Audit Sampling Using ACL
ACL may be used for attributes sampling and probability-proportional-to size sampling
(presented in Appendix A of Chapter 9). It does not have a utility for the classical variables
methods (mean-per-unit, difference, and ratio).
To use ACL for sampling, one must have a “project” open. Unless you wish to actually
select a sample (which is not done in Chapter 9), that project need have nothing to do with
the specific sampling problem you are addressing. If you have used ACL prior to Chapter 9
in your auditing course, open any project you have worked on. If this is your first
experience with ACL, use the following approach to open a project after you have installed
ACL on your computer:





Double click on the ACL Icon on your desktop.
Under ACL Projects, click “Open an existing project.”
Double click “Metaphor Employee Data” on the far left.
Double click “Agents_Metaphor” on the far left.
Select “Sampling” on the top of the screen.
You are now able to use ACL for sampling purposes. As indicated, the project you have
open (here, Metaphor Employee Data” and the table you have open (Agents_Metaphor)
need not relate to the calculations you will have ACL perform.
The approach you should use for ACL is to first read the related chapter material on attribute
and/or probability proportional-to-size sampling to obtain an understanding of the concepts
involved. Then, work through the following material to help you get started with sampling
with ACL.
Using ACL For Attributes Sampling (Calculate Sample Size in ACL)
We will use an example similar to that in the text, but with an upper error limit of 9 percent
and an expected error rate of 2 percent.* You must first align the terminology used in the
text (as well as by the AICPA) with the ACL terminology. The following summarizes the
differences:
*
The ACL software uses several differences in assumptions as compared to the text
(which uses those of the AICPA). Accordingly, sample sizes (and allowable deviations)
may differ, ordinarily by small amounts.
Using ACL for Audit Sampling, Page 1 of 7
AICPA and Text Terminology
ACL Terminology
Attributes sampling
Risk of assessing control risk too low= 5%
Record Sampling
Confidence = 1.00 – risk of assessing CR too
low
= 1 - .05 = .95 = 95 (key in whole
numbers for all
inputs)
Population = number in population. This should
be 3,653.
Upper Error Limit = 9
Expected Error Rate = 2
Population size (we don't use)
Tolerable Deviation Rate= 9%
Expected Population Deviation Rate = 2%
We will use ACL to determine the sample size and to evaluate results—the procedures
performed manually in the text.
Determining the Sample Size
After clicking on “Calculate Sample Size” and using the inputs from the earlier table for
“Record” sampling, we click we obtain a sample size of 71 (2). This corresponds to the
sample size of 68 one may obtain from Figure 9.4 Again, small differences are to be
expected. Also, we do not use the “Interval” information.
Using ACL for Audit Sampling, Page 2 of 7
Evaluating Results (Evaluate in ACL)
Example a: Assume you find no deviations:
1.
Approach 1: Using the text’s first approach of simply determining whether more or
less than 2 deviations are identified, we are able to accept this population since no
deviations were identified.
2.
Approach 2: Using the text’s second approach, we use the results obtained in
“Evaluate Error” (Sampling  Evaluate Error) as follows:
Record
Confidence = 95
Sample size = 71
Number of errors = 0
ACL generates 4.23%.
Using ACL for Audit Sampling, Page 3 of 7
ACL generates an upper error limit frequency of 4.23. Following is the ACL Printout of
the results:
As of: 03/11/2007 09:47:14
Command: EVALUATE RECORD CONFIDENCE 95 SIZE 71 ERRORLIMIT
0 TO SCREEN
Confidence: 95, Sample Size: 71, Number of Errors: 0
The upper error limit frequency is: 4.23%
Example b: Assume you find 3 deviations
1.
Approach 1: Because you found more than 2 deviations, you have not met your
audit objective. Accordingly the auditors conclude that the achieved upper
deviation rate is greater than 9 percent.
“The achieved upper deviation rate is higher than 9 percent.” The planned
assessed level of control risk is not achieved. You need to consider increasing
the assessed level of control risk above the planned assessed level.
1.
Approach 2:
Use ACL "Evaluate"
Record
Confidence = 95
Sample size = 71
Number of errors = 3
Using this second approach, the achieved upper deviation rate is 10.93.
ACL Printout of the results
As of: 03/11/2007 09:48:06
Command: EVALUATE RECORD CONFIDENCE 95 SIZE 71 ERRORLIMIT
3 TO SCREEN
Confidence: 95, Sample Size: 71, Number of Errors: 3
The upper error limit frequency is: 10.93%
Using ACL for Audit Sampling, Page 4 of 7
Using ACL For Probability-Proportional-to Size Sampling
For PPS sampling we provide an example with the same parameters as that in the text—in
this case in Appendix 9A.
The following summarizes differences in terminology for PPS Sampling:
AICPA (text) terminology
PPS sampling
Risk of incorrect acceptance
Book Value = $6,250,000
Tolerable Misstatement= $364,000
Expected Misstatement = $50,000
ACL Terminology
Monetary Sampling
Confidence = 1 – risk of incorrect
acceptance = 1 - .05 = 95 (key in whole
numbers for all inputs)
Population = 6250000 (no commas)
Materiality = 364000
Expected Total Errors = 50000
Determining the Sample Size (Calculate Sample Size in ACL)
Inputting the information in the above table we obtain the following:
Using ACL for Audit Sampling, Page 5 of 7
ACL arrives at a sample size of 67, with a sampling interval of $92,166.66. The text’s
sample establishes a sample size of 66, and a sampling interval of $95,000. This small
difference is again due to small differences in underlying statistical assumptions. While in
practice we would certainly use ACL’s numbers, to better tie to the text in this one
presentation, we will now assume the text’s sampling interval of $95,000. We do not use
the “Maximum Tolerable Taintings (%) generated by ACL.
Evaluating Results (Evaluate in ACL)
We will use the text’s results presented in the "Illustration of PPS Sampling" section, in
which the following three misstatements were identified.
Book Value
$
100
2,000
102,000
Audited Value
$
90
1,900
102
Inputting the appropriate information we obtain the following:
Using ACL for Audit Sampling, Page 6 of 7
Following is the ACL Printout of the results
As of: 03/11/2007 09:38:50
Command: EVALUATE MONETARY CONFIDENCE 95 ERRORLIMIT 100,
10,2000,100,102000, 101898 INTERVAL 95000 TO SCREEN
Confidence: 95, Interval: 95000
Item
Error
Most Likely Error Upper Error Limit
285,000.00
Basic Precision
100.00
10.00
9,500.00
16,625.00
2,000.00
100.00
4,750.00
7,362.50
102,000.00 101,898.00
101,898.00
101,898.00
116,148.00
410,885.50
Totals
To summarize the results:




Most likely error ($116,148) is the text’s Projected misstatement
Basic Precision ($285,000) is the text’s Basic Precision.
Upper Error Limit ($410,885.50) is within .50 of the text’s rounded total of
$410,886.
The incremental allowance is not explicitly printed out by ACL. One may obtain
it by using the upper limit on misstatement formula:
Upper Limit on
Misstatements
=
Projected
Misstatement
+ Basic precision + Incremental Allowance
(SWITCHING
TO ACL TERMS)
Upper Error Limit = Most likely Error + Basic Precision + Incremental Allowance
Upper Error Limit - Most Likely Error -Basic Precision: = Incremental Allowance
$410,888
-
- $116,148
$9,740
-
$285,000
= Incremental Allowance.
= Incremental Allowance.
Using ACL for Audit Sampling, Page 7 of 7