HOW
DOES CLASSICAL VARIABLES SAMPLING (傳統的變量抽樣) WORK?
By Maire Loughran
【Adapted from Wiley CPA】
運用在證實測試的統計抽樣(=變量抽樣Variables sampling)可分為:
l 機率與金額大小成比率法(PPS sampling technique)，及
l 傳統的變量抽樣(Classic Variable Sampling)，而傳統的變量抽樣常用的方法(method)又可分為:
n 單位平均估計法(Mean-Per-Unit Estimation)
n 差額估計法(Difference Estimation)
n 比率估計法(Ratio Estimation)
n Regression Estimation
When using classical variables sampling, auditors treat each individual item in the
population as a sampling unit. This method is most like the statistics classes
you had to take in high school and college. You
use this method to evaluate your entire population based on your sample data. You
can use three common types of
classical variables sampling estimators:
1.
mean-per-unit,
2.
ratio, and
3.
difference.
Mean-per-unit uses the familiar statistical concept of mean. For instance, if you add 10 + 30 + 50 to get 90, and then divide 90 by 3 (the
number of values in this example), you get 30, which is the mean. As an
auditor, you apply this statistical concept to evaluate characteristics of your
total population. Taking the average value (mean) of items in your sample, you
can estimate the true population value.
For example, you have a total population of
3,000 items in accounts receivable, and your sample size is 50. Adding up the
individual values of the 50 items, you get a total of $2,000; therefore, your mean is $40 (2,000/50). Your
mean estimate of the
true value of accounts receivable is $120,000 ($40 x
3,000).
Considering this data with your sampling
risk, confidence level, and error rate, if your confidence level is 95
percent and your error rate is 10 percent, you can say that you’re 95 percent
confident that the total value of accounts receivable is $120,000, plus or minus $12,000 ($120,000 times your error
rate of 10 percent).
The mean-per-unit
method is a very good one to use if you don’t have
the underlying documents that support the account balance--if, for instance,
your client’s balance sheet shows a total
for accounts receivable, but the individual invoices supporting the balance
aren’t available.
Another method of classical variables
sampling is ratio estimation,
which applies the sample ratio
to an entire population. If your sample for any of your client’s accounts shows
errors of $1,000 in a total sample of $10,000, your misstatement ratio is 10 percent
(1,000/10,000).
You would then apply this ratio to the entire population. If the
entire population totals $50,000, your projected misstatement, which is an estimation of the misstatement
in the entire population, is $5,000 ($50,000 x 10 percent).
【交叉相乘】
1,000 : 10,000
X : 50,000
X = 5,000 = projected misstatement
For sampling risk, if projected misstatement doesn’t exceed
expected error, you can reasonably conclude that actual misstatement doesn’t
exceed your tolerable
misstatement.
l projected misstatement v. expected
error
Lastly, difference is another classical variables sampling
method. It’s similar to ratio estimation, except it incorporates the items in
the population. For example, your population consists of 5,000 items and your
sample consists of 1,000 items. Your audit procedures find errors totaling $500. The projected
misstatement is $2,500 [($500/1000) x 5,000 items].
【交叉】
500 : 1,000 items
X : 5,000 items
X = 2,500 = projected misstatement
