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What is Audit Sampling?

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Applying a procedure to less than 100% of a population

To estimate some characteristic of the population

Qualitative

Quantitative

Sampling risk

risk that the auditors’ conclusions based on a sample may be different from the conclusion they would reach if they examined every item in the population

Nonsampling risk

risk pertaining to nonsampling errors

Can be reduced to low levels through effective planning and supervisions of audit engagements

The auditor estimates sampling risk by using professional judgment rather than statistical techniques

Provides no means of quantifying sampling risk

Sample may be larger than necessary or auditors may unknowingly accept a higher than acceptable degree of sampling risk

Allows auditors to measure and control sampling risk which helps:

Design efficient samples

Measure sufficiency of evidence

Objectively evaluate sample results

Random sample results in a statistically unbiased sample that may not be a representative sample

Random sample techniques

Random number tables

Random number generators

Systematic selection

Random Number Table

Other methods

Haphazard selection

Select items on an arbitrary basis, but without any conscious bias

Block selection

Block sample consists of all items in a selected time period, numerical sequence or alphabetical sequence

Stratification

Technique of dividing population into relatively homogeneous subgroups

Attributes sampling

Discovery sampling

Classical variables sampling

Mean-per-unit estimation

Ratio estimation

Difference estimation

Probability-proportional-to-size sampling

Tested used both as a test of control and substantiating the dollar amount of an account balance

Ex. Test to evaluate the effectiveness of a control over recording sales transactions and to estimate the total overstatement or understatement of the sales account

Amount used to create a range, set by + or – limits from the sample results, within which the true value of the population characteristic being measured is likely to lie

Precision

Wider the interval, more confident but less precise conclusion

Can be used to construct a dollar interval

Significant effect on allowance for sampling risk and sampling risk

Sample size increase -> sampling risk and allowance for sampling risk decrease

Sample size affected by characteristics of population

Generally as Population increases -> sample size increase

When planning the sample consider:

The relationship of the sample to the relevant audit objective

Materiality or the maximum tolerable misstatement or deviation rate

Allowable sampling risk

Characteristics of the population

Select sample items in such a manner that they can be expected to be representative of the population

Sample results should be projected to the population

Items that cannot be audited should be treated as misstatements or deviations in evaluating the sample results

Nature and cause of misstatements or deviations should be evaluated

Actual Extent of Operating Effectiveness

of the Control Procedure is

AdequateInadequate

The Test of Controls

Sample Indicates:

Extent of Operating

Effectiveness is

Adequate

Extent of Operating

Effectiveness

Inadequate

Correct

Decision

Incorrect

Decision

(Risk of Assessing

Control Risk

Too Low)

Incorrect

Decision

(Risk of Assessing

Control Risk

Too High)

Correct

Decision

Determine the objective of the test

Define the attributes and deviation conditions

Define the population to be sampled

Specify:

The risk of assessing control risk too low

The tolerable deviation rate

Estimate the population deviation rate

Determine the sample size

Select the sample

Test the sample items

Evaluate the sample results

Document the sampling procedure

- Risk of Assessing Control Risk Too Low—5 percent
- Tolerable Deviation Rate—9 percent
- Expected Population Deviation Rate—2 percent

Sample size using Figure 9-4 (next slide)

=68 (2)

- This means the auditor should select a sample of 68 items. We will discuss the (2) in a few slides.

2 possible approaches:

- Use the bracketed number from Table 9.4. If you find that number or less deviations, conclude that you have accomplished your audit objective.
- Use Table 9.5 for a more precise conclusion.

Approach 1—You have met your audit objective (because the bracketed number was (2), you meet objective when you identify 0, 1 or 2 deviations). What can you say?

“I believe that the deviation rate in the population is less than 9 percent.” You will be wrong 5 percent of the time when the deviation is exactly 9 percent. If the deviation rate is in excess of 9 percent you will be wrong even less than 5 percent of the time. The planned assessed level of control risk is achieved.

Approach 2

You have tested 68 items, a number not on Table 9-5 (next slide

To be conservative go to next lowest number on table (65) and use it for your conclusions (we could, but won't interpolate for a more precise answer).

You have met your audit objective. Table 9-5 gives us an answer of 4.6 percent. What can you say?

"I believe that the deviation rate in the population is less than 4.6 percent.” You will be wrong 5 percent of the time when the deviation rate is exactly 4.6 percent. If the deviation rate is in excess of 4.6 percent you will be wrong even less than 5 percent of the time. The planned assessed level of control risk is achieved.

Figure 9.5Statistical Sampling Results Evaluation Table for Tests of Controls: Achieved Upper Deviation Rate at5 Percent Risk of Assessing Control Risk Too Low

Approach 1—You have not met your audit objective. What can you say?

“The achieved upper deviation rate is higher than 9 percent.” The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.

Accordingly, you may not “rely” on internal control to the extent planned. Thus, the auditor will need to increase the scope of substantive procedures (the nature, timing, and/or extent).

Approach 2—You have not met your audit objective. Table 9-5 provides us an answer of 11.5 percent

“I believe that the deviation rate in the population is less than 11.5 percent.” You will be wrong 5 percent of the time when the deviation rate is exactly 11.5 percent. But this is not good enough as you wanted 9 percent rather than 11.5 percent. The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.

As per Approach 1, an increase in the scope of substantive procedures is appropriate.

Discovery sampling

Purpose is to detect at least one deviation, with a predetermined risk of assessing control risk too low if the deviation rate in population is greater than specified tolerable deviation rate

Useful in suspected fraud

Sequential (Stop-or-Go) Sampling

Audit sample taken in several stages

The Population Actually is

Not MateriallyMaterially

MisstatedMisstated

The Substantive

Procedure Sample

Indicates

Misstatement in

Account Exceeds

Tolerable Amount

Misstatement in

Account Is Less

Than Tolerable

Amount

Correct

Decision

Incorrect

Decision

(Risk of Incorrect

Rejection)

Incorrect

Decision

(Risk of Incorrect

Acceptance)

Correct

Decision

Determine the objective of the test

Define the population and sampling unit

Choose an audit sampling technique

Determine the sample size

Select the sample

Test the sample items

Evaluate the sample results

Document the sampling procedure

ItemPopulation APopulation B

1 2,100 8,000

2 2,100 25

3 2,1002,000

4 2,100 400

5 2,100 75

Mean 2,1002,100

Standard

deviation -0- 3,395

The variability determines how much information each of the items in the population tells you about the other items in the population.

Factors Affecting Sample Size

Population Size = 100,000 accounts

Book value = $6,250,000

Other information:

Tolerable misstatement = $364,000

Sampling risk

Incorrect Acceptance = 5%

Incorrect Rejection = 4.6 %

= 225 Accounts

Adjusted allowance

for sampling risk =

Tolerable_ (Population size * Incorrect acceptance coef. * Sample stan. dev.)

misstatementSample size

This formula “adjusts” the allowance for sampling risk to consider the standard deviation of the audited values in the sample. It holds the risk of incorrect acceptance at its planned level.

Variables Sampling Illustration--MPU

Using the text example with a standard deviation of audited values of $16

Adjusted allowance

for sampling risk =

Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.)

misstatement Sample size

= $364,000 _ ($100,000 * 1.64 * $16)

225

= $189,067

- We would still “accept” the book balance because the $6,250,000 (book value) falls within this interval
Estimate of total + Adjusted allowance

audited value for sampling risk

$6,100,000 + $189,067

[$5,910,933 to $6,289,067]

Difference

Use sample to estimate the avg. difference between the audited value and book value of items in population

Projected =Sample Net Misstatement * Pop. Items

Misstatement Sample items

Most appropriate when size of misstatements does not vary significantly in comparison to book value

Use a sample to estimate the ratio of misstatement in a sample to its book value and project it to population

Projected =Sample Net Misstatement * Pop. Book Value

Misstatement Book Value of Sample

Preferred when the size of misstatements is nearly proportional to the book values of the items

Large accounts have large misstatements

Plan Sample:

Population:

Size = 363 items

Book value = $200,000

Tolerable misstatement = $10,000

Risk assessments:

Inherent and control risk = Slightly below maximum

Other substantive tests = Moderate

Sample size = Population book value X Reliability factor

Tolerable misstatement

= $200,000 X 2.0 = 40 items

$10,000

Sample results:

40 accounts in sample

$350 net overstatement

$60,000 book value of sample items

Projected misstatement:

= [Sample net misstatement] X Book value of population

[ Book value of sample ]

= [ $350 ] X $200,000

[$60,000]

= $1,167

Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct.

Population book value = $6,250,000

Other Information:

Tolerable misstatement = $364,000

Sampling risk--Incorrect acceptance = 5%

Expected misstatement = $50,000

Use Figures 9-14 and 9-15 to obtain a “reliability factor” and an “expansion factor”--next slide

Sample size =

Recorded amount of population * Reliability factor

Tolerable misstatement - (Expected misstatement * Expansion factor)

= $6,250,000 * 3.0 = 66

$364,000 - ($50,000 * 1.6)

Sampling interval = Book value of the population

Sample size

= $6,250,000 = $95,000 (approximately)

66

Upper Limit on misstatement =

Projected misstatement

+ Basic precision (Rel. factor x interval)

+ Incremental allowance

Calculation of Upper Limit on Misstatement

AR = IR x CR x DR

where

AR=The allowable audit risk that a material misstatement might remain undetected for the account balance and related assertions.

IR= Inherent risk, the risk of a material misstatement in an assertion, assuming there were no related controls.

CR= Control risk, the risk that a material misstatement that could occur in an assertion will not be prevented or detected on a timely basis by internal control.

DR= Detection risk, the risk that the auditors’ procedures will fail to detect a material misstatement if it exists.