist in population
• Based on prior years results or pilot sample
• If expected population deviation rate gt tolerable
  rate, DO NOT TEST
• SAMPLE SIZE TABLES

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STEP 3 DETERMINE THE SAMPLE SIZE

• Testing multiple attributes on the same sample
• Select largest sample size and audit all of them
  for all attributes
• Result is some overauditing BUT may take less
  time than trying to remember which sample items
  need to be tested for which attribute

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FINITE POPULATION CORRECTION FACTOR

• When population size lt 500
• Apply finite population correction factor
• v1-(n/N)
• Where n sample size from table and N number
  of units in population

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STEP 4 SELECT THE SAMPLE ITEMS

• Sample must be selected to be representative of
  the population
• Each item must have an equal opportunity of being
  selected

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STEP 4 SELECT THE SAMPLE ITEMS

• Random number selection
• Unrestricted random sampling without replacement
  (once selected cannot be selected again)

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STEP 4 SELECT THE SAMPLE ITEMS

• Random number table
• Need to document
• Correspondence relationship between population
  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 sample
  items if needed

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RANDOM NUMBER TABLE ILLUSTRATION

• Select a sample of 4 items from prenumbered
  canceled checks numbered from 1 to 500. Start at
  row 5, column 1, digit starting position 1.
  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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RANDOM NUMBER TABLE ILLUSTRATION

• To minimize discards, table numbers gt 500 can be
  reduced by 500 to produce a sample item within
  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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RANDOM NUMBER TABLE ILLUSTRATION

• Select 4 sales invoices numbered from 5000 to
  12000. Start at row 21, column 2, digit starting
  point 1. Rather than use a 5-digit number, which
  produces a large number of discards, add a
  constant to get a population with 4 digits. If a
  constant of 3000 is used, the usable numbers
  selected from 2000 to 9000 are
• 6,043 (sample item 1 3043 3000)
• 10,120 (sample item 2 7120 3000)
• 10,212 (sample item 3 7212 3000)
• 5,259 (sample item 4 2259 3000)

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STEP 4 SELECT THE SAMPLE ITEMS - EXCEL

• Excel
• Select Tools
• Select Data Analysis
• Select Sampling

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STEP 4 SELECT THE SAMPLE ITEMS - EXCEL
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STEP 4 SELECT THE SAMPLE ITEMS

• Input Range
• Enter the references for the range of data that
  contains the population of values you want to
  sample. Microsoft Excel draws samples from the
  first column, then the second column, and so on.
• Labels
• Select if the first row or column of your input
  range contains labels. Clear if your input range
  has no labels Excel generates appropriate data
  labels for the output table.
• Sampling Method
• Click Periodic or Random to indicate the sampling
  interval you want.
• Period
• Enter the periodic interval at which you want
  sampling to take place. The period-th value in
  the input range and every period-th value
  thereafter is copied to the output column.
  Sampling stops when the end of the input range is
  reached.

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STEP 4 SELECT THE SAMPLE ITEMS

• Number of Samples
• Enter the number of random values you want in the
  output column. Each value is drawn from a random
  position 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 output table. 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 the input range,
  divided by the sampling rate. If you select
  Random, the number of values in the output table
  is equal to the number of samples.

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STEP 4 SELECT THE SAMPLE 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 risk of missing systematic deviations
• Select every nth item
• Continue sample selection until population is
  exhausted
• (Last sample selected sampling interval) gt Last
  item in population
• In other words, dont stop when desired sample
  size reached

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STEP 5 PERFORM THE AUDITING PROCEDURES

• Conduct planned audit procedures
• What if?
• Voided documents - if properly voided, not a
  deviation replace with new sample item
• Unused or inapplicable documents replace with
  new sample item
• Inability to examine sample item deviation
• Stopping test before completion large number of
  deviations detected

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STEP 5 PERFORM THE AUDITING 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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STEP 6 CALCULATE RESULTS

• Summarize deviations for each control
• Calculate sample deviation rate and computed
  upper deviation rate
• Sample deviation rate Allowance for sampling
  risk Computed upper deviation rate
• Statistical sampling results evaluation tables

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STEP 7 DRAW CONCLUSIONS

• If Computed Upper Deviation Rate gt Tolerable
  Rate, control is ineffective and cannot be relied
  upon.
• If Computed Upper Deviation Rate lt Tolerable
  Rate, control is effective

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EVALUATION OF EXPOSURE

• In a sample of 25 manual control operations from
  a population of 3,000 control operations, 1
  deviation was identified. The sample was designed
  with an expectation that 0 deviations would be
  found.
• Looking up the results (in 90 confidence level
  table) Computed upper error limit 14.7

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EVALUATION OF EXPOSURE

• The sample did not meet its design criteria, so
  there is a higher than desired risk that the
  control will fail to prevent or detect a
  misstatement.
• To assess the magnitude of the exposure
• Identify the gross exposure of the account or
  process. This is based on the volume of dollars
  processed through the control.
• The upper limit on the control deviations was
  14.7.
• The adjusted exposure is 735,000 (14.7
  5,000,000).
• The 735,000 exposure may assist the auditor in
  evaluating the severity of the control deficiency.

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IN-CLASS EXERCISES NO. 2 NO. 3
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IN-CLASS EXERCISE NO. 2
Problem 1 Prenumbered sales invoices where the lowest invoice number is 1 and the highest is 6211. Problem 1 Prenumbered sales invoices where the lowest invoice number is 1 and the highest is 6211.
Sampling unit Sales invoice
Population numbering system 1 to 6211
Random number table correspondence Use 4 digits with random start at 0029-05 going down and then right
First 5 items in sample 3553 0081 4429 0484 4881
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IN-CLASS EXERCISE NO. 2
Problem 2 Prenumbered bills of lading where the lowest document number is 21926 and the highest is 28511. Problem 2 Prenumbered bills of lading where the lowest document number is 21926 and the highest is 28511.
Sampling unit Bill of lading
Population numbering system 21926 to 28511
Random number table correspondence Use last 4 digits with random start at 0005-07
First 5 items in sample 7744 7632 8120 3736 4091
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IN-CLASS EXERCISE NO. 2
Problem 3 Accounts Receivable on 10 pages with 60 lines per page except the last page, which has only 36 full lines. Each line has a customer name and an amount receivable. Problem 3 Accounts Receivable on 10 pages with 60 lines per page except the last page, which has only 36 full lines. Each line has a customer name and an amount receivable.
Sampling unit Each line
Population numbering system 9 60 540 36 576 lines Add 2000 (2001 to 2576)
Random number table correspondence Use last 4 digits with random start at 00040-01 going down and then right
First 5 items in sample 2240 2055 2094 2087 2608
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IN-CLASS EXERCISE NO. 2
Problem 4 Prenumbered invoices in a sales journal where each month starts over with number 1. (Invoices for each month are designated by the month and document number.) There is a maximum of 20 pages per month with a total of 185 pages for the year. All pages have 75 invoices except for the last page for each month. Problem 4 Prenumbered invoices in a sales journal where each month starts over with number 1. (Invoices for each month are designated by the month and document number.) There is a maximum of 20 pages per month with a total of 185 pages for the year. All pages have 75 invoices except for the last page for each month.
Sampling unit Page of invoices
Population numbering system Starting with January, first page is 1 (up to 185)
Random number table correspondence Random start at 0008-03 going down then right, subtract random number from next 1000
First 5 items in sample 4000 3982 18 7000 6847 153 5000 - 4956 44 6000 5985 15 5000 4941 59
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IN-CLASS EXERCISE NO. 3
For which of these auditing procedures can attribute sampling be conveniently used? For which of these auditing procedures can attribute sampling be conveniently used?
1 No
2 No
3 No
4 Yes
5a Yes
5b Yes
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IN-CLASS EXERCISE NO. 3
For which of these auditing procedures can attribute sampling be conveniently used? For which of these auditing procedures can attribute sampling be conveniently used?
5c Yes
5d Yes
5e Yes
6 Yes
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IN-CLASS EXERCISE NO. 3
2. Considering the audit procedures to be performed, what is the most appropriate sampling unit for conducting most of the audit sampling tests?
Sales invoice
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IN-CLASS EXERCISE NO. 3
For each T of C or ST of T, identify the attribute being tested and the exception condition. For each T of C or ST of T, identify the attribute being tested and the exception condition.
Attribute Exception Condition
4. Existence of the sales invoice number in the sales journal No record of the sales invoice number in the sales journal
5a. Amount and other data in MF agree with the sales journal entry The amount recorded in the MF differs from the amount recorded in the sales journal.
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IN-CLASS EXERCISE NO. 3
For each T of C or ST of T, identify the attribute being tested and the exception condition. For each T of C or ST of T, identify the attribute being tested and the exception condition.
Attribute Exception Condition
5b. Amount and other data on the duplicate sales invoice agree with the sales journal entry Customer name and account number on the invoice differ from the information recorded in the sales journal
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IN-CLASS EXERCISE NO. 3
For each T of C or ST of T, identify the attribute being tested and the exception condition. For each T of C or ST of T, identify the attribute being tested and the exception condition.
Attribute Exception Condition
5b. Evidence that pricing, extensions, and footings are checked (initials and correct amounts). Lack of initials indicating verification of pricing, extensions, and footings.
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IN-CLASS EXERCISE NO. 3
For each T of C or ST of T, identify the attribute being tested and the exception condition. For each T of C or ST of T, identify the attribute being tested and the exception condition.
Attribute Exception Condition
5c. Quantity and other data on the bill of lading agree with the duplicate sales invoice and sales journal Quantity of goods shipped differs from quantity on sales invoice
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IN-CLASS EXERCISE NO. 3
For each T of C or ST of T, identify the attribute being tested and the exception condition. For each T of C or ST of T, identify the attribute being tested and the exception condition.
Attribute Exception Condition
5d. Quantity and other data on the sales order agree with the duplicate sales invoice Quantity on the sales order differs from quantity on the duplicate sales invoice
5e. Quantity and other data on the customer order agree with the duplicate sales invoice Product number and description on the customer order differ from information on the duplicate sales invoice
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IN-CLASS EXERCISE NO. 3
For each T of C or ST of T, identify the attribute being tested and the exception condition. For each T of C or ST of T, identify the attribute being tested and the exception condition.
Attribute Exception Condition
5e. Credit is approved Lack of initials indicating credit approval
6. For recorded sales in the sales journal, the file of supporting documents includes a duplicate sales invoice, BL, sales order, and customer order. BL is not attached to the duplicate sales invoice and the customer order.
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IN-CLASS EXERCISE NO. 3
See Solution
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STEPS IN NONSTATISTICAL ATTRIBUTE SAMPLING
APPLICATION

• Planning
• Determine the test objectives
• Define the population characteristics
• Determine the sample size
• Performance
• Select sample items
• Perform the auditing procedures
• Evaluation
• Calculate the results
• Draw conclusions

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STEP 3 DETERMINE THE SAMPLE SIZE

• Consider desired confidence level, tolerable
  deviation rate, and expected population deviation
  rate
• Judgmentally determine sample size
• NOTE Check against statistical sample size
  tables to verify adequacy

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STEP 3 DETERMINE THE SAMPLE SIZE

• Guidelines for nonstatistical sample sizes for
  tests of controls
• If any errors found, increase sample size or
  increase control risk

Desired level of controls reliance Sample size
Low 15-20
Moderate 25-35
High 40-60
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STEP 4 SELECT SAMPLE ITEMS

• Random sample
• Systematic sample (with random start)
• Haphazard selection
• Still desire representative sample
• Avoid unusual, large, first or last

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STEP 6 CALCULATE THE RESULTS

• No computed upper deviation rate
• If sample deviation rate gt expected population
  deviation rate, control not effective

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COMPLIANCE AUDITING

• Performance of auditing procedures to determine
  whether an entity is complying with specific
  requirements of laws, regulations, or agreements
• Governmental entities and other recipients of
  governmental financial assistance
• Compliance with laws and regulations that
  materially affect each major federal assistance
  program

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COMPLIANCE AUDITING OF FEDERAL ASSISTANCE PROGRAMS

• Definition of population for testing of an
  internal 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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COMPLIANCE AUDITING - EXAMPLE

• Federal financial assistance for Island City
• Three major federal financial assistance programs
• Four nonmajor programs
• Control Transaction review to ensure that only
  legally allowable costs are charged to each
  program

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COMPLIANCE AUDITING - EXAMPLE

• More efficient to select one sample from
  population of all transactions (major and
  nonmajor programs)
• Confidence level 95
• Tolerable deviation rate 9
• Expected population deviation rate 1
• Sample size 51
• 1 allowable deviation

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SMALL POPULATIONS AND INFREQUENTLY OPERATING
CONTROLS
Small Population Sample Size Table Small Population Sample Size Table
Control Frequency and Population Size Sample Size
Quarterly (4) 2
Monthly (12) 2-4
Semimonthly (24) 3-8
Weekly (52) 5-9
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IN-CLASS EXERCISE NO. 4
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IN-CLASS EXERCISE NO. 4
Selected Payroll T of C Selected Payroll T of C
1. Examine the time card for approval of a supervisor Moderately critical affects E/O of S W
2. Account for a sequence of payroll checks in the payroll journal Very critical affects E/O of SW
3. Recompute hours on the time card Moderately critical affects V of SW
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IN-CLASS EXERCISE NO. 4
4. Compare the employee name in the payroll journal to personnel records Very critical affects E/O - affects E/O of S W also an area subject to fraud
5. Review OT charges for approval of a supervisor Moderately critical affects E/O and V of SW
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IN-CLASS EXERCISE NO. 4
Selected Cash Disbursement T of C Selected Cash Disbursement T of C
6. Examine voucher for supporting invoices, receiving reports, etc. Very critical affects E/O of purchase transactions
7. Examine supporting documents for evidence of cancellation (paid) Moderately critical affects validity of purchase transactions and relates to double payment
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IN-CLASS EXERCISE NO. 4
Selected Cash Disbursement T of C Selected Cash Disbursement T of C
8. Ascertain whether cash discounts were taken Least critical affects V of purchase transactions amounts usually minor
9. Review voucher for clerical accuracy Moderately critical affects V of purchase transactions
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IN-CLASS EXERCISE NO. 4
Selected Cash Disbursement T of C Selected Cash Disbursement T of C
10. Agree purchase order price to invoice Moderately critical affects V of purchase transactions
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MONETARY UNIT SAMPLING

• Uses attribute sampling theory to express
  conclusions 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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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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DISADVANTAGES

• Zero or negative balances must be tested
  separately
• Assumes audited amount of sample items is not in
  error by more than 100
• When more than 1 or 2 misstatements found,
  allowance for sampling risk may be overstated
• Auditor more likely to reject balance and
  overaudit

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STEPS IN MONETARY UNIT SAMPLING APPLICATION

• Planning
• Determine the test objectives
• Define the population characteristics
• Determine the sample size
• Performance
• Select sample items
• Perform the auditing procedures
• Evaluation
• Calculate the results
• Draw conclusions

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STEP 1 DETERMINE THE TEST OBJECTIVES

• Substantive testing To test the reasonableness
  of an amount, i.e., that an amount is fairly
  stated
• To test the assertion that no material
  misstatements exist in an account balance, class
  of transactions, or disclosure component of the
  financial statements

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STEP 2 DEFINE THE POPULATION CHARACTERISTICS

• Define the sampling population
• Monetary value of an account balance
• Verify completeness of population
• Define the sampling unit - Each individual dollar
• Define the logical unit - The account or
  transaction that contains the sampling units
• Define a misstatement The difference between
  the book value and the audited value

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STEP 3 DETERMINE THE SAMPLE 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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STEP 3 DETERMINE THE SAMPLE SIZE

• Computing sample sizes using the attribute
  sampling tables
• Select desired confidence level
• Compute tolerable misstatement as percentage of
  book value
• Compute expected misstatement as percentage of
  book value
• Look up sample size in attribute sampling table

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STEP 4 SELECT THE SAMPLE ITEMS

• Systematic selection approach called probability
  proportional to size (PPS)
• Calculate sampling interval
• Book value / sample size
• From random start (within first interval), select
  every nth dollar
• Logical unit included only once even if includes
  more than one sample unit

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STEP 5 PERFORM THE AUDITING PROCEDURES

• Conduct planned audit procedures on logical units
• What if?
• Missing document consider to be a misstatement

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STEP 6 CALCULATE RESULTS

• Projected misstatement Projection of the errors
  to the population
• Upper limit on misstatement Adds an allowance
  for sampling risk to the projected misstatement

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STEP 6 CALCULATE RESULTS

• Sort misstatements into two groups
• Group 1 Logical unit equal to or greater than
  the sampling interval
• Group 2 Logical unit less than the sampling
  interval
• For Group 2, compute the tainting factor for each
  misstatement
• Tainting factor Book value Audit value
• Book value

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STEP 6 CALCULATE RESULTS

• Place the Group 2 items in rank order by tainting
  factor (from largest to smallest)
• Compute the projected misstatement
• Calculate the upper limit increments (using the
  Monetary Unit Sampling Confidence Factors for
  Sample Evaluation table)
• Calculate upper misstatement for each Group 2
  item
• Add differences for Group 1
• Total Upper misstatement limit

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STEP 6 CALCULATE RESULTS - 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, round to 1

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STEP 6 CALCULATE RESULTS - EXAMPLE

• Sample size 93
• Sampling interval 33,333
• Expected misstatement 25,000

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STEP 6 CALCULATE RESULTS - 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 4,200
Item 5 740 555 185
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STEP 6 CALCULATE RESULTS - EXAMPLE
Item Book Value Audited Value Difference
Group 1 BV gt SI (33,333) Group 1 BV gt SI (33,333) Group 1 BV gt SI (33,333) Group 1 BV gt SI (33,333)
Item 2 35,000 32,000 3,000
Item 4 45,200 41,000 4,200
7,200
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STEP 6 CALCULATE RESULTS - EXAMPLE
Item Difference Book Value Tainting Factor
Group 2 BV lt SI (33,333) Group 2 BV lt SI (33,333) Group 2 BV lt SI (33,333) Group 2 BV lt SI (33,333)
Item 1 8,880 12,000 .74
Item 3 1,400 1,400 1.0
Item 5 185 740 .25
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STEP 6 CALCULATE RESULTS - EXAMPLE
Item 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
100
STEP 6 CALCULATE RESULTS - EXAMPLE
Item 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
101
STEP 6 CALCULATE RESULTS - EXAMPLE
Item Projected Misstatement 95 Upper Limit Increment Upper Misstatement
Group 2 154,431
Group 1 7,200
Upper Misstatement Limit Upper Misstatement Limit Upper Misstatement Limit 161,631
102
STEP 7 DRAW CONCLUSIONS

• If Upper Misstatement Limit gt Tolerable
  Misstatement, balance is materially misstated.
• If Upper Misstatement Limit gt Tolerable
  Misstatement, balance is not materially misstated

103
IN-CLASS EXERCISES NO. 5 TO NO. 6
104
IN-CLASS EXERCISE NO. 5

• Sampling interval 746,237 / 10 74,624

Loan Recorded Amount
1 141,100
3 66,600
5 10,230
11 4,350
20 16,530
24 2,950
26 131,200
27 50,370
32 5,900
105
IN-CLASS EXERCISE NO. 5

• Sampling items always included
• The loans gt the sampling interval
• Loan 1 141,100
• Loan 26 131,200

106
IN-CLASS EXERCISENO. 6

• Recorded 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

107
IN-CLASS EXERCISENO. 6
Error Recorded Amount Audit Amount Difference Tainting
1 400 320 80 20
2 500 0 500 100
3 7,000 6,500 500 NA
108
IN-CLASS EXERCISENO. 6
Error Tainting Sampling Interval Projected Misstate-ment Upper Limit Increment Upper Limit Misstate-ment
Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval
2 100 6,780 6,780 1.7 11,526
1 20 6,780 1,356 1.5 2,034
109
IN-CLASS EXERCISENO. 6
Error Tainting Sampling Interval Projected Misstate-ment Upper Limit Increment Upper Limit Misstate-ment
Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval
3 NA NA 500 NA 500
Basic Precision 3.0 6,780 20,340 Basic Precision 3.0 6,780 20,340 Basic Precision 3.0 6,780 20,340 Basic Precision 3.0 6,780 20,340 Basic Precision 3.0 6,780 20,340 Basic Precision 3.0 6,780 20,340
110
IN-CLASS EXERCISENO. 6
Error Tainting Sampling Interval Projected Misstate-ment Upper Limit Increment Upper Limit Misstate-ment
Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval Logical unit BV lt Sampling Interval 13,560
Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval Logical unit BV gt Sampling Interval 500
Basic Precision Basic Precision Basic Precision Basic Precision Basic Precision 20,340
Upper Misstatement Limit Upper Misstatement Limit Upper Misstatement Limit Upper Misstatement Limit Upper Misstatement Limit 34,400
Conclusion The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000. Conclusion The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000. Conclusion The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000. Conclusion The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000. Conclusion The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000. Conclusion The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000.
111
NONSTATISTICAL SAMPLING BALANCE TESTING

• Differences in
• Identifying individually significant items
• Determining sample size
• Selecting sample items
• Calculating sample results

112
IDENTIFYING INDIVIDUALLY SIGNIFICANT ITEMS

• Selected due to large size
• Tested 100
• Results similar to PPS selection
• For example, selecting all items gt 100,000

113
DETERMINING SAMPLE SIZE

• Sample size
• Sampling Population BV Assurance
• (Tolerable Expected Factor
• Misstatement)
• where Sampling Population BV excludes
  individually significant items

114
DETERMINING SAMPLE SIZE
Assessment of RMM Desired Level of Confidence Assurance Factors Desired Level of Confidence Assurance Factors Desired Level of Confidence Assurance Factors Desired Level of Confidence Assurance Factors
Assessment of RMM Maximum Slightly below maximum Moderate Low
Maximum 3.0 2.7 2.3 2.0
Slightly below maximum 2.7 2.4 2.0 1.6
Moderate 2.3 2.1 1.6 1.2
Low 2.0 1.6 1.2 1.0
115
DETERMINING SAMPLE 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

116
SELECTING SAMPLE ITEMS

• Random selection
• Systematic selection
• Haphazard selection

117
CALCULATING SAMPLE RESULTS

• Sample misstatement MUST be projected to
  population
• Two acceptable methods
• Apply sample misstatement ratio to population
  (ratio estimation)
• Apply average misstatement of each item in
  sample to all items in population (difference
  estimation)

118
CLASSICAL SAMPLING

• Ratio estimation
• Difference estimation

119
RATIO ESTIMATION

• Sample misstatements 19,000
• Sample book value 175,000
• Sample error rate 10.9, round to 11
• Total population BV 1,840,000
• Projected misstatement 1,840,000 11
  202,400
• Compare projected misstatement to tolerable
  misstatement

120
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 tolerable
  misstatement

121
IN-CLASS EXERCISE NO. 7
122
IN-CLASS EXERCISE NO. 7

• Nonstatistical Sample Results
• Errors in accounts gt 10,000 33,000
• Errors in accounts lt 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

123
IN-CLASS EXERCISE NO. 7 - PPS

• PPS Sample Results
• Accounts receivable recorded
• balance 2,760,000
• Accounts gt 10,000 (tested
• separately) (465,000)
• Accounts receivable population
• PPS 2,295,000
• Tolerable misstatement 81,500

124
IN-CLASS EXERCISE NO. 7 - PPS

• Sample 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 are
  both high)
• Sample size 74
• Sampling interval 2,295,000 / 74 31,014

125
IN-CLASS EXERCISE NO. 7 - PPS
Recorded Value Audited Value Difference Tainting
Item 12 5,120 4,820 300 5.85
Item 19 485 385 100 20.6
Item 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
126
IN-CLASS EXERCISE NO. 7 - PPS
of Overstatement Misstatements
of Overstatement Misstatements 5 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
127
IN-CLASS EXERCISE NO. 7 - PPS
Tainting Sampling Interval Projected Misstatement Upper Limit Factor Upper 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
128
IN-CLASS EXERCISE NO. 7 - PPS

• Items lt Sampling Interval 120,282
• Items gt 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 gt tolerable
  misstatement 81,500

129
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, 12th Edition,
  Arens, Elder Beasley

130
THE END!