Does the usage of an online EFL workbook conform to Benford’s law?

Abstract

The aim of this paper is to explore if English as a Foreign Language (EFL) learners' usage of an online workbook follows Benford's law, which predicts the frequency of leading digits in numbers describing natural phenomena. According to Benford (1938), one can predict the frequency distribution of leading digits in numbers describing natural datasets, e.g. river lengths. In such numbers, the digit 1 occurs most frequently, while the digit 9 occurs least-frequently. This counterintuitive phenomenon attracted the attention of researchers seeking inconsistencies in data, e.g. false tax claims (Miller, 2015). We show that the practical application of Benford's law could extend to detecting abnormal learner behaviour in online EFL products. First, we show that the distributions of leading digits of the number of online activities submitted by EFL learners on an e-learning platform and the time spent on those activities do indeed follow Benford's law. Then, we show that some learners whose behaviour does not conform to Benford's law show online behaviour that is abnormal relative to their peers-in particular, they submit many activities in a few days, which could suggest, for example, poor time management.