1. BA 427 – Assurance and Attestation Services
Lecture 23
Audit Sampling

2. Audit Sampling
Definition: Audit sampling is the application of an audit procedure to less than 100% of the items in an account balance or class of transactions, for the purpose of evaluating some characteristics of the balance or class.
There are two general approaches to sampling:
Non-statistical sampling (a.k.a. judgment sampling)
Statistical sampling

3. Statistical Sampling Statistical sampling has two essential features:
The items in the sample have a known probability of selection.
The sample results are evaluated mathematically, in accordance with probability theory.
The advantage of statistical sampling is that it allows the auditor to objectively state audit risk associated with testing less than 100% of the population.

4. Statistical Sampling Essential terminology:
Risk is the complement of reliability:
One minus reliability is risk
95% reliability equates to 5% risk.
Auditors talk about risk, statisticians talk about reliability.
Reliability and confidence levels are synonymous.
A confidence level of 95% is equivalent to 95% reliability.

5. Statistical Sampling Essential terminology:
Precision defines the maximum degree of sampling error that is acceptable.
Precision can be a percentage or a dollar amount.
The precision of an estimate describes the range of values around the point estimate within which the true value is expected to fall. The lower and upper bounds are the precision limits.

6. Statistical Sampling Essential terminology:
Precision defines the maximum degree of sampling error that is acceptable.
When we talk about error rates, the lower bound is usually zero, and the upper precision limit is sometimes referred to as the allowable exception rate or the tolerable exception rate.

7. Statistical Sampling Essential terminology:
Precision and reliability have no meaning unless they are paired together.
Reliability expresses the probability that the precision interval contains the true value.

8. Statistical Sampling
Statistical sampling can result in two types of errors:
Sampling Error
The sample is not representative of the population.
Sampling error is eliminated if the auditor examines the entire population.
Nonsampling Error
All other errors

9. Statistical Sampling Two possible types of sampling error:
Incorrect acceptance (type II error): The risk that the auditor will incorrectly conclude that the error rate does not exceed the allowable rate. This can result in an audit failure.
Incorrect rejection (type I error): The risk that the auditor will incorrectly conclude that the error rate does exceed the allowable rate. This can cause the auditor to over-audit.

10. Statistical Sampling Nonsampling Error
Examples of nonsampling errors include
Inappropriate test design.
Failure to adequately define exceptions in the sample population.
Failure to recognize that an exception satisfies the definition of one.
Failure to draw a random or representative sample.
Failure to evaluate the findings properly.

11. Statistical Sampling Nonsampling Error
Nonsampling errors are human errors, and can be reduced or eliminated.

12. Statistical Sampling Steps in a statistical sampling plan:
Determine the objective of the test.
Define the population.
Determine the acceptable level of sampling risk.
Calculate the sample size.
Choose a sampling approach.
Identify and examine the sample.
Evaluate and document the test results.

13. Statistical Sampling Sampling with or without replacement:
Statistical sampling auditing techniques usually rely on statistical properties that assume sampling with replacement.
In fact, auditors usually sample without replacement.
For large populations and relatively small samples, the difference is not important.

14. Statistical Sampling Statistical sampling has three broad categories:
Attribute
Variable
Probability-proportional-to-size

15. Attribute Sampling
Attribute sampling examines qualitative characteristics of the population.
Attribute sampling is used primarily for tests of controls.
Three types of attribute sampling plans:
Fixed sample-size
Sequential sampling (a.k.a. stop-or-go)
Discovery sampling

16. Attribute Sampling Fixed sample-size
Used to estimate the percentage rate of occurrence of a specific quality (or attribute) in a population.
Example: How often are the wrong goods shipped?

17. Attribute Sampling Fixed sample-size The auditor chooses
The reliability desired from the test (e.g., 95%).
The anticipated exception rate.
The upper limit on the allowable exception rate.
Based on these choices, and on the population size, a sample size is generated (from an audit software package, a statistical package, or a table).

18. Attribute Sampling Fixed sample-size Example:
Auditor wants to achieve 95% reliability.
Auditor anticipates a 1% exception rate.
Auditor can accept an exception rate of 5%.
For a relatively large population, the sample size is 93.
If no more than 1 exception is identified in the sample, the desired result is achieved.

19. Attribute Sampling Fixed sample-size
Even if the desired result is not achieved, the sampling technique allows the auditor to quantify the exception rate.
For example, using the previous data:
2 exceptions allows the auditor to be 95% certain that the exception rate does not exceed 6.9%.
3 exceptions allows the auditor to be 95% certain that the exception rate does not exceed 8.4%.

20. Attribute Sampling Sequential sampling
This is a sampling plan that also tests for attributes, but it is designed to minimize the likelihood of over-sampling.
It is an efficient sampling plan when the auditor believes that the occurrence rate is very low.
The sample is selected in several steps; each step relies on the results of the previous step.

21. Attribute Sampling Sequential sampling The auditor chooses
The reliability desired from the test (e.g., 95%)
The upper limit on the allowable exception rate (e.g., 5%)
Based on these choices, and on the population size, an initial sample size is generated (from an audit software package, a statistical package, or a table).

22. Attribute Sampling Sequential sampling
A typical initial sample size in this setting is 60 items.
If no exceptions are found in this sample, the auditor is done.
If one exception is found, the auditor is 95% certain that the exception rate does not exceed 8%, but 8% is greater than the desired allowable exception rate of 5%.

23. Attribute Sampling Sequential sampling
The auditor can extend the sample. In this situation, if the auditor examines another 36 items and finds no exceptions, the 5% allowable exception rate is achieved.
Following is an example of a decision table that might be used for sequential sampling:

24. Attribute Sampling Sequential sampling decision table Step
Cumulative sample size to use
Stop if cumulative deviations are equal to
Sample more if deviations are
Go to Step 5 if deviations are at least 1 30
1 – 3 4 2 48
2 – 3 3 63 78 5
Consider increasing assessed level of control risk

25. Attribute Sampling Discovery sampling
This sampling plan is appropriate when the following conditions are met:
the auditor believes that the attribute occurrence rate is extremely low (or even zero).
the identification of a single exception is likely to cause the auditor to significantly alter scope.
Example: How many checks were signed by individuals without check-signing authority?

26. Attribute Sampling Discovery sampling The auditor chooses
The reliability desired from the test (e.g., 90%)
The upper limit on the allowable exception rate (e.g., 1%)
Based on these choices, and on the population size, a sample size is generated (from an audit software package, a statistical package, or a table).

27. Attribute Sampling Discovery sampling
The auditor pulls and examines a sample of the appropriate size.
Such a sample could be 240 items
If no exceptions are found, the auditor is 90% certain that the maximum exception rate is 1%.
The auditor might choose to stop examining the sample as soon as the first exception is found.

28. Variable Sampling
Variable sampling is also called quantitative sampling.
Variable sampling is frequently used when performing substantive tests of account balances.
Three types of variable sampling plans:
Unstratified mean-per-unit
Stratified mean-per-unit
Difference estimation

29. Variable Sampling Unstratified mean-per-unit Stratified mean-per-unit
A sample mean is calculated and projected as an estimated total.
Stratified mean-per-unit
A more efficient sampling technique that divides the population into subgroups, and samples from each group.
Difference estimation
A statistical plan used to estimate the difference between two populations (e.g., audited values vs. book values)

30. Variable Sampling Unstratified mean-per-unit
Sampling for substantive testing provides evidence about whether an account balance is materially misstated.
Management provides an assertion about an account balance.
The amount is expected to represent the true value, but the true value is not known.
The auditor collects evidence as to whether management’s assertion is a fair representation of the true value.

31. Variable Sampling Unstratified mean-per-unit
By taking a sample and drawing an inference about the population, the auditor either supports or rejects the conclusion that management’s reported number is a fair representation.

32. Variable Sampling Unstratified mean-per-unit The auditor chooses
The reliability desired (e.g., 90%)
The precision interval (based on materiality)
Based on these choices, and on both the population size and the estimated standard deviation of the population, a sample size is generated (from an audit software package, a statistical package, or a table).

33. Variable Sampling Unstratified mean-per-unit
The sample is pulled, and the sample mean is extrapolated to estimate the population mean.
If the standard deviation of the sample differs significantly from the estimate used to determine the sample size, the precision interval will have to be updated (i.e., it will not be as planned).

34. Variable Sampling Stratified mean-per-unit
Appropriate when the population has a large standard deviation. (The size of the items in the population is highly variable.)
Reduces the required sample size, relative to unstratified mean-per-unit.
In order to apply stratified mean-per-unit, every item in the population must belong to one and only one stratum, and the exact number of elements of each stratum must be known.

35. Probability-Proportional-to-Size
Also called Dollar-Unit Sampling
PPS uses a dollar as the sampling unit.
PPS sampling gives each individual dollar in the population an equal chance of selection.
However, individual dollars do not constitute the sample, but rather, the items that contain those dollars.
Consequently, large dollar-value items have a greater chance of being selected.

36. Probability-Proportional-to-Size
PPS is appropriate for identifying overstatement of assets (e.g., inventory or accounts receivable).
PPS allows the auditor to draw a conclusion about the likelihood that an account is overstated by more than a specified amount.