Attribute Sampling


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Attribute Sampling

The statistical analysis of a sample involving characteristics that units in the sample either have or do not have. For example, a loan is either in default or it is not. Attribute sampling is useful when attempting to determine the extent to which a characteristic exists in a sample.
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This type of sampling is called "attribute sampling"; the relevant attribute in this case is "nonexistence of supporting documents." From sampling, the auditor wants to predict the occurrence rate in the population.
Usually in attribute sampling, we test whether the occurrence rate, P, of an attribute in the population is equal to a certain value Po or different.
TABLE 1 Sample Size for Attribute Sampling Using Binomial Distribution for a Desired Belief in the Interval B = [0, TER] with TER = 0.10 Expected Desired Sample Number Level of Size n Corresponding of Belief from Probability Occurrence in the Equations (1-[beta]), in the Interval (17) and from Sample (k) [0, 0.10] (18) Equation (1) 0 0.95 28 0.95 0.90 22 0.90 0.80 15 0.80 0.70 11 0.70 0.60 9 0.60 0.50 7 0.50 1 0.95 56 0.9802 0.90 47 0.9560 0.80 39 0.9124 0.70 34 0.8671 0.60 30 0.8163 0.50 26 0.7487 2 0.95 74 0.9825 0.90 65 0.9640 0.80 56 0.9281 0.70 50 0.8883 0.60 45 0.8410 0.50 41 0.7914 Example
We consider an auditing example here to illustrate the process of determining the sample size for an attribute sampling using belief functions.
TABLE 2 Sample Size for Attribute Sampling Using Binomial Distribution for a Desired Belief in the Interval B = [0, TER] with TER = 0.05 Desired Expected Level of Sample Number of Belief Size n Corresponding Occurrence in the from Probability in the Interval Equations (14), Equation Sample (k) [0, 0.10] (17) and (18) from (1) 0 0.95 58 0.95 0.90 45 0.90 0.80 31 0.80 0.70 24 0.70 0.60 18 0.64 0.50 14 0.50 1 0.95 113 0.9789 0.90 96 0.9560 0.80 79 0.9103 0.70 68 0.8601 0.60 60 0.8085 0.50 53 0.7500 2 0.95 151 0.9826 0.90 133 0.9648 0.80 113 0.9256 0.70 100 0.8817 0.60 91 0.8391 0.50 82 0.7837 First, as one can see, the sample size decreases as the desired belief in the interval decreases (compare columns 2 and 3 in Tables 1 and 2).
We have demonstrated in this article how beliefs can be assessed from the statistical evidence based on attribute sampling. We have illustrated using an auditing example how to determine the sample size for a desired level of belief in an interval B = [0, TER], and what level of belief is obtained when the sample results are analyzed, with TER representing the auditor's judgment about the highest occurrence rate tolerable.
Note that attribute sampling in the form used in auditing results in an assessment of uncertainty relating to the rate of occurrence of some attribute (such as a control exception).
Although based on attribute sampling principles, the objective of MUS (estimating the monetary misstatement in the population) is quite different from the objective of "traditional" attribute sampling (estimating the population misstatement rate).