1. Chapter 9
Audit Sampling – Part b

2. Sampling to Test for Account Balance Misstatements (Substantive Testing)
Basic steps:
Specify audit objective of the test
Define misstatement
Define population (and sampling units)
Choose sampling method
Determine sample size
Select sample
Audit selected items
Evaluate sample results
Perform follow-up work as necessary
Document sampling procedure and results

3. 1. Define Specify Audit Objective
Sampling always relates to one specific procedure usually testing one specific assertion
Specifying the audit objective determines the population to test
For example:
If objective is to determine existence, the sample should be selected from recorded information
- On the other hand, if the objective is to determine completeness, the sample should be selected from a complementary population such as source documents (or cash disbursements if testing for unrecorded payables)

4. 2. Define Misstatements
Misstatement is usually defined as difference that affects the correctness of the overall account balance
Misstatements should be defined before sampling to:
Preclude auditor from rationalizing away misstatements as isolated events
Provide guidance to the audit team

5. 3. Define the Population
Group of items in an account balance that the auditor wants to test. It does not include:
Items the auditor has decided to examine 100%
Items that will be tested separately
Important to properly define the population:
Sample results can be projected only to the group from which the sample is selected
The population must be directly related to the audit objective

6. 3. Define the Sampling Unit
Sampling units are the individual auditable elements that make up the population
Example: sampling units for confirming accounts receivable could be the individual customer's balance or individual unpaid invoices

7. Identify Individually Significant Items
Many account balances are comprised of a few large dollar items and many smaller items
Dividing a population into two or more subgroups based on dollar amount can increase audit efficiency
Items in excess of a specified dollar amount (top stratum items) are examined 100%
Items less than the specified amount (lower stratum items) are sampled
This process (stratification) allows the auditor to examine a significant portion ($ value) of an account balance even though s/he examines a relatively few items

8. 4. Choosing a Sampling Method
There are a number of sampling methods an auditor may use
Non-statistical
Probability proportional to size (PPS)
Classical sampling methods (not covered in this text/course)
Mean-per-unit
Ratio estimation
Difference estimation

9. 4. Choosing a Sampling Method – Cont’d - Differences between methods)
Measure of sampling risk
Statistical methods provide an objective measure of sampling risk
Non-statistical methods do not provide such a measure
Tests for account balance
PPS is designed to test for overstatement of an account balance
Classical methods test for both overstatement and understatement

10. 4. Choosing a Sampling Method – Cont’d (differences between methods)
Statistical estimates
PPS provides an estimate of the amount of misstatement in the account
Classical methods provide an estimated range of the account balance
Sample selection
PPS is a dollar-based approach; each dollar is a sampling unit
Classical samples are selected using a variety of sampling units e.g. balances or items

11. 4. Choosing a Sampling Method – Cont’d
Use of PPS would be appropriate if
Auditor is testing for overstatements in an account balance
A dollar-based sampling approach increases the probability of selecting overstated items
Few or no misstatements expected
Individual book values (like a subsidiary ledger) are available

12. 4. Choosing a Sampling Method – Cont’d
One of the classical methods would be appropriate if the auditor
Is concerned about understatements in an account balance
Expects numerous misstatements
Is examining an account balance based on estimates rather than a total of individual items
Is trying to estimate an account balance

13. 5 – 8. Determining Sample Size, Selecting Sample, Evaluating Results
Sample size, method of selecting the sample, and the approach to evaluating sample results all depend on the sampling method used
Whichever sampling method is used, consideration must be given to the risk of misstatement, sampling risk, and the auditor's assessment of tolerable and expected misstatement
Tolerable misstatement
Maximum misstatement an auditor will accept before deciding the recorded account balance is materially misstated
Expected misstatement
Based on results of other substantive tests and auditor's prior experience with the client
Expected misstatement should be less than tolerable misstatement

14. Steps in non-statistical sampling?
Determine sample size
All significant items should be tested
No way to mathematically control sampling risk
Select the sample
Sample must be representative of population
Could use random-based method or haphazard selection
Evaluate sample results
Project misstatements to the population
Consider sampling error
Make judgment as to whether account is likely to be materially misstated

15. Probability Proportional to Size (PPS) Sampling
Dollar-based sampling approach where the population is the number of dollars in the account balance examined
Using dollars as sampling units means larger dollar items in the account balance are more likely to be selected in the sample
PPS is an effective sampling approach when the auditor is testing for overstatements
Appropriate when few misstatements are expected and individual book values are available

16. Probability proportional to size (PPS) sampling: TD risk
To use PPS, the auditor must determine the allowable risk of the sample failing to detect a material misstatement (test of details risk) and tolerable and expected misstatements for the account balance
Detection risk is the risk that the substantive audit procedures will fail to detect material misstatements
There are two types of substantive audit procedures - those that use sampling, and other (non-sampling) substantive procedures
Test of details (TD) risk is the part of detection risk related to sampling; the risk that substantive sampling procedures will fail to detect a material misstatement
Other substantive procedures risk (OSPR) is the risk that the non-sampling procedures will fail to detect a material misstatement

17. Probability Proportional to Size (PPS) Sampling: TD risk– Cont’d:
The relation between TD risk and inherent and control risks and OSPR is inverse
High inherent risk means the auditor is examining transactions that are susceptible to misstatement
High control risk means the client controls are weak
High OPSR means the non-sampling audit procedures are not effective in detecting material misstatements

18. Probability Proportional to Size (PPS) Sampling: TD risk– Cont’d:
In each of these situations, the auditor would want to be more careful with his/her sampling procedures
The auditor would want lower TD risk; less chance of failing to detect material misstatements with sampling procedures
Lower TD risk means the auditor wants a lower risk of sampling procedures failing to detect material misstatements
To achieve this lower risk of failing to detect, the sample size must increase

19. Probability Proportional to Size (PPS) Sampling: Sample Size
PPS samples are usually selected using a fixed interval sampling approach
The sampling interval (I) is calculated as
I = TM - (EM x EEF) RF
TM = Tolerable misstatement (in population)
EM = Expected misstatement (in population)
EEF = Error expansion factor (derived form tables)
RF = Reliability factor (derived form tables)
Error expansion and reliability factors are based on TD risk

20. Probability Proportional to Size (PPS) Sampling: Sample Size
Sample size (n) is computed by dividing the account book value by the sampling interval
n = Population Book Value
Sampling Interval

21. Probability Proportional to Size (PPS) Sampling - Sample Selection
Sample items are often selected using a fixed interval approach
Every nth dollar after a random start
A random start is required to give every dollar in the population an equal chance to be included in the sample
The first sample item is the one that first causes the cumulative total (cumulative book value + random start) to equal or exceed the sampling interval
Successive sample items are those first causing the cumulative total to equal or exceed multiples of the interval
Sample composition:
All top stratum items will be included in the sample
Lower stratum items will be sampled

22. Probability Proportional to Size: Zero or Negative Balances
Zero balances
Items with zero balances have no chance of being selected using PPS
If evaluation is necessary, zero balance items should be audited as a different population
Two approaches to deal with population items with negative balances:
Exclude them from the selection process and test them as a separate population
Include them in the selection process and ignore the negative sign

23. Probability Proportional to Size: Sample Evaluation
Based on sample results, the auditor computes the upper misstatement limit
Upper misstatement limit (UML)
Maximum dollar overstatement that might exist in the population
Given the misstatements detected in the sample, at the specified TD risk level, UML is the sum of three components:
Basic precision
Most likely misstatement
Incremental allowance for sampling error.

24. Probability Proportional to Size: Sample Evaluation – Cont’d
If the UML is less than the tolerable misstatement, the account balance is considered fairly presented
If the UML exceeds the tolerable misstatement, the account balance is not fairly presented and further work is necessary