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### ACCT 4240: Auditing

Introduction to Audit Sampling

Definitions

- Sampling is the examination of less than 100% of the population for the purpose of evaluation some aspect of the population
- Each item in the population is a population unit
- Each population unit selected for examination is a sampling unit

Sampling: Purpose & Definition

- Obtaining information about a lot from a little
- Used in everyday life
- Need to understand principles
- Use when they fit objectives
- Identify population (universe, field)
- Base opinions only on what is sampled
- Nothing in sampling is precise
- Confidence level
- Precision

Inclusions and Exclusions

- A 100% audit does not involve sampling
- Analytical procedures normally are not applied to samples
- Procedures usually involved with sampling include
- Recalculation
- Physical observation of inventory
- Confirmations
- Document examination

Projecting the Error in the Sample to the Population

Book value of the population………… $1,500,000

Book value of the sample……………… $1,000,000

Dollar amount of error in the sample…… $10,000

Projected Error = $15,000

Statistical Sampling

- Uses the laws of probability for selecting and evaluating the sample items
- Selected at random so each population unit has an equal chance of being selected
- Statistical calculations are used for selecting sample units and evaluating audit results
- Sample size determines the level of confidence in the results

Nonstatistical Sampling

- Results are evaluated judgmentally rather than statistically
- Sample selection can be random or nonrandom
- Block sampling
- Select a group of items in sequence
- Sample may not be representative of the population

- Haphazard sampling - may introduce bias
- Judgmental sampling - sample size and items selected depends on auditor judgment

Biased samples (nonstatistical):

Purposeful

Deliberate exclusions

Patterns in population

Statistical:

Random sample selection

Interval sampling

Cluster sampling

Stratified sampling

Example

When to stratify

Sample Selection: Random vs. Haphazard SelectionSampling Risk and Non-Sampling Risk

- Sampling risk is the risk that the sample is not representative of the population
- Non-sampling risk results from human error
- Failure to recognize a mistake
- Use of an ineffective audit procedure

- Non-sampling risk is not quantifiable
- Level is reduced through
- Adequate supervision
- Quality control standards

Attribute Sampling

- Primary purpose is to estimate how effectively a specific accounting control performs a specified function
- Example: Comparison of a vendor’s invoice to a corresponding receiving report

Invoice

Receiving Report

Compare

Qty = 15

Qty = 15

Attribute Sampling

- Used to estimate the RATE of OCCURRENCE of a specific quality within a population
- Generally viewed as a YES/NO or TRUE/FALSE outcome
- A deviation occurs when an attribute is not present

Steps in Attribute Sampling

- Determine the audit objectives of sampling plan
- Define population and sampling unit
- Specify attributes of interest
- Determine sample size
- Determine sample selection method
- Execute sampling plan
- Evaluate sample results

Steps in Performing a Statistical Test of Controls

- Determine the control to be sampled
- Define the population and the sampling unit
- Determine the initial sample size
- Specify the tolerable deviation rate (e.g. 5%)
- Specify Beta risk (risk of over-reliance) (e.g. 5%)
- Estimate the expected population deviation rate
- Estimate the population size

Statistical Tests of Controls

- Select the sample
- Random sampling
- Systematic selection - auditor picks every nth item from one or more random starting points

- Audit the selected items

Statistical Tests of Controls

- Evaluate the sample results
- Determine why errors occurred
- Evaluate effect of results on related substantive audit procedures

Evaluation

- Determining reasons for deviations
- Purpose of examination – opinion
- Factors relevant to an overall opinion
- Internal control
- Supervisory review
- Administration
- Experience and training of personnel
- Materiality of errors
- Effect on other transactions
- Risk analysis

Sampling Risk - Attribute Sampling

- Sampling Risk - the risk that the sample is not representative of the population

Tested Control Actually Is

Effective

Not Effective

Alpha Risk

Not

Correct

Effective

Decision

Risk of assessing

Tests of Controls

control risk too high

Indicate that

Controls Are

Beta Risk

Correct

Effective

Decision

Risk of assessing

control risk too low

Sequential (Stop-or-Go Sampling)

- Select initial (smaller) sample and consider results
- Decision
- Rely on control; discontinue sampling
- Cannot rely on control
- Select additional items; make decision
- Discontinue sampling

- Advantage is that evidence may support reliance on control with a relatively small sample size
- Disadvantage is that auditor may continually extend the sample, creating inefficiencies

Discovery Sampling

- Used when deviations from control are expected to be infrequent but very critical
- Allows the auditor to
- Determine the necessary sample size to find at least one example of a deviation if such deviations exist
- Determine the probability that the rate of occurrence of a deviation is less than a specific (low) level

Discovery Sampling

- Used when expected error rate is low or near zero
- Sample is designed to identify at least one example of an error if it occurs in the population at a specified error rate
- Probabilities determined by using Appendix AC

Audit Sampling for Substantive Tests

- Define the objective of the test
- Define the population to be sampled
- Identify individually significant items
- Determine the method of sampling
- Determine the sample size
- Select the sample and examine the items
- Evaluate the sample results
- Project sample results to N
- Make decision about N

Statistical Sampling for Substantive Testing

- Hypothesis testing - measures whether an estimated book value determined by statistical sampling is substantially different than the book value recorded by the client
- Materiality
- Sampling risk

Statistical Sampling Techniques for Substantive Tests

- Dollar-Unit Sampling
- Most efficient when population error rate is very low
- Book value must generally be available for each item in the population

- Ratio and Difference Estimation
- Moderate error rate must exist in the population
- Book value must generally be available for each item in the population
- Ratio estimation is more efficient when the errors are proportionate to the book values

- Stratified Mean-per-Unit Estimation
- May be used under any circumstance

Evidence

Indicates

Sampling Risk - Substantive Procedures

- Sampling Risk - the risk that the sample is not representative of the population

Recorded Amount Actually Is

Materially

Not Materially

Misstated

Misstated

Alpha Risk

Reject as

Correct

Materially

Risk of Incorrect

Decision

Misstated

Rejection

Accept as

Beta Risk

Correct

Not

Risk of Incorrect

Decision

Materially

Acceptance

Misstated

Steps in Sampling

- Determine the objective of the sampling
- Define the population and sampling unit
- Determine the method of sampling

Methods of Sampling

- Classical variables sampling
- Mean-per-unit estimation
- Difference estimation
- Ratio estimation

- Probability Proportional to Size (PPS) - Also called Dollar-Unit Sampling

Steps in Sampling

- Determine the initial sample size
- Using random sampling techniques, identify the items to audit
- Audit the selected items and identify monetary misstatements
- Evaluate the sample results
- Amount of known misstatement
- Project known amount to population (likely misstatement)

Classical Variables Sampling

- For difference and ratio estimation methods, a minimum of about 30 errors are necessary to ensure a reasonable estimate of the true but unknown monetary balance
- For Mean-per-Unit sampling, auditors usually stratify populations into smaller sub-populations to reduce total sample size
- Book values must be available for difference and ratio estimation techniques

Probability Proportional to Size

- Uses attribute sampling theory to estimate the maximum amount of misstatement in an account balance
- The sampling unit is an individual dollar of the account balance
- PPS is more effective for identifying overstatements of account balances

Determining the Sample Size (n)

Where:

α = planned level of risk of incorrect rejection

zα = reliability coefficients for the risk of incorrect rejection

Pre = precision per item in the population

sd = standard deviation of the population to be sampled

TE = tolerable error (material amount)

N = number of items in population

zβ = reliability coefficient for risk of incorrect acceptance risk

Probability Proportional to Size (PPS) Sampling

- Defines the sampling unit as individual dollar in an account balance
- Auditor will select individual dollars for examination
- Auditor will verify entire “logical unit” containing the selected dollar
- Accounts receivable: Customer account
- Inventory: Inventory item

Advantages of PPS Sampling

- Results in smaller sample sizes
- Includes transactions or components reflecting larger dollar amounts
- Effective for overstatement errors
- Generally simpler to use than classical variables sampling

Disadvantages of PPS Sampling

- Provides a conservative (higher) estimate of misstatement
- Not effective for understatement or omission errors
- Expanding a PPS sample is difficult if the initial conclusion is to reject account balance
- Requires special consideration for accounts with zero or negative balances

PPS

- Calculate sample size using
- Calculate sampling interval using

Probability Proportional to Size

Invoice No. AmountIntervalSample?

1 $ 700 700 NO

2 400 100 YES

300

3 900 500 YES

400

4 300 300 NO

5 400 100 YES

300

6 1700 500YES

800 YES

400

7 400 400 YES

Next Time

Completing the Audit

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