Why does the risk of overreliance have an inverse relationship with sample size?

Pa rt (2 )

Se c t ion (1 )

T e rm s Re la t e d t o Sa m ple Size

T e rm s Re la t e d t o Pla nning

1 - T ole ra ble

Ex c e pt ion Ra t e

(T ER)

Exception rate that the auditor will permit in the population , and still be willing to use the assessed control risk and or the amount of monetary misstatements TER is determined by the auditor based on his professional judgment Example : The auditor decides that TER for attribute (1) is 6% ,This means that the auditor has decided that evenif 6% of the duplicate sales invoices are not approved for credit , the credit approval control is still effective TER & Sample size inverse relationship 2 - Ac c e pt a ble Risk

of Ove r-re lia nc e

(ARO)

1 - The risk that the auditor concludes that controls are effective than they actually are is the Risk of over- reliance 2 -The risk that the auditor is willing to take of accepting a control as effective, when the true population exception rate is greater than the tolerable exception rate (TER)** Note :Control as effective when the true population exception rate is greater than TER

3 - Est im a t e d Popula t ion

Ex c e pt ion Ra t e

(EPER)

Exception rate that the auditor expects to find in the population before testing begins EPER And small sample size , Direct relationship

4 -I nit ia l (St a t ic a lly)

Sa m ple size

Sample size decided after considering the following factors : 1 - Population size 2 - TER (Tolerable Exception Rate) 3 - ARO (Acceptable Risk of Over-reliance) 4 - EPER (Estimated Population Exception Rate)

7 - De t e rm ine T he I nit ia l Sa m ple Size

1 - I n N on- St a t ist ic a l Sa m pling

Auditors using non-statistical sampling decide the sample size using

Profe ssiona l J udge m e nt rather than using a statistical formula or

tables

2 - St a t ist ic a l Sa m pling

Use The Tables To Determine Initial Sample Size (Table 15-8) Three Factors determine the initial sample size 1 - ARO 2 - TER 3 - EPER Example : 1 -Select the table Corresponding ARO (Two levels %5 & 10%) For example , the auditor selected ARO = 5% 2 - Locate TER 6% , at the top of the table 3 -LocateEPER is equal 2% , at the far left column 4 -Determine the initial size through the intersects TER 6% and EPER 2% , The Sample size = 127 ARO 5% EPER TER 2 3 4 5 6 ......... . .

2

149 99 74 59 49

236..........................................

................................

..................................

X=127... Sample size

Rule s

1- TER .... Increase ..... Sample size ... ... Inverse TER .... always 2,3,4,5.... the table *** 2- EPER .... Increase ..... Sample size .... Increase.... Direct EPER .... 0, 0, 0. 0. 1 ........ In the table* 3- Another Table ...... ARO is 10%, the same in first table except ARO**

4- Pre c ision Est im a t e = TER – EPER ,More Precision Required Large Sample size

Determining Sample Size In Case TER is not Provided in

Table

Example: An auditor is willing to reduce assessed control risk for the agreement between payroll sheet and time card does not exceed 5% (TER) at a 5% (ARO) on the basis of past experience , EPER set at 1% ,and Sample size at 5% TER = 124 , sample size at 6% TER = 103 Required Calculate the initial Sample size at TER 5% Answer 1- ARO = 5% 2- TER = 5% is not provided in the table 3- EPER = 1% 4- In this case Cross multiplication is used

• Sample size at 5% TER = 124

• sample size at 6%TER = 103

• sample size at 1% = 21

• To compute the items relevant to 0% 1% TER : 21 0% TER : ?? (x) x = 0% x - 21 / 1% = - 10 items Sample size at 5% = Size at 5% + Size at 0%.. Increase TER... Minus = 124 – 10 = 113 = 114 items Example: The auditor is willing to reduce assessed control risk for the agreement between purchases and purchases orders does not exceed 4% TER , at a 10% ARO on the basis of past experience ,EPER set at1% , Sample size at TER 4% is 132 and at TER 5% is 105 Required What is the initial sample size at TER 4% Answer 1- ARO = 10% 2- TER = 4% is not provided in the table 3- EPER = 1% 4- In this case Cross Multiplication is used

• Sample size at 4% TER = 132

• sample size at 5% TER = 105

• sample size at 1% = Difference = 132 – 105 = 27 items

• To compute the items relevant to 0% 1% TER : 27 0% TER : ?? (x) x = (0% x 27) / 1% = - 13 items Sample size at 4% = Size at 4% + Size at 0% = 132 – 13 = 118. 5 = 118 items %.. Increase TER... Minus Question .M The following are the results of the statistical sampling of 8 large population 1 2 3 4 5 6 7 8 ARO TER EPER Statistical Sample Size

5%

4%

1%

156

5%

4%

1%

192

5%

4%

1%

?

10%

7%

2%

94

5%

5%

1%

93

10%

6%

2%

110

10%

7%

2%

?

10%

7%

2%

75

Required Determine the Statistical Sample Size in population (3) and (7) Answer Sample size in Population (3) Use Population 1 & 5 Population (1) At TER 4% Sample size 156 Population (5) At TER 5% Sample size 93 TER 1% 63 items 1% TER 63 items 0% TER X items X items = (0 x 63) / 1 = 50 items Sample size at 4% TER = Sample size at 4 % TER +Sample size at 0% % +TER Minus = 156 – 50= 105 = 105 items

Which factors have an inverse relationship to sample size?

What is the relationship between sample size and sampling risk?

What is risk of overreliance?

What effect on sample size does increasing the allowable risk of incorrect acceptance have for a substantive test?