# Auditing & Assurance Services, 6e

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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 Approaches Monetary unit sampling (MUS) Classical variables sampling

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

Effect of Factors on Sample Size
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 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 Based on the recorded balance in the account balance or class of transactions

Summary: Sampling Risks Under Variables Sampling
Decision Based on Population Account is not misstated (AM ≤ TM) Account is misstated (AM > TM) (ULM ≤ TM) Correct decision Risk of incorrect acceptance (ULM > TM) Risk of incorrect rejection Decision Based on Sample AM = Actual misstatement TM = Tolerable misstatement ULM = Upper limit on misstatements

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

MUS: Measuring Sample Items

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

Upper Limit on Misstatements
If ULM = \$50,000 and risk of incorrect acceptance = 5% \$0 \$50,000 95% probability (1 – risk of incorrect acceptance) 5% probability (risk of incorrect acceptance)

MUS: Making the Decision
Upper Limit on Misstatement Tolerable Misstatement Account balance is not misstated Upper Limit on Misstatement Tolerable Misstatement Account balance is misstated >

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

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

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

Sampling Methods MUS 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

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

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