# Chapter 12 and 13

What is audit sampling?

Audit sampling is the performance of an audit procedure to less than the entire population of items in an account balance or class of transactions.

Audit sampling is applicable...

to both tests of controls and substantive testing.

What does sampling assume?

Sampling assumes that the population that is being sampled is normally distributed (i.e., it can be described by a bell-shaped curve).

To be valid, a sample needs to be......

unrestricted and randomly selected, which means:
1) Every item in a population must have an absolutely equal chance of being selected.
2) Auditor cannot use "bias" in deciding which item will be selected.

If the sample is large enough and randomly selected.....

the sample will have the same characteristics (mean and standard deviation) as the underlying population (i.e., it will be representative of the population).

Overall, an auditor uses professional judgment to

determine which items should be subject to sampling. For example, certain items may be individually examined (i.e., 100% of such items are examined) and/or items subject to
sampling may also be separated into relatively homogeneous groups (called stratifi

Non-statistical sampling

uses the auditor's subjective judgment to determine the
sample size and the sample selection. (5000 items, I pick 50)

Statistical sampling

provides an objective method of determining the sample size and the sample selection (reduces judgement - doesnt eliminate it)

Although non-statistical sampling can provide sufficient competent evidential matter, statistical sampling provides an auditor with the following advantages:

1) Measures the sufficiency of the evidential matter obtained
2)Provides an objective basis for quantitatively evaluating sample results
3) Designs an efficient sample
4) Quantify sampling risk so as to limit risk to an acceptable level
(once you have tes

Although statistical sampling aids the auditor in quantitative ways, it is not a substitute for professional judgment. The auditor must exercise the following
professional judgments in both statistical and non-statistical sampling:

(statistical still has subjective decisions-doesnt eliminate it)
1) Define the population and the sampling unit
2) Select the appropriate sampling method
3) Evaluate the competence of evidential matter
4) Evaluate the nature of deviations or errors
5) Con

What is sampling risk?

Sampling risk is the risk that the auditor's conclusions based on a sample drawn from a population will differ from the conclusions that would have been made had the entire population been examined.
(risk that sample is not representative of population)
(

Sampling risk in tests of controls

1) Risk of assessing control risk too low
2) Risk of assessing control risk too high

Risk of assessing control risk too low

1) The risk of assessing control risk too low is the risk that the auditor's sample will indicate that a control is operating effectively when, in fact, it is not operating effectively.
2) The risk of assessing control risk too low relates to audit
effect

Risk of assessing control risk too high

1) The risk of assessing control risk too high is the risk that the auditor's sample will indicate that a control is not operating effectively when, in fact, it is operating effectively.
2) The risk of assessing control risk too high relates to audit effi

Sampling risk in substantive tests

1) Risk of incorrect acceptance
2) Risk of incorrect rejection

Risk of incorrect acceptance

1) The risk of incorrect acceptance is the risk that the auditor's sample will support the conclusion that an account balance is not materially misstated when, in fact, it is materially misstated.
2) The risk of incorrect acceptance relates to audit effec

Risk of incorrect rejection

risk that the auditor's sample will support the conclusion that an account balance is materially misstated when, in fact, it is not materially misstated. The risk of incorrect rejection relates to audit efficiency because an auditor may unnecessarily exte

What is non-sampling risk?

Non-sampling risk includes all risks other than sampling risk. It includes the risk that an inappropriate audit procedure will be applied and the risk of auditor negligence or nonperformance.

Types of statistical sampling

1) Attribute sampling
2) Monetary-unit sampling (MUS)
3) Variables sampling

Attribute sampling

(doesnt test dollar values)
-generally used for tests of controls.
-determines whether or not the estimated error rate indicates that control is working effectively.

Monetary-unit sampling (MUS)

(test dollar values)
(most prefer to use this because doesnt require normal distribution)
(cant use this if concerned about understatements)
-generally used for substantive tests. It uses attribute-sampling theory and techniques to estimate the monetary a

Variables sampling

-generally used for substantive tests.
-determines whether or not the estimated value is close enough to management's assertion of the value.

Steps in Attribute sampling

1) determine the control to be tested and identify the type of error that would indicate that the control is not effective
2) define the population
3) Determine the sample size
4) select and test the sample
5) perform the audit procedures
6) calculate the

Attribute sampling: determine the control to be tested

determine the control to be tested and identify the type of error that would indicate that the control is not effective.
(EX: all bills paid have an invoice, receiving report and purchase order. Exception is bill paid did not include all 3)

Attribute sampling: define population

define the population - it includes all instances in which an internal control policy or procedure should have been applied.
(EX: all bills paid)

Attribute sampling: determine sample size

To determine the sample size, an auditor must consider:
1) Tolerable (deviation) rate
2) Allowable risk of assessing control risk too low
3) Expected population deviation rate
(see table for determining sample size)

Tolerable (deviation) rate

-A deviation is an instance in which a selected internal control policy or procedure is not functioning as intended.
-The tolerable rate is the maximum error rate that the auditor will allow and still consider the control effective (i.e., control procedur

Allowable risk of assessing control risk too low

(desired confidence level) - risk that the auditor's sample will indicate that the control is operating effectively when, in fact, it is not operating effectively.
(risk increases=sample size decreases)

Expected population deviation rate

deviation rate the auditor expects to observe in the population of interest.

Attribute sampling: select and test the sample

random selection or systematic selections

random selection

whereby each item in a population has an equal opportunity to be included in the sample.

Systematic selection

(i.e., a random starting point is chosen and then every nth
item is selected) is also acceptable, but a disadvantage is that results may be skewed if errors occur in a systematic pattern.

Block (cluster) sampling

where groups of adjacent items are selected, is not
acceptable.
(picking first 78)
-never use block

Voided documents

do not represent a deviation and should be replaced with a new sample item.

Unused or inapplicable documents

do not represent a deviation and should be replaced with a new sample item.

Inability to examine a sample item

represents a deviation for purposes of evaluating sampling results.

Stopping the test before completion

if a large number of deviations are detected early in the tests of controls, auditor should consider stopping the test as soon as it is clear that the results of the test will not support the planned assessed control risk.

Attribute: calculate the sample deviation rate

-The sample deviation rate is the auditor's best estimate of the true deviation rate in the population.
-Sample deviation rate = number of errors in sample � number of items in sample

Attribute: calculate the computed upper deviation rate

Use table
-upper deviation rate = sample deviation rate + allowance for sampling risk
(if sample size is not there-pick lower)

Attribute: reach conclusions and document results

1) If the computed upper deviation rate is less than or equal to the tolerable (deviation) rate, the auditor concludes that the control tested can be relied upon.
2) If the computed upper deviation rate is greater than the tolerable (deviation) rate, the

MUS

-MUS was developed by auditors to overcome the computational complexity of other statistical sampling techniques because most accounting populations contain relatively little misstatement. Overall, classical variables sampling is not very effective in pop

Advantages of MUS over variable sampling:

1) When applied using a probability-proportional-to-size, MUS automatically emphasizes larger items by stratifying the sample. The chance of an item being selected is proportionate to its dollar amount.
2) If no errors are expected, MUS generally requires

Disadvantages of MUS over variables sampling

(dont get understatements)
1) Understated items have a lower probability of being selected.
2) Items with zero or negative balances are generally not selected in the sample and need special consideration.
3) A high frequency of misstatements results in an

When is MUS most effective?

Overall, MUS is most effective when a few or no errors are expected and the auditor is concerned about overstatement of the account.

Steps in monetary-unit sampling

1) determine the balance to be tested.
2) define the population, sampling unit, and misstatement
3) determine the sample size
4) select sample items (using probability-proportional-to-size) and test the sample
5) calculate the projected misstatement and t

MUS: define the population, sampling unit, and misstatement.

1) Population includes all transactions or components underlying the class of transactions or account balance that an auditor wants to test.
2) Sampling unit is an individual dollar.
3) Misstatement is the difference between monetary amounts in the client

MUS: Determine sample size-what must an auditor consider?

1)Tolerable misstatement (mistatement increases=sample size decreases)
2) Risk of incorrect acceptance (desired confidence level) (risk increases=sample size decreases)
3) Expected misstatement (mist increases=sample size increases)
4) Population size (si

sampling interval

Total recorded amount of account / Sample size

MUS: select sample items and test the sample

(using probability-proportional-to-size)
1) List items in the population in logical sequence (i.e., invoice number)
2) Based on the amount of an item and the total amounts of all previous items, each item will represent a cumulative amount.
3) Assign each

MUS: calculate the projected misstatement and the upper misstatement limit

1) The misstatements detected in the sample must be projected to the population. The projection of the errors to the population is referred to as the projected
misstatement (it is comparable to the sample deviation rate for attribute sampling).
2) The aud

BV > sampling interval

no tainting factor

BV < sampling interval

tainting factor

Tainting factor

(BV-audit value) / Book value

MUS: draw final conclusions

1) If the upper misstatement limit is less than or equal to the tolerable misstatement, the evidence supports the conclusion that the account balance is not materially
misstated.
2) If the upper misstatement limit exceeds the tolerable misstatement, the a

If upper mistatement limit > tolerable misstatement, the auditor has 2 main options:

1) increase the sample size (possible in theory but not practical in many audit settings) and/or
2) request that the client adjust the accounting records.

Steps of Variables sampling

1) determine the balance to be tested
2) define the population
3) determine the sample size
4) select and test the sample
5) calculate the projected misstatement
6) reach conclusions and document results

Variable: define the population

includes all transactions or components underlying the
class of transactions or account balance that an auditor wants to test

Variable: determine the sample size-To determine the sample size, an auditor must consider:

1) Tolerable misstatement (TM increases=sample size decreases)
2) Risk of incorrect acceptance (risk increases=sample size decreases)
3) Risk of incorrect rejection (risk increases=sample size decreases)
4) Population size (pop increases=sample size incre

Tolerable misstatement

difference between the actual balance and the reported balance that will not prevent the auditor from issuing an unqualified opinion. Materiality should be considered in this determination.

Risk of incorrect acceptance

auditor's sample will support the conclusion that an account balance is not materially misstated when, in fact, it is materially misstated

Risk of incorrect rejection...

risk that the auditor's sample will support the conclusion that an account balance is materially misstated when, in fact, it is not materially misstated.

Population variability (i.e., standard deviation)

represents the homogeneity of the size of transactions or components within the account balance or class of transactions.

Stratified

the population is divided into subgroups based on the size of the transaction or component. Selecting samples from each subgroup allows different magnitudes to be identified and sampled separately. Compared to an
unstratified method, a stratified method p

Variable: reach conclusions and document results

1) If the projected misstatement plus the allowance for sampling risk is less than or equal to the tolerable misstatement, the opinion will not require modification.
2) If the projected misstatement plus the allowance for sampling risk is greater than the