Audit Sampling
Sampling refers to the examination of less than 100% of a population & using the results as a basis for drawing a general conclusion on the entire population.
Nonsampling Risk
vs.
Sampling Risk (2)
Nonsampling Risk  The risk that human error will lead to drawing the wrong conclusion. (Human error, misinterpreting audit test results, not recognizing misstatments in documents audited)
Sampling Risk  The risk of drawing the wrong conclusion based on a bad sample. Two types of sampling risks:

Type I  Efficiency Error
 Population is OKAY, but sample is BAD
 Underrely on I/C = High RMM assessment
 Incorrectly Reject an accont balance for substantive testing purposes.
 Population is OKAY, but sample is BAD

Type II  Less Effectiveness
 Population is BAD, but sample is OKAY
 Overrely on I/C = Low RMM assessment
 Incorrectly Accept an account balance for substantive testing
 Population is BAD, but sample is OKAY
There are two times when audit sampling are used, when are they?
 During the internal control phase of the audit, the auditor will perform test of controls on a sample basis to determine the operating effectiveness of controls they plan to rely on. (called Attribute Sampling)
 During the substantive testing phase of the audit, auditor will perform test of details details (ICORRIIA) of transactions , accounts & disclosures on a sample basis to obtain sufficient appropriate audit evidence to support managenent assertions. (called Variable Estimation Sampling)
What are two ways sample size is determined?
_{Statistical & Nonstatistical (Judgemental)}
Statistical Sampling  refers to the use of quantitative measures of the auditor s taking in the use of sampling. Formulas are used to determine the sample size necessary.
Nonstatistical Sampling  (Judgemental Sampling) a method of sampling under which the auditor applies judgement to determine sample size & to interpret sample results.
 Auditors using nonstatistical sampling tends to overestimate the needed sample size. Therefore, audit tends to be inefficent despite being effective.
Sampling Risk Summary
(Internal Ctrl vs. Substantive Testing)
Internal Control: Attribute Sampling (Characteristics)
 Assessing RMM HIGH (under rely) = Inefficient
 Assessing RMM LOW (over rely) = Ineffective
Substantive Testing: Variable Sampling ($ Amounts)
 Incorrect Rejection = Inefficient
 Incorrect Acceptance = Ineffective
Attribute Sampling
(two risks,sample size,evaluation)
 Attribute sampling is for Internal Controls

Two Risks
 Assessing RMM too Low = Audit ineffective (T2)
 Assessing RMM too High = Audit inefficient (T1)

Factors affecting Sample Size (Tested)
 Tolerable Rate  Inverse effect
 Expected Error Rate (Deviation)  Direct effect
 Acceptable Risk (Allowance) = Inverse effect
 Population Size = Little or No effect

Evaluation of Sample Results
 Calculate Sample Deviation Rate
 Deviation Rate = # of errors / sample size
 Calculate Maximum Deviation Rate (MDR)
 MDR = Sample Deviation + Allowance
 Compare Maximum Deviation Rate vs. Tolerable Rate
 Maximum Deviation Rate must NOT exceed Tolerable rate or else Auditor must modify planned reliance
 Assessing RMM too Low = Audit ineffective (T2)
 Assessing RMM too High = Audit inefficient (T1)
 Tolerable Rate  Inverse effect
 Expected Error Rate (Deviation)  Direct effect
 Acceptable Risk (Allowance) = Inverse effect
 Population Size = Little or No effect
 Calculate Sample Deviation Rate
 Deviation Rate = # of errors / sample size
 Calculate Maximum Deviation Rate (MDR)
 MDR = Sample Deviation + Allowance
 Compare Maximum Deviation Rate vs. Tolerable Rate
 Maximum Deviation Rate must NOT exceed Tolerable rate or else Auditor must modify planned reliance
Attribute Sampling
What are the two risks associated with Attribute Sampling?
 Attribute sampling is for Internal Controls

Two Risks
 Assessing RMM too Low = Audit ineffective (T2)
 Assessing RMM too High = Audit inefficient (T1)
 Assessing RMM too Low = Audit ineffective (T2)
 Assessing RMM too High = Audit inefficient (T1)
Attribute Sampling
What are factors affecting sample size? (TEA)
 Attribute sampling is for Internal Controls

Factors affecting Sample Size (Tested)
 Tolerable Rate  Inverse effect
 Expected Error Rate (Deviation)  Direct effect
 Acceptable Risk (Allowance) = Inverse effect
 Population Size = Little or No effect
Attribute Sampling
How to evaluate sample results?
 Attribute sampling is for Internal Controls

Evaluation of Sample Results
 Calculate Sample Deviation Rate
 Deviation Rate = # of errors / sample size
 Calculate Maximum Deviation Rate (MDR)
 MDR = Sample Deviation + Allowance
 Compare Maximum Deviation Rate vs. Tolerable Rate
 Maximum Deviation Rate must NOT exceed Tolerable rate or else Auditor must modify planned reliance
 Calculate Sample Deviation Rate
Attribute Sampling
Sampling Methologies (4)
_{(Random Number,Systemic,Haphazzard,Block)}
A sample, by definition, should be representative of the population under consideration. For a sampling method to be valid, all items in the population should have an equal opportunity to be selected. Such methods include:
 RandomNumber Sampling  numbered documents or transactions are selected through the use of random number tables or computer software.
 Systemic Sampling  every "Nth" item is selected from a randomlydistributed population from a randomlyselected starting point.
 Haphazard Sampling  a sample consisting of units selected without any conscious bias  again assuming the random distribution of the population.
 Block Sampling  a sample consisting of contiguous units, example: a selection of three blocks of ten vouchers each.
Variable Sampling
What are the two risks?
What affects Sample Size? TAPES
 Substantive Testing  Test of Details

Two Risks:
 Incorrect Acceptance = Audit Ineffective
 Incorrect Rejection = Audit Inefficient

Factors affecting Sample Size (TESTED)

Tolerable misstatement  Inverse

Accetance Risk  Inverse

Population Size  Direct

Expected Misstatement  Direct

Standard Deviation  Direct
 RMM  Direct
 Incorrect Acceptance = Audit Ineffective
 Incorrect Rejection = Audit Inefficient
 Tolerable misstatement  Inverse
 Accetance Risk  Inverse
 Population Size  Direct
 Expected Misstatement  Direct
 Standard Deviation  Direct
 RMM  Direct
Variable Sampling & Sample Size Formula
What makes sample size increase or deacrease? TAPES
TESTED
To be more Precise, Sample Size (SS) will need to increase.
 Tolerable Rate = Inverse
 Acceptable Risk = Inverse
 Population Size = Direct (very little)
 Expected Misstatements/Errors = Direct
 Standard Deviation = Direct
 Risk of Material Misstatements = Direct
SS = (Std Deviation + Reliability + Population) / Allowance
Types of Classical Variables Sampling (4)
_{(MPU,difference estimation,ratio estimation,stratified)}

MeanperUnit
 MPU = Average Actual Audit Results x Total Population

Difference Estimation
 DE = ((Actual  Sample) x Total Population) + Base

Ratio Estimation
 RE = Avg Ratio x Population
 The use of the ratio estimation sampling technique is most effective when the calculated audit amounts are approximately proportional to the client's book amounts.

Stratified Sampling

Population is divided into groups
 Sample size is drawn from each group
 MPU = Average Actual Audit Results x Total Population
 DE = ((Actual  Sample) x Total Population) + Base
 RE = Avg Ratio x Population
 The use of the ratio estimation sampling technique is most effective when the calculated audit amounts are approximately proportional to the client's book amounts.
 Population is divided into groups
 Sample size is drawn from each group
Probability Proportional to Size Sampling (PPS)
PPS  A sampling plan under which items exceeding a certain dollar amount (sampling interval) are always included in a sample &, for remaining items, the greater the amount, the greater the likelihood of being included in the sample.
Calculations Needed:

Sampling Interval (SI): 2 Ways to Calculate
 SI = Tolerable Misstmt / Reliability Factor (from Table)
 SI = Population Amount / Sample Size
 Sample Size = Population Amount / Sampling Interval
To Determine Projected Misstatements (PM):
 Misstatement = Book (Recorded) Amt  Audited Amt
 Tainting Factor (TF%) = Misstatement / Book Amount
 Projected Misstatements (PM)  Audit Adjustment
 If SI > Book (Recorded) Amount
 PM = TF% * SI
 If SI < Book (Recorded) Amount
 PM = Book Amount  Audited Amount
 If SI > Book (Recorded) Amount
PPS Advantages (4)
vs.
PPS Disadvantages (2)
Advantages of PPS over classical variable are:
 Standard deviation is NOT needed
 Stratifies sample automatically
 Smaller sample usually results in few errors expected
 Able to start sampling without having entire population available or finished
Disadvantages of PPS over classical variable are:
 NOT Useful to detect understatement
 Zero & negative balances require special handling