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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