Statistical laws in linguistics
This work addresses the problem of accurately interpreting and testing linguistic laws for researchers in computational linguistics and statistical analysis, but it is incremental as it builds on existing critiques and methods.
The paper critically examines statistical laws in linguistics, such as Zipf's law, by analyzing large text databases to test their validity and fluctuations, finding that fluctuations are larger than expected and can lead to misinterpretations in falsification tests.
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern availability of large databases of written text allows for tests with an unprecedent statistical accuracy and also a characterization of the fluctuations around the typical behavior. We find that fluctuations are usually much larger than expected based on simplifying statistical assumptions (e.g., independence and lack of correlations between observations).These simplifications appear also in usual statistical tests so that the large fluctuations can be erroneously interpreted as a falsification of the law. Instead, here we argue that linguistic laws are only meaningful (falsifiable) if accompanied by a model for which the fluctuations can be computed (e.g., a generative model of the text). The large fluctuations we report show that the constraints imposed by linguistic laws on the creativity process of text generation are not as tight as one could expect.