HOW
DOES ATTRIBUTE SAMPLING (屬性抽樣) WORK?
By Maire Loughran
Auditors choose from several types of
sampling when performing an audit. Attribute sampling means that an item being
sampled either will or won’t possess
certain qualities, or attributes.
An auditor selects a certain number of records to estimate how many times a
certain feature will show up in a population. When using attribute sampling, the sampling unit is a single record
or document. Auditors typically
use attribute sampling to test internal controls.
An example of an attribute sampling feature
may be that per the client’s internal control procedures,
all purchases over $50 are supposed to be authorized by a purchase order. So every purchase
over $50 either will or won’t be authorized by a purchase order-- attribute
sampling has no gray area.
Here’s how you’d use attribute sampling
to see whether the client’s internal control is
working properly: Your population
consists of all vendor invoices for purchases over $50, and the number of
records you sample from that population is set at 75 records. Looking through
your sample, you see that 3 of the
75 records aren’t supported by a purchase order. That gives you a population
error rate of 4 percent (3/75).
How do you decide if this population error rate is okay? That decision is based on what figures you set for tolerable
error, expected error, sampling risk, and confidence level.
For example, let’s say that
l The tolerable error rate
is 7 percent.
l The expected error rate
is 5 percent.
l The sampling risk is 2 percent.
l The confidence level is 98 percent. (Remember that the confidence
level plus the sampling risk always equal 100 percent.)
l The population error rate is 4 percent (which we just figured out).
The next question is, what do you do with
this information? First, remember that you’re looking at a sample of only 75 vendor invoices,
not the entire population. Even though the 4 percent population error rate is
less than the tolerable error rate of 7 percent, you can’t just use this fact
to prove that your sample is sufficient.
When using attribute sampling, to make sure
your sample is representative of the
whole, you have to add the sampling risk of 2 percent to the 4 percent
population error rate. These two figures combined are referred to as
the computed
upper deviation rate.
【computed upper deviation rate = population
error rate (樣本來的) + sampling risk】
So the computed upper deviation rate
is 6 percent (2 percent plus 4 percent). That’s good news for you, because it’s below the tolerable error rate of
7 percent. This fact means that you can rely on the purchase order internal
control. What’s the big deal about this? Well, when you start your
testing of account balances, you
rely on this internal control to limit
your testing of the purchases account balance.
Suppose the sample size was 50 instead of
75. Your population error rate would change to 6 percent (3/50), making your computed upper deviation rate
equal to 8 percent. That’s over
the tolerable error rate of 7 percent. Therefore, you must conclude that the
purchase order internal controls aren’t operating at an acceptable level. So
rather than decreasing your purchases account balance testing, you’d need to increase it. You could also increase
your sample, redo your calculations, and see if a larger sample size brings the
computed upper deviation rate back down to under the tolerable error rate of 7
percent. Your firm will have field
procedures in place to guide
you in choosing between the two options.
