An investigation of the validity of auditing procedures used in mean-per-unit sampling plans

Abstract

Information from accounting literature indicates that the mean-per-unit (MPU) estimator may not properly control the alpha and beta risks under conditions of non-normality. This study concerns the effect of non-normal distributions on the validity of existing auditing procedures used in MPU sampling plans. The following question was specifically addressed: Are alpha and beta risk levels effectively controlled under conditions of non-normality when using the MPU estimator in conjunction with the sample size formula?

One objective of the study was to provide evidence that a potential problem exists when using traditional statistical sampling techniques with non-normal auditing populations. Another objective of the research was to provide recommendations that would lead to better auditing practices involving the MPU estimator.

A simulation study using positively skewed J-shaped distributions was conducted to provide a means for achieving the objectives of the research. The distributions used in the study ranged in degrees of skewness and kurtosis from 0.0 and 3.0081 to 25.6089 and 37.7937, respectively. Simulation procedures considered a two-sided alpha level, an upper beta level concerning the potential acceptance of a materially overstated account, and a lower beta level for the potential acceptance of an account that is materially understated.

Simulation results indicate that specified alpha and beta levels are not always attained when using the MPU estimator under conditions of non-normality. Guidelines were then developed for Simultaneous control of alpha and beta risk levels under the non-normal conditions simulated in the research. Case studies were utilized to test and illustrate use of the guidelines. Results of the study are limited, however, because implementation of the guidelines requires a positively skewed audit population reflected by a J-shaped distribution within the degrees of skewness and kurtosis Simulated in the study.