Statistical Sampling as an Auditing Tool
BY OSCAR S. GELLEIN Partner, Newark Office
Presented at the Annual Meeting of the American Institute of Certified Public Accountants, San Francisco — October 1959
STATISTICAL sampling requires selection of the items making up the sample in such a way that the laws of probability determine the manner of occurrence of the items in the sample. When the selection
is carried out in this way, measurements can be made with respect to the sample and mathematical inferences drawn from them. The measurements are called precision and reliability (or level of confidence). The sense of these measurements is not alien to our intuition.
We know intuitively that there is one chance in two that a tossed coin will show a head. We also know intuitively that if a coin is tossed a large number of times it is likely that a head will appear approximately 50 per cent of the time. We are prudent enough, however, to avoid saying with certainty that a head will appear, say, 5,000 times out of 10,000 tosses. I am sure, however, that our intuition
tells us that the greater the number of tosses the greater the reliability, or the confidence, that a head will appear one-half the time.
Now statistical sampling adds another dimension which also falls within the purview of our intuition. It says that with certain precision
for a given degree of reliability a statement can be made about the number of heads that will appear if a coin is tossed, say, 100 times. In other words, if the statement is to be made with 95 per cent reliability it must refer to a range around 50—in this case about 40 to 60—the precision would be ± 10, the reliability 95 per cent. Another way to say it is that if, day after day, 100 persons each made 100 tosses of a coin, on the average, 95 of them would show a number of heads falling in the range of 40 to 60. These results are calculated, not estimated. They can be stated with mathematical certainty.
We could look at this situation another way, too. Suppose that we had no previous knowledge about a coin, that is, about the number of times that a head might be expected to appear in any given number of tosses. Could we in these circumstances, after tossing it a number of times, make any statement about this feature of a coin? I think