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Module G Variables SamplingLearning Objectives

1. Define variables sampling and understand when variables sampling is used in the audit.

2. Understand the basic process underlying monetary unit sampling (MUS) and when to use it.

3. Identify the factors affecting the size of an MUS sample and calculate the sample size for an MUS application.

4. Evaluate the sample results for an MUS sample by calculating the projected misstatement, incremental allowance for sampling risk, and basic allowance for sampling risk.

5. Understand the basic process underlying classical variables sampling and the use of classical variables sampling in an audit.

6. Understand the use of nonstatistical sampling for variables sampling.

Mod G-2

Variables Sampling

• Used to estimate the amount (or value) of a population

• Substantive procedures

• Types of variables sampling approaches– Monetary unit sampling (MUS)

– Classical variables sampling

Mod G-3

Monetary Unit Sampling (MUS)

• Defines the sampling unit as individual dollar (or Euro, Yen, Yuan, etc.) in an account balance

• Auditor will select individual dollars for examination• Auditor will verify entire “logical unit” containing the

selected dollar

Mod G-4

When to use MUS

• ADVANTAGES OF MUS

• DISADVANTAGES OF MUS

Mod G-5

Major Steps in Variables Sampling: Planning

1. Determine the objective of sampling

2. Define characteristic of interest

3. Define the population

Mod G-6

Major Steps in Variables Sampling: Performing

4. Determine sample size

5. Select sample items

6. Measure sample items

Mod G-7

Using AICPA MUS Tables

• Ratio of Expected to Tolerable Misstatement

• Tolerable Misstatement as a Percentage of Population

• Find appropriate Risk of Incorrect Acceptance

• Find Appropriate Ratio of Expected to Tolerable Misstatement

• Read across to “Tolerable Misstatement as a Percentage of Population” column

Mod G-8

Major Steps in Variables Sampling: Evaluating

7. Evaluate sample results

Upper Limit on Misstatements

Mod G-9

Upper Limit on Misstatements

• If Upper Limit on Misstatements is $50,000 and risk of incorrect acceptance is 5%– There is a 5% probability that the true

misstatement exceeds $50,000– There is a 95% probability that the true

misstatement is less than or equal to $50,000

95% 5%

$0 $50,000

Mod G-10

Projected Misstatement

• Assumes the entire sampling interval contains the same percentage of misstatement as the item examined by the auditor

• Do not calculate if balance > sampling interval

• Tainting % = Amount of Misstatement

Recorded Balance of Item

• Projected = Sampling Interval x Tainting %Misstatement

Mod G-11

Basic Allowance for Sampling Risk

Incremental Allowance for Sampling Risk

Mod G-12

Evaluate Results

• If upper limit on misstatements < tolerable misstatement

• If upper limit on misstatements > tolerable misstatement

Mod G-13

MUS Sampling vs. Classical Variables Sampling

• MUS is more appropriate when:

• Classical variables sampling is more appropriate when:

Mod G-14

Mean per Unit Sampling (Sample Size)

• Sample size

N x [R(IR) + R(IA)] x SD 2

TE - EE

• Differences from MUS sampling

Mod G-15

Evaluating Results

• Precision = N X R(IA) X (SD ÷ √n )• Project sample average to population estimate• Add/subtract precision to get precision interval• Determine difference between account balance and

furthest bound of precision interval• If greater than tolerable misstatement—reject balance

• Determine cause of all misstatements

Mod G-16

Other Approaches

• Stratified sampling

• Difference estimation

• Ratio estimation

Mod G-17

Nonstatistical Sampling• Does not measure the auditor’s exposure to sampling risk

• Permitted under generally accepted auditing standards

• Differences

– Does not consider sampling risk in determining sample size or evaluating sample results

– May use a nonprobabilistic selection technique

Mod G-18

BASIC PROCEDURE

• Select sample

– Does not explicitly consider sampling risk in determining sample size

– May use block or haphazard selection methods

• Measure sample items (same as statistical sampling)

Mod G-19

Evaluate Sample Results

• Difference estimation

• Ratio estimation

• Use judgment to allow for sampling risk

• Normally reject if projected misstatement exceeds expected misstatement

Mod G-20

Documentation

• Objective and assertions evaluated

• Sampling technique used and definition of a misstatement

• Method and parameters used to determine sample size

• Sample size

• Selection method

• Description of audit procedures

• Determination of upper limit on misstatement, precision, or projected misstatement

• Conclusion—effect on audit opinion

Mod G-21