Chapter 9

SAMPLING IN SUBSTANTIVE TESTING

 

	Planning:
		1.	Determine objectives
		2.	Define population
		3.	Sampling unit
		4.	Choose sampling technique (We will use MUS or PPS)
		5.	Determine sample size
				Consider variation within the population
				Determine acceptable risk of incorrect acceptance
				Determine tolerable misstatement
				Determine expected amount of misstatement
				Consider population size
	Performance:
		6.	Determine method of selecting sample items
		7.	Perform audit procedures
	Evaluation:
		8.	Calculate sample results
		9.	Perform error analysis
		10.	Draw final conclusions

SAMPLING PLAN - PROBABILITY PROPORTIONAL TO SIZE

I.	Objective - Test for overstatement.  For example, test existence and rights of account balance - Accounts Receivable (by confirming).
II.	Population and sampling unit
   	A.	Sampling unit is the individual dollar but the "logical sampling unit" is the location (document) containing the "dollar"
		1.	Possible - All balances, Debit, Credit, or Zero 
		2.	Problems with zero and negative balances - these have no chance of selection
	
   	B.	For example assume the following:
		1.	Population is A/R with debit balances
		2.	Sampling unit is each of the $600,000 aggregate amount
		3.	Auditor concludes that $30,000 is a material misstatement
		4.	The auditor anticipates error of $6,000
		5.	Customer account is logical sampling unit
		6.	Risk of incorrect acceptance is 5%
	
III.	Sample size


	BV =	Book value of population (sampling units)
	RF =	Reliability Factor (From Table 9-4 - based on beta risk)
	TM =	Tolerable misstatement
	AM =	Anticipated misstatement
	EF =	Expansion factor (From Table 9-5 - based on beta risk)
	
	Thus for our example

	
IV.	Sample selection method
	
	A.	Systematic 

	B.	For our example

	Random start of $5,000 (assume) then every $6,818 dollar

SYSTEMATIC SELECTION PROCESS

 Customer Number

Book Value

Cumulative Balance

Dollar Unit Selected

Book Value of Sample Item

01001

$1,200

$ 1,200

 

 

01025

6,043

7,243

5,000

$6,043

01075

2,190

9,433

 

 

01140

3,275

12,708

11,818

3,275

01219

980

13,688

 

 

01365

1,647

15,335

 

 

01431

4,260

19,595

18,636

4,260

10592

480

20,075

 

 

01667

7,150

27,225

25,454

7,150

.

.

 

 

 

.

.

 

 

 

 

 

 

 

 

 

 

 

 

 

Total

600,000

 

 

 

V.	Execute plan - audit the items
	
VI.	Evaluate results
	
	A.	Steps
	
		1.	Projected misstatement from sample to population
		2.	Determine allowance for sampling risk
		3.	Calculate the upper misstatement limit
	
   	B.	Considerations
	
   		1.	The above steps are analogous to the sample occurrence
			rate, allowance for sampling risk and upper occurrence
			limit for attribute sampling
	
   		2.	Upper misstatement limit = projected misstatement
				 + allowance for sampling risk
	
				UML = PM + ASR
	
				ASR = BP + IA
	
   		3.	Evaluation process depends on whether any errors are found in the sample.
	
   	C.	If no errors
	
   		1.	Projected misstatement to population = $0  (That is PM = 0)
	
   		2.	Thus, the allowance for sampling risk = upper misstatement limit
	
			And since IA = 0 for no errors, ASR = BP

				BP = RF x SI
	
			BP = "Basic precision" or allowance for sampling risk
			RF = Reliability factor as used from Table 9-4
			SI = Sampling interval

		3.	For our example
	
			BP = 3.0 x $6,818 
			BP = $20,454
	
		What statement can be made?

   	D.	If some errors
	
		1.	Project sample results to population

   			a.	For each logical unit with BV less than SI 
				calculate tainting percentage:

				Projected misstatement = SI X Tainting %
	
	   		b.	Each logical unit equal to or greater than SI, use actual errors.
	
	   		c.	Sum errors for projected population misstatement

Calculation of Projected Misstatement

 Book Value

Audit Value

Tainting %

 

Sampling Interval

Projected Misstatement

950

855

10

6,818

682

2,500

1,250

50

6,818

3,409

7,650

6,885

N/A

N/A

765

5,300

5,035

5

6,818

341

8,000

0

N/A

N/A

8,000

24,400

14,025

 

 

13,197

		2.	Calculate allowance for sampling risk 
			and determine upper misstatement limit (UML)

			a.	Two components - Sum of basic precision (BP) 
				and incremental allowance for misstatements (IA)

			b.	BP is same as with no errors - SI x RF

			c.	Determine IA
				1.	Use errors related to logical units less than SI
				2.	Use Incremental change factors from Table 9-4
				3.	Rank errors by size
				4.	Extend factors times errors
				5.	Sum IA and BP

 Ranked PM

Factor

IA

3,409

.75

2,557

682

.55

375

341

.46

157

 

 

3,089

	Ranked logical units less than SI


	   		d.	Add projected misstatements and
				allowance for sampling risk to get upper 
				misstatement limit (UML)

					UML  =  PM     +    ASR

						   BP       IA

				36,740 = 13,197 + 20,454 + 3,089

	
VII.	Review Advantages and Disadvantages - Page 340-341