Internal Revenue Bulletin:  2007-23 

June 4, 2007 

APPENDIX C

TECHNICAL FORMULAS

The formulas below are included to clarify the statistical sampling terms used and to ensure consistent application of the procedures described in the revenue procedure.

Definition of Symbols
TERM DEFINITION
n Sample Size
N Population Size
x The value of the sampling unit that is being used as the primary variable of interest. In audit sampling, this would be the audited (or revised) value of the transaction.
y The value of the sampling unit that is being used as the “paired” variable that is related to the variable of interest. In audit sampling, this would be the reported (or original) value of the transaction.
d The value of the sampling unit that is the difference between “paired” variable (y) and the variable of interest (x). That is, d = x - y. In audit sampling, this would be the difference (or the change) of each transaction’s value.
X The total value of the primary variable of interest. In audit sampling, this would be the estimated total audited value of the population. Typically, this value is not known for the entire population and is estimated based on the statistical sample selected.
Y The total value of the variable that is paired with variable of interest. In audit sampling, this would be the total reported value of the population. Typically, this value is known for the entire population and may be estimated based on the statistical sample selected.
D The total value of the difference between the “paired” variable and the variable of interest. In audit sampling, this would be the estimated total difference of the population. Typically, this value is not known for the entire population and is estimated based on the statistical sample selected.
UR The confidence coefficient which is based on either the Student’s t-distribution or the normal distribution. For example, a 95% one-sided confidence coefficient based on the normal distribution is 1.645. This term is often referred to as the t-value and the z-value.

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