Study on the effect of sample size on type I error,in the first,second and first-two digits excessmad tests |
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| Affiliation: | 1. Department of Economics, National Tsing Hua University, Taiwan;2. Department of Economics, National Taiwan University, Taiwan;3. Department of Business Administration, National Central University, Taiwan;1. Case Western Reserve University, Weatherhead School of Management, 10900 Euclid Ave., Cleveland, OH 44106, United States of America;2. Nova Southeastern University, H. Wayne Huizenga School of Business and Entrepreneurship, 3301 College Avenue, Davie, FL 33314, United States of America;3. University of Kansas, School of Business, Capitol Federal Hall, 1654 Naismith Drive, Lawrence, KS 66045, United States of America;1. University of Antwerp, Belgium;2. University of Antwerp, Belgium & Tilburg University, The Netherlands;3. University of Antwerp & KU Leuven, Belgium;1. Universidad de Huelva, Faculty of Business, Department of Financial Economics and Accounting, Spain;2. Universidad Pablo de Olavide, Faculty of Business, Department of Financial Economics and Accounting, Spain;3. Department of Financial Economics, Accounting and Operations Management, University of Huelva, Spain and Higher Institute for Accountancy and Administration, University of Aveiro, Portugal;1. Business School, University of Shanghai for Science and Technology, 516 Jungong Rd., Shanghai, 200093, China;2. School of Mathematics & Data Science, Shaanxi University of Science & Technology, 7 Xuefu RD., Xi''an, 710021, China;3. College of Economics and Management, Shaanxi University of Science & Technology, 7 Xuefu RD., Xi''an, 710021, China |
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| Abstract: | The first-two digits ExcessMAD test was created in 2016, allowing to evaluate whether a certain data set conforms to Benford’s Law (BL). The purpose of this study is to explore some questions that remained open: develop the exact and approximate mathematical formulation of the first and second digit ExcessMAD test and study the type I error of these tests when applied to different sample sizes conforming to BL and to the uniform distribution, due to its wide use in accounting data. The importance of this study is to make available to accountants, auditors and researchers the first and second digit ExcessMAD tests, which will make it possible to conduct further investigations involving BL, especially for smaller samples. In addition, the relevance of the type I error analysis stems from the reduction of unnecessary additional studies for the investigation of non-conformity, in the case of the erroneous rejection of the null hypothesis stated as conforming to BL. The application of the second digit ExcessMAD test in the uniform distribution reveals that the close proximity between the uniform and BL distributions can lead to misinterpretations. Based on the exact and approximate mathematical formulations of the three ExcessMAD tests and the use of the Monte Carlo simulation technique, samples were generated in accordance with the BL and uniform distributions, with sizes between 100 and 3,500 elements, which allowed the study of type I error and the comparison of the tests applied to those distributions. This paper seeks to cover three gaps in the literature on ExcessMAD tests. In the previous studies, the following approaches were not found: the exact and approximate mathematical formulation of the first and second digit ExcessMAD tests; the analysis of type I error in these tests and the comparison of such results in the BL and Uniform distributions. |
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| Keywords: | Benford’s Law First Second and first-two digits ExcessMAD test Monte Carlo simulation Type I error |
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