Abstract
A new method of statistical analysis of texts is suggested. The frequency distribution of the first significant digits in numerals of connected authorial English-language texts is considered. Benford's law is found to hold approximately for these frequencies with a marked predominance of the digit 1. Deviations from Benford's law are statistically significant author peculiarities that allow, under certain conditions, to consider the problem of authorship and distinguish between texts by different authors. At the end of {1, 2,…, 8, 9} row, the digits distribution is subject to strong fluctuations and thus unrepresentative for our purpose. The approach suggested and the conclusions are backed by the examples of the computer analysis of works by W. M. Thackeray, M. Twain, R. L. Stevenson et al. The results are confirmed on the basis of non-parametric range Mann-Whitney and Kruskal-Wallis tests as well as the parametric Pearson's chi-squared test.
Highlights
The scope of the practical use of Benford’s law [1] has significantly expanded
Known for over a hundred years, Benford's law refers to the probability of occurrence of a certain first significant digit in the distribution of various real life data
We present here new research results concerning the distribution of the first significant digits of numerals contained in coherent English-language texts
Summary
The scope of the practical use of Benford’s law [1] has significantly expanded. In contrast to the traditional methodology of application of Benford's law, which treats deviations from the law as an indication of the possible existence of "falsification" (broadly defined), he placed emphasis on the comparison of these deviations for texts by different authors, showing that these deviations are statistically robust author features that allow to distinguish between texts by different authors (under certain conditions, the most important of which is a sufficiently large text) Basing on these ideas, we present here new research results concerning the distribution of the first significant digits of numerals contained in coherent English-language texts. For all (English-language fiction) texts subjected to computer-aided statistical analysis, we have studied the frequency of occurrence of various first significant digits of numerals, taking into account cardinal as well as ordinal numerals expressed both in figures, and (considerably more often) verbally. Texts analyzed are mainly taken from the Project Gutenberg website http://www.gutenberg.org
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