Construction of Strata Boundaries in Tax Auditing

Abstract: Practice and Applications

The cumulative square root of the frequency (the "cum√f ") method is a generally accepted statistical technique used for the construction of strata boundaries in sampling. Many statistical consultants and state and federal taxing and auditing agencies utilize this method originally developed by Dalenius and Hodges (1959). But there is a general lack of guidance on the determination and effects of interval (i.e., class) widths. Dalenius and Hodges proposed the application of their method using frequency distributions with class widths of 5 units. In this paper, we present the results of empirical tests to contrast Dalenius' method with different class widths and to other approximate, non-iterative methods using several typical skewed accounting populations.

What is the problem and why? Most state revenue agencies use only the "cum√f ") method and with no prescribed class width usage. The purpose of the cum√f method is to approximate optimal boundaries by minimizing the product of the stratum weight multiplied by the true variance which the method seeks to accomplish by equalizing the cum√f across the strata (Cochran 1977). But this does not frequently happen with the common skewed accounting data.

What additional value does the presenter's approach provide? The research supports the conclusion that interval width (i.e., class width) has a meaningful effect on the cum√f method and the associated representativeness of the sample and the accuracy and precision of the estimate … and thus should be used dynamically and not as a one size fits all.

statistical sampling,

ax auditing

cumulative root frequency,

class width 

Practice and Applications

Symposium on Data Science and Statistics (SDSS) 2024