Audit Chapter 9 Notes

i Chapter 9 Notes

What is Audit Sampling? * Audit Sampling – applying a procedure to less than 100% of a population to estimate some characteristic of that population * Sampling Risk – risk that a sample may not be representative of the population * Risk that the auditor’s conclusion based on the sample may be different from the conclusion they would reach if they examined every item in the population * Non-sampling Risk – risk pertaining to non-sampling errors (due to human error) * The sample is good but the auditor simply misses a deviation from a control, or misunderstands the procedure * Can be reduced to low levels through effective planning and supervisions of audit engagements

SLIDE 9-3

Statistical Sampling * Relies on the laws of probability, but does not eliminate judgment * Allows auditors to measure risk and control sampling risk, which helps: * Designs efficient samples – provides the smallest sample size for a given risk/confidence level * Measures sufficiency of evidence – adds an allowance for sampling risk depending on the confidence or risk level desired * Objectively evaluates sample results – indicates whether you’ve exceeded the tolerable deviation rate or tolerable misstatement

Non-statistical Sampling * Auditor uses judgment, rather than statistical techniques * This provides no means of quantifying sampling risk * Auditor may also sample haphazardly, which selects items on an arbitrary basis, but without any conscious bias. * Downside: sample may be larger or smaller than needed, making auditors unknowingly accept a higher than acceptable degree of sampling risk

Selection of Random Samples * Random Selection – every items in the population has an equal chance of being selected * Deviation – if an item cannot be found * Random sample results in a statistically unbiased sample, but it still may not be a perfect representation (because of sampling risk)

Random sample selection techniques: 1. Random Number Tables 2. Random Number Generators 3. Systematic Selection a. Advantage: items do not have to be pre-numbered

Other Methods of Sample Selection * Haphazard – select items on an arbitrary basis, but without any conscious bias. (not random) * Block – consists of all items in a selected time period, numerical sequence, etc. (not random, rarely used, and least desirable of the methods) * Stratification – technique of dividing a population into relatively homogeneous subgroups (called stratum) * If there is a lot of variability, then you would stratify the population

Types of Statistical Sampling Plans * Attribute Sampling – used for sampling the characteristics of internal controls (check mark or initials) * Variables Sampling – used for substantive testing (looking for material misstatements) * Discovery – sampling for just 1 case of fraud * Classical Variables – sampling for misstatements * Mean-Per-Unit estimation * Ratio estimation * Difference estimation * PPS (Probability-Proportional-to-Size) Sampling – sampling for misstatements based on the systematic selection methods

Allowance for Sampling Risk * An amount used to create a range, set by + or – limits from the sample results, within which the true value of the population characteristic being measured is likely to lie between * Allows a greater range of precision: the wider the interval, the more confidence you’ll have * Allowance for Control Tests: a 7% deviation rate + or – 2% means the controls do not work between 9% and 5% or the time * Allowance for Substantive Tests: a $10,000 account balance + or - $1500 means the actual amount will likely lie between $11,500 and $8,500 * The more confident I want to be, the larger the number

Sample Size and Dual Purpose Tests * Sample Size vs. Sampling Risk Inverse Relationship * As sample size increases, sampling risk and the allowance for sampling risk decreases * Dual Purpose Tests: * 1. Tests for evaluating the effectiveness of a control, and * 2. Tests used to look for a material misstatement * Both tests are made on the same invoice, using one sample for both tests

Sampling Risks – Tests of Controls
Beta: effectiveness implications (*beta is badder says everything is okay, when it really isn’t)
Alpha: efficiency implications

Actual Extent of Operating Effectiveness of CorrectDecision | Beta: Incorrect Decision(Risk of Assessing Control Risk Too Low) | Alpha: Incorrect Decision(Risk of Assessing Control Risk Too High) | CorrectDecision | The Control Procedure: The Test of Control Sample Indicates The control works The control doesn’t work

The control works, It’s effective

The control doesn’t work, It’s not effective

Steps for Tests of Controls * Determine the objective of the test (credit approval on sales order) * Define the attributes and deviation conditions (authorized initials; initials are missing or not acceptable) * Define the population to be sampled (sales orders from Jan to May) * Specify: * The risk of assessing control risk too low (select a table, e.g., 5% risk) * The tolerable deviation rate (the amount you can live with) * Estimate the population deviation rate (deviations from prior year) * Determine the sample size (provided from the tables) * Select the sample (you could use a number generator) * Test the sample items (look for deviations from the control) * Evaluate the sample results (do the actual deviations found plus the allowance exceed the tolerable deviation rate?) * Document the sampling procedure (put all procedures and findings and conclusions in the work papers)

Attributes Sampling: Relationship b/w the Planned Assessed Level of Control Risk and the Tolerable Deviation Rate

* Even though controls might not work 5 times out of 100, or at a 5% rate, that would still be assessed a low level * As long as the expected deviation rate doesn’t exceed the tolerable deviation rate we would rely on the controls * Note: if we thought the expected actual rate would exceed our tolerable rate, we wouldn’t bother testing the control

Statistical Sample Sizes for Tests of Controls at 5% Risk of Assessing Control Risk Too Low

* Sample Size vs. Tolerable Rate: Inverse * Expected Rate vs. Sample Size: Direct

* The smaller the deviation rate, the bigger the sample size Inverse

* As the expected rate gets larger, the sample gets larger Direct

* Sample Size vs. Tolerable Rate: Inverse * Expected Rate vs. Sample Size: Direct

* The smaller the deviation rate, the bigger the sample size Inverse

* As the expected rate gets larger, the sample gets larger Direct

Sample Risks – Substantive Tests
Looking for material misstatements

The Account is Actually: CorrectDecision | Beta: Incorrect Decision(Risk of Incorrect Acceptance) | Alpha: Incorrect Decision(Risk of Incorrect Rejection) | CorrectDecision | The Substantive Procedure Sample Indicates Fairly Stated Materially Misstated

The account is Fairly Stated

The account is Materially Misstated

Population Variability – Why It Matters * Significant variability usually results in stratification of the population

Allowance for Sampling Risk used in Substantive Testing * Sampling Error: even with statistical sampling using unrestricted random selection, there’s always a risk that the sample is not representative of the population * The Allowance for Sampling Risk used in Substantive Testing – is the dollar amount used to create a range within which the true value of the population is likely to lie * In substantive testing, we’re concerned about both over and under stating the balance. * With control testing, we’re more concerned about only one direction * The more confidence you need, the larger the range will be

Classical Variables Sampling
Use when you are looking for material misstatements * Difference Estimation * Ratio Estimation * Mean-Per-Unit Estimation * All, plus or minus an allowance for sampling risk

PPS Advantages * Line up all the individual invoices in one column and create another column which is a running cumulative total * Make a random start at $50 (from any number 1 to 90, the interval given) * After starting at $50, we then hop over every 90th dollar * Systematic Selection * Note: any invoice that is $90 (the interval) or larger will get picked with certainty * This method automatically stratifies the population