©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Module E Overview of Sampling “There are three kinds of lies: lies, damned lies, and statistics.” – Benjamin Disraeli McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Learning Objectives Understand the basic principles of sampling, including the differences between statistical and nonstatistical sampling and sampling and nonsampling risk. Understand the basic steps and procedures used in conducting a sampling plan. Identify the two situations in which sampling is used in an audit examination. Understand how the basic steps and procedures used in a sampling plan apply to an audit engagement. McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

©2005 by the McGraw-Hill Companies, Inc. All rights reserved. When is Sampling Used? Study and evaluation of internal control Selecting control procedures to verify compliance Attribute sampling Substantive procedures Selecting components or transactions of account balances for verification Variables sampling McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sampling Risk Risk that the decision made based on the sample differs from the decision that would have been made by examining the population Cause is a nonrepresentative sample Controlled by: Determining an appropriate sample size Ensuring that all items have an equal opportunity of selection Mathematically evaluating sample results McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Sampling Approaches Statistical sampling methods use the laws of probability to: Select sample items Evaluate sample results Statistical sampling methods control the auditor’s exposure to sampling risk Nonstatistical sampling violates one or both of the above criteria Both statistical sampling and nonstatistical sampling can be used in a GAAS audit McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Major Steps in Sampling Determine the objective Define characteristic of interest Define the population Determine sample size Select the sample Measure sample items Evaluate sample results Planning Performing Evaluating McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Steps in Sampling: Planning Determine the objective of sampling Drawing conclusion about some population of interest (e.g., amateur golfers) Define the characteristic of interest Question of interest to person conducting sampling plan (e.g., does brand of golf ball provide increased distance?) Define the population Item(s) about which question is asked Must be sure to completely and carefully define McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Steps in Sampling: Performing Determine sample size Under statistical sampling, sample size considers exposure to sampling risk Select sample items Measure sample items McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Steps in Sampling: Performing Determine sample size Select sample items Unrestricted random selection: Select items based on random numbers matched to items in population Systematic random selection: Bypass a fixed number of items in population, selecting every nth item Block selection: Select contiguous units Haphazard selection: Select items in a nonsystematic manner Measure sample items McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Steps in Sampling: Performing Determine sample size Select sample items Measure sample items Perform procedure and make appropriate evaluation/measurement Determine sample estimate Nonsampling risk can occur if incorrect procedures are performed or mistakes in evaluation or measurement are made McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Steps in Sampling: Evaluating Evaluate sample results In statistical sampling, evaluating sample results controls exposure to sampling risk Parameters Sample estimate Precision Reliability McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Precision and Reliability Precision (Allowance for sampling risk) Closeness of sample estimate to true population value Reliability (Confidence) Likelihood of achieving a given level of precision McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Example of Evaluating Sample Results Parameters Sample estimate = 43 years Reliability = 10 years Confidence = 90% (Sampling risk = 10%) McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Example of Evaluating Sample Results (Continued) Precision Interval Estimate Estimate Estimate - Precision + Precision McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Example of Evaluating Sample Results (Continued) Precision Interval 33 yrs 43 yrs 53 yrs Estimate Estimate Estimate - Precision + Precision McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Example of Evaluating Sample Results (Continued) Precision Interval 33 yrs 43 yrs 53 yrs Estimate Estimate Estimate - Precision + Precision 90% McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Example of Evaluating Sample Results (Continued) A 90% probability exists that the true average age is between 33 and 53 years (sample estimate  precision) A 10% probability exists that the true average age is less than 33 years or greater than 53 years McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Attribute Sampling Used to estimate the extent to which a characteristic exists within a population Used in the auditor’s study of internal control Goal: Estimate the rate at which the client’s internal control is failing to function effectively and compare to an allowable level (tolerable deviation rate) McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Decisions in Attribute Sampling Sample Tolerable Rely on Deviation  Deviation controls as Rate Rate planned Sample Tolerable Reduce Deviation  Deviation planned reliance Rate Rate on controls McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Risks Associated with Attribute Sampling McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

©2005 by the McGraw-Hill Companies, Inc. All rights reserved. Variables Sampling Used to estimate the amount (or value) of some characteristic of a population Used in the auditor’s substantive procedures Goal: Estimate the amount of error in an account balance or class of transactions and compare to an allowable level (tolerable error) McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Decisions in Variables Sampling Sample Tolerable Account Estimate of  Error balance is Error (Materiality) not misstated Estimate of  Error balance is Error (Materiality) misstated McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Risks Associated with Variables Sampling McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Summary of Sampling Risks Effectiveness Losses Risk of assessing control risk too low (overreliance) Risk of incorrect acceptance Efficiency Losses Risk of assessing control risk too high (underreliance) Risk of incorrect rejection McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.

Factors Affecting Sample Size McGraw-Hill/Irwin ©2005 by the McGraw-Hill Companies, Inc. All rights reserved.