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Sampling for Tests of Transactions. Objective of Tests TOC - Determine if control is effective STOT - Determine existence of monetary errors in transactions. Objective of TOC and STOT. Both are tests of transactions Evaluated yes / no control is / is not effective

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sampling for tests of transactions
Sampling for Tests of Transactions
  • Objective of Tests
  • TOC - Determine if control is effective
  • STOT- Determine existence of monetary errors in transactions
objective of toc and stot
Objective of TOC and STOT
  • Both are tests of transactions
  • Evaluated yes / no
    • control is / is noteffective
    • transaction is / is notcorrectly recorded
  • Auditor should consider qualitative aspectsof deviations
evaluation of results
Evaluation of Results
  • TOC- assessment of control risk
  • affects PDR and evidence (STOT and TODB)
  • STOT - are transactions correctly recorded
  • affects extend to TODB
  • also has implications for control risk
risk model
Risk Model
  • TOC CR
  • Lower CR PDR
  • Evidence
  • (less STOT & TODB for related objective)
risk model5
Risk Model
  • STOT
  • CR PDR
  • STOT affect CR assessment.
  • Good results also lowers TODB
  • (STOT and TODB both part of PDR)
slide6
Relationship between selection and evaluation
  • Statistical Sampling must be
  • evaluation random(probabilistic)
  • Nonstatistical Judgmental selection
  • evaluation allowed, but random
  • selection is still preferable
  • Point: Random selection is always desirable
selection methods
Selection Methods
  • Random - Each item has equal chance of selection (TOT)
  • Probabilistic - each item has a know probability of selection (TODB)
sampling risk
Sampling Risk
  • Sampling Risk- Risk the sample is not representative; inherent with sampling. Reduce by:
  • Using appropriate sampling
  • Increasing sample size
  • Is a random sample representative?
nonsampling risk
Nonsampling Risk
  • Nonsampling error- is the risk the auditor fails to uncover existing errors in the sample. Reduce by:
  • Carefully defining and performing the test(text example of incorrectly selecting an existence sample from shipping documents)
  • Control over sample
15 27 a test with attributes sampling
15-27 (a) - Test with attributes sampling?
  • Review CR journal for unusual transactions.
  • Trace prelisting amts. to CR journal
  • Compare info on prelisting with CR journal
  • Examine remittance advices to see if discounts approved
  • Trace entries from prelist to deposit
15 27 a test with attributes sampling11
15-27 (a) - Test with attributes sampling?
  • Review CR journal for unusual transactions.
  • Trace prelisting amts. to CR journal
  • Compare info on prelisting with CR journal
  • Examine remittance advices to see if discounts approved
  • Trace entries from prelist to deposit
sample selection
Sample Selection
  • 2. Trace prelisting amts. to CR journal (completeness)
  • 3. Compare info on prelisting with CR journal (accuracy)
  • 4. Examine remittance advices to see if discounts approved (accuracy)
  • 5. Trace entries from prelist to deposit (completeness)
  • Draw sample from prelist (source for directional completeness tests)
sampling for exception rates
Sampling for Exception Rates
  • Objective- Estimate maximum error rate in population based on sample
  • determine if control can be relied on or results for STOT acceptable
maximum error rate cuer
Maximum Error Rate (CUER)
  • Sample exception rate (SER) is best estimator of population exception rate
  • Maximum rate is the computed upper exception rate (CUER) and includes allowance for sampling risk (ASR)
  • CUER = SER + ASR
slide15
Larger n
  • sample exception rateCUER
  • (SER)
slide16
Variable Description Definition
  • EPER Expected Last year’s results
  • population or auditor exception rate expectations
  • TER Tolerable Maximum rate
  • (precision) exception that auditor will rate allow. Lower for imp. objectives
  • ARACR Acceptable Risk of relying
  • (confidence risk of on control/STOT level) assessing CR when it is too low ineffective
changes in variables on sample size
Changes in variables on sample size
  • Planning relation:
  • TER = EPER + ASR (allowance for sample risk)
  • Increases in sample size lower sampling risk
slide18
Effect on Changes in Variables on
  • Sample Size
  • Change in Effect
  • Factor on n Reason
  • EPER increase Increase Less allowance for
  • sampling risk for given TER
  • TERincrease Decrease More allowance for sampling risk for given EPER
  • ARACR Decrease Less reliance on increase controls; less evidence needed
slide19
The biggest effect on sample size is TER - EPER
  • Bigger differences provides larger allowance for sampling risk
15 22 a
15-22(a)
  • If all other factors remain constant, changing ARACR from 10% to 5% would cause sample size to:
  • 1. Increase
  • 2. Remain the same
  • 3. Decrease
  • 4. Become indeterminate
slide21
Problem 15-28 Part c: (increase in ARACR)
  • 12 34
  • ARACR 10 5 5 5
  • TER 6 6 5 6
  • EPER 2 2 2 2
  • Population
  • size 1,000 100,000 6,000 1,000
  • Sample
  • Size 88 127 181 127
slide22
Problem 15-28 Part c: (increase in TER)
  • 1 2 34
  • ARACR 10 5 5 5
  • TER 6 6 5 6
  • EPER 2 2 2 2
  • Population
  • size 1,000 100,000 6,000 1,000
  • Sample
  • Size 88 127 181127
slide23
Problem 15-28 Part c: (increase in EPER)
  • 5 67
  • ARACR 10 10 5
  • TER 20 20 2
  • EPER 8 2 0
  • Population
  • size 500 500 1,000,000
  • Sample
  • Size 25 18149
slide24
Problem 15-28 Part c: (increase in POP)
  • 1 2 3 4
  • ARACR 10 5 5 5
  • TER 6 6 5 6
  • EPER 2 2 2 2
  • Population
  • size 1,000 100,000 6,000 1,000
  • Sample
  • Size 88 127181127
evaluating the sample
Evaluating the Sample
  • TER, ARACR, and n as before
  • SER = Sample exception rate
  • (# of exceptions/n)
  • CUER = maximum error rate
  • = SER + ASR
evaluation decision nonstatistical sampling
Evaluation Decision - Nonstatistical sampling
  • Approach 1:
  • Accept if CUER < TER
  • Approach 2:
  • ASR = TER - SER
  • Accept if ASR large enough (SER sufficiently less than TER)
options when cuer exceeds ter
Options when CUER exceeds TER
  • 1. Increase sample size - lowers ASR and CUER
  • (may also reduce SER if initial sample not representative)
  • 2. Don’t rely upon control/STOT
  • CR and substantive tests
options when cuer ter
Options when CUER > TER
  • TOC fails -can increase STOT or TODB. Usually increase STOT
  • STOT fails- Increase TODB
  • 3. Revise TER or ARACR -
  • usually not recommended
change in variables on cuer
Change in variables on CUER
  • Evaluation relation:
  • CUER = SER + ASR
  • Remember: increase in sample size lowers sampling risk
  • Increase in n may also lower SER if initial sample not representative
effect of changes in variables on cuer
Effect of Changes in Variables on CUER
  • Change in Effect on
  • Factor CUER Reason
  • SER Increase Increase CUER = SER+ASR
  • n increase Decrease Lower sampling risk
  • ARACR Decrease Less reliance on
  • increase controls; threshold for accepting a control is lower
slide31

Lower ARACR is

farther out curve

  • Larger n
  • sample exception rateCUER
  • (SER)

5% ARACR

15 23 a
15-23 (a)
  • An auditor estimates with 10% ARACR (90% confidence) that CUER is between 4% and 6%. The auditor’s major concern is that there is one chance in 20 that the true exception rate is:
  • 1. More than 6%
  • 2. Less than 6%
  • 3. More than 4%
  • 4. Less than 4%
slide33
Problem 15-29 Part c: (decrease ARACR)
  • 1 23 4
  • ARACR 10 5 5 5
  • Population Size 5,000 5,000 5,000 50,000
  • Sample size 200 200 50 200
  • Number of
  • exceptions 4 4 1 4
  • CUER 4.0 4.59.1 4.5
slide34
Problem 15-29 Part c:(decrease n)
  • 1 2 3 4
  • ARACR 10 5 5 5
  • Population Size 5,000 5,000 5,000 50,000
  • Sample size 200 200 50 200
  • Number of
  • exceptions 4 4 1 4
  • CUER 4.0 4.5 9.1 4.5
slide35
Problem 15-29 Part c:(decrease exceptions)
  • 5 6 7 8
  • ARACR 5 5 5 5
  • Population Size 500 900 5,000 500
  • Sample size 100 100 100 25
  • Number of
  • exceptions 2 10 0 0
  • CUER 6.2 16.4 3.0 11.3