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Auditing & Assurance Services, 6e. Variables Sampling. Variables sampling is used to estimate the amount (or value) of a population Substantive procedures Estimate account balance or misstatement Compare estimated account balance or misstatement to recorded amount or tolerable misstatement - PowerPoint PPT Presentation
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Auditing & Assurance Services, 6e
Mod G-2
Variables Sampling
• Variables sampling is used to estimate the amount (or value) of a population
• Substantive procedures– Estimate account balance or misstatement
– Compare estimated account balance or misstatement to recorded amount or tolerable misstatement
• Approaches– Monetary unit sampling (MUS)
– Classical variables sampling
Mod G-3
Monetary Unit Sampling (MUS)• Defines the sampling unit as an individual dollar (or
other monetary unit) in an account balance• Auditor will select individual dollars (or monetary
units) for examination• Auditor will verify the entire “logical unit”
containing the selected dollar (or monetary unit)– Accounts receivable: Customer account
– Inventory: Inventory item
Mod G-4
Effect of Factors on Sample SizeFactor Effect How Determined
Sampling risk (risk of incorrect acceptance)
Inverse Using the audit risk model and based on prior assessments of audit risk, risk of material misstatement, and analytical procedures risk
Tolerable misstatement Inverse Based on recorded account balance and relationship between the recorded account balance and important financial statement subtotals
Expected misstatement Direct Based on prior experience with the client (for recurring audits) or a pilot sample (for initial audits)
Population size Direct Based on the recorded balance in the account balance or class of transactions
Mod G-5
Summary: Sampling Risks Under Variables Sampling
Account is not misstated(AM ≤ TM)
Account is misstated(AM > TM)
Account is not misstated(ULM ≤ TM)
Correct decision Risk of incorrect acceptance
Account is misstated(ULM > TM)
Risk of incorrect rejection
Correct decision
Decision Based on Population
Decision Based on Sample
AM = Actual misstatementTM = Tolerable misstatementULM = Upper limit on misstatements
Mod G-6
MUS: Selecting Sample Items
• Use systematic random sampling
• Calculate sampling interval as:
Population size ÷ Sample size
• Process– Identify random start
– Skip number of items equal to sampling interval
– Select item (dollar in account) and examine entire logical unit containing that item (customer account)
– May select same logical unit multiple times
Mod G-7
MUS: Measuring Sample Items
Mod G-8
MUS: Evaluating Sample Results• Determine the upper limit on misstatements,
which has a (1 – Risk of incorrect acceptance) of equaling or exceeding the true amount of misstatement
• Components:– Projected misstatement
– Incremental allowance for sampling risk
– Basic allowance for sampling risk
Mod G-9
Upper Limit on Misstatements• If ULM = $50,000 and risk of incorrect
acceptance = 5%
95% probability (1 – risk of incorrect acceptance)
$0 $50,000
5% probability (risk of incorrect acceptance)
Mod G-10
MUS: Making the Decision
Upper Limit on Misstatement
Upper Limit on Misstatement
≤
>
Tolerable Misstatement
Tolerable Misstatement
Account balance is not misstated
Account balance is misstated
Mod G-11
Classical Variables Sampling
• Uses normal distribution theory and the central limit theorem to provide an estimated range of– Recorded account balance or class of transactions
– Misstatement in an account balance or class of transactions
• Basic methodology– Determine estimated range of account balance or
misstatement
– Evaluate using tolerable misstatement
Mod G-12
Additional Considerations in Classical Variables Sampling• Consider the following additional factors in
determining sample size– Risk of incorrect rejection– Population variability
• To reduce population variability, auditors may choose to stratify the population
Mod G-13
Classical Variables Sampling Approaches• Mean-per-unit:
– Assumes each item in population (component of account) has similar balance
– Estimates recorded balance by multiplying number of components by average audited value
• Difference estimation:
– Assumes each item in population (component of account) has similar difference between recorded and audited value
– Estimates the amount of misstatement by multiplying number of components by average misstatement
– Estimates recorded balance using estimated misstatement
• Ratio estimation:
– Assumes a constant percentage misstatement in population
– Estimates recorded balance by multiplying recorded balance by ratio of audited value to recorded balance
Mod G-14
Sampling MethodsMUS Classical Variables Sampling
Overstatement errors are greatest concern
Both overstatement and understatement errors are of concern
Standard deviation difficult to estimate Standard deviation can be estimated
Smaller number of misstatements anticipated
Larger number of misstatements anticipated
Population has high degree of variability and large dollar components exist
Population is homogenous (in terms of dollar balances) and large dollar components do not exist
Mod G-15
Nonstatistical Sampling
• Permissible under GAAS• Does not permit auditors to control
exposure to sampling risk• Major differences in:
– Determining sample size– Selecting sample items– Evaluating sample results