Benford’s Phenomenon to Scientific Explanation in Kennesaw, GA
Disciplines
Mathematics
Abstract (300 words maximum)
This research investigates the application of Benford’s Law in analysing the first-digit probabilities of real-world functions, focusing on economic data. Six datasets were collected, each containing an index and actual data values, ensuring statistical fairness and a sample size exceeding 100 for validity. Using Excel, the data was structured and transformed to simplify calculations, enabling graphical representations for analysis.
The study found that Benford’s Law, which was originally developed for datasets following exponential rules, was not observed in the analysed functions due to the specific nature of the data. While the law can be applied to other algebraic functions, each type of function provides a unique formula for first-digit probabilities. The selected datasets did not align with the expected probability distribution, partly due to inconsistencies such as abrupt jumps instead of a continuous sequence. The graphical visualization of data played a crucial role in identifying these deviations.
These findings emphasize that while Benford’s Law is a powerful tool for detecting irregularities in naturally occurring datasets, its applicability depends on the dataset's underlying structure. The study highlights that the law's effectiveness is not universal and varies with different algebraic functions. Understanding when Benford’s Law does not apply is equally valuable, as it prevents misinterpretation in fraud detection and data validation. This study reinforces the importance of careful dataset selection in statistical analysis and data science applications.
Academic department under which the project should be listed
CSM - Mathematics
Primary Investigator (PI) Name
Irina Pashchenko
Benford’s Phenomenon to Scientific Explanation in Kennesaw, GA
This research investigates the application of Benford’s Law in analysing the first-digit probabilities of real-world functions, focusing on economic data. Six datasets were collected, each containing an index and actual data values, ensuring statistical fairness and a sample size exceeding 100 for validity. Using Excel, the data was structured and transformed to simplify calculations, enabling graphical representations for analysis.
The study found that Benford’s Law, which was originally developed for datasets following exponential rules, was not observed in the analysed functions due to the specific nature of the data. While the law can be applied to other algebraic functions, each type of function provides a unique formula for first-digit probabilities. The selected datasets did not align with the expected probability distribution, partly due to inconsistencies such as abrupt jumps instead of a continuous sequence. The graphical visualization of data played a crucial role in identifying these deviations.
These findings emphasize that while Benford’s Law is a powerful tool for detecting irregularities in naturally occurring datasets, its applicability depends on the dataset's underlying structure. The study highlights that the law's effectiveness is not universal and varies with different algebraic functions. Understanding when Benford’s Law does not apply is equally valuable, as it prevents misinterpretation in fraud detection and data validation. This study reinforces the importance of careful dataset selection in statistical analysis and data science applications.