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Module G Variables Sampling Learning 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