Discussant's response to the sample of one: Indispensable or indefensible?;

              Discussant's Response to
The Sample of One: Indispensable or Indefensible?
Alvin A. Arens
Michigan State University
Before examining in somewhat greater detail the content of Mr. Boni's stimulating paper, I would like to establish my perceptions of the primary differences between the "Sample of One: Indispensable or Indefensible" and Howard Stettler's classic original article of which this is an extension, "Some Observations on Statistical Sampling in Auditing."1 My reason for doing this in no way is to criticize Boni's paper, but rather to demonstrate that the basic concepts so well known from Stettler's article are completely different from the ones included in this paper.
The relevant section in Stettler's article is where he rejects the recommenda­tion
of the AICPA Committee on Statistical Sampling for use of reliability levels of 50 to 95 percent confidence for compliance testing and states instead:
By contrast, it is my contention that the auditor may properly ignore the question of sample reliability when adequate controls over internal control are present, reducing reliability practically to zero, so that only one of each type of item need be tested. On the other hand, if internal control is deficient, the auditor's modification of his examina­tion
should not be in the direction of increasing sample size for his tests of transactions to achieve increased reliability for his conclusions about compliance with the system of internal control. The sample of one of each type of transaction should suffice to indicate that the system such as it is, is operative, and a larger sample that would disclose the extent of compliance helps very little in assessment of the fairness or propriety of the account balances produced by the system.2
The point Stettler was making, using the terminology of SAS #1, section 320, is that compliance testing is not necessary beyond a walk-through test to help understand the system and that the emphasis should be on substantive testing.
Boni takes a similar but much broader view of the meaning of a sample of one. Although he certainly believes in the concept of a walk-through test, his use of the term "a sample of one" is a much broader concept than Stettler's. He gives an example near the end of the paper where a sample of confirmations of accounts receivable is used to test for aging and other attributes of interest. Since the items included in the sample are dealing with one question, the test is referred to as a part of a sample of one. Similarly, he also talks about com­pliance
tests with a random sample and statistical theory being used to estimate the aggregate effect of certain occurrences.
While Stettler restricted his use of a sample of one to a sample of one or
109