Mastering Substantive and Variable Sampling Techniques in Auditing

What is variable sampling in substantive audit testing?

An audit sampling technique used to estimate the true dollar value of a population account balance or class of transactions.

How does tolerable misstatement in variable sampling differ from tolerable deviation rate in attribute sampling?

Tolerable misstatement measures monetary dollar errors in account balances, whereas tolerable deviation rate measures internal control error rates.

Define tolerable misstatement.

The maximum dollar amount of error an auditor is willing to accept in an account balance or transaction class without considering it materially misstated.

What is stratification in audit sampling?

The technique of separating a population into relatively homogeneous sub-populations (strata) and treating each stratum as an independent population.

Under what population condition should an auditor stratify a sample?

When the population contains highly variable dollar amounts (a high standard deviation).

What is the primary benefit of stratifying a population in variable sampling?

It reduces overall population variability, which typically results in a reduced required sample size.

What is Mean-Per-Unit (MPU) estimation in variable sampling?

A classical variable sampling plan where the projected population value is calculated by multiplying the average audited dollar value of sample items by the total number of items in the population.

What is the formula for the point estimate using Mean-Per-Unit (MPU) estimation?

Total Audited Value of Sample/n where

n is sample size and N is total population items.

Why is Mean-Per-Unit (MPU) estimation sensitive to population variability?

Because MPU relies entirely on the average audited dollar value of sample items without using recorded book values as a benchmark.

What action should an auditor take if selecting Mean-Per-Unit (MPU) estimation on a population with high dollar variability?

Stratify the population into homogeneous dollar groups prior to sampling.

How is the sample ratio calculated in ratio estimation sampling?

Total Audited Value of Sample / Total Book Value of Sample

What is the formula for the point estimate using ratio estimation sampling?

Sample Ratio X Total Recorded Population Book Value

Under what general condition are ratio and difference estimation methods most effective?

When the auditor expects large numbers of overstatements or understatements across items in the population.

How is the average dollar difference per item calculated in difference estimation sampling?

Book Value of Sample - Audited Value of Sample

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n

How is projected total error calculated in difference estimation sampling?

Average Difference per Item X N

N is total population items.

How is the point estimate calculated in difference estimation sampling?

Total Recorded Population Book Value - Projected Overstatement Error

How do sample size requirements for ratio and difference estimation compare to Mean-Per-Unit (MPU) estimation?

Ratio and difference estimation methods typically require smaller sample sizes than MPU when misstatements are present.

How does an increase in expected misstatement affect variable sample size?

Direct relationship: expecting more misstatements increases required sample size.

How does an increase in population standard deviation affect variable sample size?

Direct relationship: greater population variability increases required sample size.

How does an increase in assessed risk of material misstatement affect required sample size?

Direct relationship: higher assessed risk decreases acceptable detection risk, requiring a larger sample size.

How does an increase in tolerable misstatement affect variable sample size?

Inverse relationship: accepting a larger tolerable misstatement decreases required sample size.

How does an increase in acceptable level of sampling risk affect variable sample size?

Inverse relationship: willingness to accept higher risk permits a smaller sample size.

What is the first step in executing a substantive variable sampling plan?

Define the specific objective of the test (e.g., estimating the true dollar value of an account balance).

In variable sampling, what is a point estimate?

The auditor's projected best estimate of the true total population dollar balance based on sample findings.

Why does an auditor calculate a precision interval (allowance for sampling risk) around a point estimate?

To establish an acceptable range around the point estimate that accounts for potential sampling error.

Under what condition can an auditor conclude that a recorded book value is fairly stated?

"When the recorded book value falls within the projected interval range ($

An auditor samples 200 items from 5,000 accounts ($4.5M book value). Sample total audited value is $175,000. What is the MPU point estimate?

Average item value = $175,000 / 200} = $875

Point Estimate = $875×5,000=$4,375,000.

A sample shows audited value of $175,000 and book value of $184,200. Population book value is $4,500,000. Calculate the ratio point estimate.

Sample Ratio = $184,200 / $175,000 ​≈0.95.

Point Estimate = 0.95×$4,500,000=$4,275,000.

In a 200-item sample (N = 5,000$, book value $4.5M), sample book value is $184,200 and audited value is $175,000. What is projected error using difference estimation?

Sample overstatement = $184,200−$175,000=$9,200.

Average error = $9,200 / 200 ​=$46.

Projected error = $46×5,000=$230,000 overstatement.

When using Audit Data Analytics (ADA) in substantive sampling, into what three groups should data be categorized?

1. Data with no misstatements.

2. Data with misstatements clearly inconsequential in aggregate.

3. Data with causal misstatements exceeding clearly inconsequential thresholds.

What does PPS stand for in auditing, and what constitutes its sampling unit?

PPS stands for Probability Proportional to Size. Its sampling unit is an individual dollar.

What is another term used interchangeably with Probability Proportional to Size (PPS) sampling?

Dollar Unit Sampling (DUS).

What is the primary advantage of Probability Proportional to Size (PPS) sampling?

It automatically stratifies the population, emphasizing larger dollar amounts and generating smaller sample sizes.

What is a main disadvantage or design limitation of PPS sampling?

Special design considerations are required to test zero balances, negative balances, and understated accounts.

What is the formula for calculating the sampling interval in PPS sampling?

Tolerable Misstatement / Reliability Factor

What is the formula for calculating sample size in PPS sampling?

Sample Size= Recorded Population Book Value​ / Sampling Interval

If tolerable misstatement is $15,000 and the reliability factor is 3, what is the PPS sampling interval?

Sampling Interval = $15,000 / 3 = $5,000

If recorded population book value is $500,000 and the PPS sampling interval is $5,000, what is the required sample size?

Sample Size = $500,000/ $5,000 = 100

In PPS systematic selection, how are selection targets generated after choosing the random start?

Add the sampling interval repeatedly to the random start until reaching the required sample count.

In PPS sampling, what selection result occurs for any individual account balance equal to or greater than the sampling interval?

The account is automatically guaranteed to be selected for audit testing.

In PPS selection, what happens if multiple dollar targets fall within a single large customer account's cumulative range?

The account is selected once, reducing the total number of physical confirmations sent.

In PPS evaluation, if no errors are discovered in a selected item, what is its projected error?

$0

In PPS evaluation, how is the tainting percentage defined for a misstated item?

Book Value - Audited Value / Book Value

How is projected error calculated in PPS sampling when an item's book value is LESS than or EQUAL to the sampling interval?

Tainting X Sampling Interval

How is projected error calculated in PPS sampling when an item's book value is GREATER than the sampling interval?

Projected error equals the actual dollar misstatement

Book Value - Audited Value

It is NOT multiplied by a sampling interval.

A sample item with a book value of $800 has an audited value of $600. If the sampling interval is $5,000, what is the projected error?

Tainting % = $800−$600​=25%.

Projected Error = 25%×$5,000=$1,250.

A sample item recorded at $4,900 has an audited value of $0. With a sampling interval of $5,000, calculate the projected error.

Tainting % = $4,900−$0​=100%.

Projected Error = 100%×$5,000=$5,000.

A sample item recorded at $8,500 has an audited value of $6,900. If the sampling interval is $5,000, what is the projected error?

Because book value ($8,500) > sampling interval ($5,000), projected error equals actual dollar error: $8,500−$6,900=$1,600.

Why must auditors evaluate qualitative factors in addition to dollar error amounts when reviewing misstatements?

Qualitative evaluation determines whether misstatements indicate isolated unintentional errors or intentional fraud, which impacts overall engagement risk.

What is a dual-purpose sample in auditing?

A sampling design where the auditor uses the same sample items to perform both tests of controls (attribute sampling) and substantive tests of details (variable sampling).

What is the primary operational advantage of using a dual-purpose sample?

It improves audit efficiency and reduces burden by allowing one set of client documents to fulfill two testing objectives.

In variable sampling, population variability is measured by standard deviation, which has a _____ relationship with sample size.

direct

Mean-Per-Unit (MPU) estimation projects population value using population item count, whereas ratio estimation projects value using recorded population _____.

book value

Which sampling technique automatically stratifies population items by assigning higher selection probabilities to larger dollar balances: MPU or PPS?

PPS (Probability Proportional to Size) sampling.

In Probability Proportional to Size (PPS) sampling, every individual _____ acts as a distinct sampling unit.

dollar

When setting up a population listing for PPS selection, auditors convert individual balances into a _____ total column.

cumulative

Why is proper documentation essential throughout the audit sampling process?

Because unrecorded testing steps fail professional audit standards, adhering to the principle that 'if it wasn't documented, it didn't happen.'