### Mainusch, NM (2020)

#### On Benford's law - Computing a Bayes factor with the Savage-Dickey method to quantify conformance of numerical data to Benford's law

Bachelor's Thesis, University of Osnabrueck, Institute of Cognitive Science, Germany.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

**Abstract:** Benford’s law is a statistical phenomenon stating that the distribution of significant digits occurring in various natural data sets, amongst others population numbers,stock prices and physical constants, follows a logarithmically decaying pattern. By conducting an exploratory behavioral experiment, we confirm that this regularity is neglected to preserve when humans forge numbers, where forensic digit analysis can reveal the irregularities and support the detection of fraud in scientific, economic and political data. The classical null hypothesis significance testing approach, represented amongst others by the χ2-test, cannot quantify how conform the data is to the Benford distribution, but returns only dichotomous decisions. With an increasing amount of data, any deviation from Benford’s law is classified as significant, not allowing to specify the researcher’s degree of uncertainty about the data generating process. These detriments can be addressed with the Bayesian approach to hypothesis testing, as it is proposed in this thesis. Employing the Savage-Dickey method, we calculate a Bayes factor for different prior distribution specifications in the Multinomial-Dirichlet model. By means of a simulation study, we show that the proposed prior distributions allow for a differentiated evaluation of the data and that the Bayesian approach is not prone to reject the null hypothesis that the data conforms to Benford’s law disproportionately often.

**Bibtex:**

```
@mastersthesis{,
type = "Bachelor's Thesis",
author = "Mainusch, Nina M.",
title = "On Benford's law - Computing a Bayes factor with the Savage-Dickey method to quantify conformance of numerical data to Benford's law",
school = "University of Osnabrueck",
year = "2020",
month = "February"
}
```

**Reference Type:** Thesis

**Subject Area(s):** Statistics