©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 16 - 1

Audit Sampling for Testsof Details of Balances

Chapter 16

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Learning Objective 1

Differentiate audit sampling for

tests of details of balances and for

tests of controls and substantive

tests of transactions.

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Tests of Details of Balances, Controls, and Substantive Transactions

Tests of Controls

Substantive tests of transactions

Sampling for tests of details of balances

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Learning Objective 2

Apply nonstatistical sampling

to tests of details of balances.

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Nonstatistical Sampling

There are 14 steps required in auditsampling for tests of details of balance.

These steps parallel the 14 steps usedfor sampling for tests of controls and

substantive tests of transactions.

There are a few differences becauseof the different objectives of the tests.

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Tests of Controls and Substantive

Tests of Transactions

Step 1 State the objectives of the audit test.

Step 2 Decide whether audit sampling applies.

Step 3 Define attributes and exception conditions.

Step 4 Define the population.

Step 5 Define the sampling unit.

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Audit Sampling for Tests

of Details of Balances

Step 1 State the objectives of the audit test.

Step 2 Decide whether audit sampling applies.

Step 3 Define misstatement conditions.

Step 4 Define the population.

Step 5 Define the sampling unit.

Difference

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Tests of Controls and Substantive

Tests of Transactions

Specify acceptable risk of assessingcontrol risk too low.

Estimate the population exception rate.

Determine the initial sample size.

Step 7

Step 8

Step 9

Specify the tolerable exception rate.Step 6

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Audit Sampling for Tests of Details of Balances

Specify acceptable risk of incorrectacceptance.

Estimate misstatements in thepopulation.

Determine the initial sample size.

Step 7

Step 8

Step 9

Specify tolerable misstatement.Step 6

Difference

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Tests of Controls and Substantive

Tests of Transactions

Select the sample.

Perform the audit procedures.

Step 10

Step 11

This is the same as in“Audit Sampling for Tests of Details of Balances.”

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Tests of Controls and Substantive

Tests of Transactions

Generalize from the sampleto the population.

Analyze the exceptions.

Decide the acceptability of the population.

Step 12

Step 13

Step 14

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Audit Sampling for Tests of Details of Balances

Generalize from the sampleto the population.

Analyze the misstatements.

Decide the acceptability of the population.

Step 12

Step 13

Step 14

Difference

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Action When aPopulation Is Rejected

• Take no action until tests of other audit areasare completed

• Perform expanded audit tests in specific areas • Increase the sample size• Adjust the account balance• Request the client to correct the population• Refuse to give an unqualified opinion

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Learning Objective 3

Apply monetary unit sampling.

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Monetary Unit Sampling

MUS is an innovation in statisticalsampling methodology that was

developed specifically foruse by auditors.

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Differences between MUS and Nonstatistical Sampling

The definition of the sampling unitis an individual dollar.

The population size is the recordeddollar population.

Preliminary judgment of materialityis used for each account instead of

tolerable misstatement.

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Differences between MUS and Nonstatistical Sampling

Sample size is determined usinga statistical formula.

A formal decision rule is usedfor deciding the acceptability

of the population.

Sample selection is done usingprobability proportional to size

sample selection (PPS).

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The Auditor Generalizes from theSample to the Population Using

MUS

Attributes sampling tables are used tocalculate the results.

The attributes results must be converted to dollars.

The auditor must make an assumption aboutthe percentage of misstatement for each

population item that is misstated.

The statistical results when MUS is usedare called misstatement bounds.

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Generalizing from theSample to the Population

Overstatement amounts equal 100 percent;understatement amounts equal 100 percent;

misstatement bounds at a 5 percent ARIA are:

Upper misstatement bound= $1,200,000 × 3% × 100% = $36,000

Lower misstatement bound= $1,200,000 × 3% × 100% = $36,000

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Generalizing from theSample to the Population

All amounts have to be overstatements.

All population items misstated have tobe 100 percent misstated.

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Generalizing from theSample to the Population

Overstatement amounts equal 10 percent;understatement amounts equal 10 percent;

misstatement bounds at a 5 percent ARIA are:

Upper misstatement bound= $1,200,000 × 3% × 10% = $3,600

Lower misstatement bound= $1,200,000 × 3% × 10% = $3,600

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Generalizing from theSample to the Population

Overstatement amounts equal 20 percent;understatement amounts equal 200 percent;

misstatement bounds at a 5 percent ARIA are:

Upper misstatement bound= $1,200,000 × 3% × 20% = $7,200

Lower misstatement bound= $1,200,000 × 3% × 200% = $72,000

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Appropriate Percent of Misstatement Assumption

The appropriate assumptionfor the overall percent of

misstatement in thosepopulation items containing

a misstatement is anauditor’s decision.

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Generalizing When Misstatements Are Found

1. Overstatement and understatement amountsare dealt with separately and then combined.

2. A different misstatement assumptionis made for each misstatement,

including the zero misstatements.

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Generalizing When Misstatements Are Found

3. The auditor must deal with layers of thecomputed upper exception rate (CUER)

from the attributes sampling table.

4. Misstatement assumptions must beassociated with each layer.

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Illustration of the Auditor’s Decision Rule for MUS

LMB

– TolerableMisstatement $0 Misstatement

+ TolerableMisstatement

UMB

LMB UMB#4

LMB UMB

LMB

LMB UMB

UMB

#5

#3

#2

#1

#2

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Determining Sample SizeUsing MUS

Materiality

Assumption of the average percent ofmisstatement for population items

that contain a misstatement

Acceptable risk of incorrect acceptance

Recorded population value

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Determining Sample SizeUsing MUS

Estimate of the population exception rate

Relationship of the audit risk modelto sample size for MUS

PDR = AAR ÷ (IR × CR)

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Learning Objective 4

Describe variables sampling.

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Frequency Distributionof Sample Means

Value of in dollarsxF

requ

ency

of

valu

esin

per

cent

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Sampling Distribution

A corollary is that the sample mean value with the highest frequency of occurrence

is also equal to the population mean.

The mean value of all the sample meansis equal to the population mean .(X)

(x)

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Sampling Distribution

The shape of the frequency distributionof the sample means is that of a normal

distribution (curve), as long as the samplesize is sufficiently large, regardless of the

distribution of the population.

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Sampling Distribution

The percentage of sample means betweenany two values of the sampling

distribution is measurable.

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Sampling Distribution fora Population Distribution

Value of in dollarsxF

requ

ency

of

valu

esin

per

cent

Sampling distribution –Normal

Population distribution –Skewed

Mean

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Variables Methods

Difference estimation

Ratio estimation

Mean-per-unit estimation

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Stratified Statistical Methods

All of the elements of the population aredivided into two or more subpopulations.

Each subpopulation is independently tested.

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Sampling Risks(ARIA and ARIR)

Conclude that the Correct conclusion Incorrect conclusion population is – no risk – risk is ARIR materially misstated

Conclude that the Incorrect conclusion Correct conclusion population is – risk is ARIA – no risk not materially misstated

Actual State of the Population Actual Audit Materially Not Materially

Decision Misstated Misstated

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Learning Objective 5

Use difference estimation in

tests of details of balances.

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Plan the Sample andCalculate the Sample Size

State the objectives of the audit test.

Decide whether audit sampling applies.

Define misstatement conditions.

Define the population.

Define the sampling unit.

Specify tolerable misstatement.

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Plan the Sample andCalculate the Sample Size

Specify acceptable risk.

ARIA ARIR

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Estimate Misstatementin the Population

Estimate an expected point estimate.

Make an advance population standard deviationestimate – variability of the population.

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Calculate the InitialSample Size

n = {[SD*(ZA + ZB)N] ÷ (TM – E*)}2

n = initial sample sizeSD* = advance estimate of the standard deviation ZA = confidence coefficient for ARIA ZB = confidence coefficient for ARIR N = population size TM = tolerable misstatement for the population (materially) E* = estimated point estimate of the population misstatement

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Select the Sample andPerform the Procedures

Select the sample.

Perform the audit procedures.

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Evaluate the Results

Compute the point estimateof the total misstatement.

Compute an estimate of thepopulation standard deviation.

Compute the precision interval.

Compute the confidence limits.

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Effect of Changing Factors

Effect on the ComputedType of Change Precision IntervalIncrease ARIA DecreaseIncrease the point estimate of the misstatements IncreaseIncrease the standard deviation IncreaseIncrease the sample size Decrease

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Analyze the Misstatements

The auditor must evaluate misstatements todetermine the cause of each misstatementand decide whether modification of the

audit risk model is needed.

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Auditor’s Decision Rule for Difference Estimation

LCL

– TolerableMisstatement $0 Misstatement

+ TolerableMisstatement

UCL

LCL UCL#4

LCL UCL

LCL

LCL UCL

UCL

#5

#3

#2

#1

#2

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End of Chapter 16