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Classical null hypothesis significance tests are not appropriate in corpus linguistics, because the randomness assumption underlying these testing procedures is not fulfilled. Nevertheless, there are numerous scenarios where it would be beneficial to have some kind of test in order to judge the relevance of a result (e.g. a difference between two corpora) by answering the question whether the attribute of interest is pronounced enough to warrant the conclusion that it is substantial and not due to chance. In this paper, I outline such a test.
In the first volume of Corpus Linguistics and Linguistic Theory, Gries (2005. Null-hypothesis significance testing of word frequencies: A follow-up on Kilgarriff. Corpus Linguistics and Linguistic Theory 1(2). doi:10.1515/cllt.2005.1.2.277. http://www.degruyter.com/view//cllt.2005.1.issue-2/cllt.2005.1.2.277/cllt.2005.1.2.277.xml: 285) asked whether corpus linguists should abandon null-hypothesis significance testing. In this paper, I want to revive this discussion by defending the argument that the assumptions that allow inferences about a given population – in this case about the studied languages – based on results observed in a sample – in this case a collection of naturally occurring language data – are not fulfilled. As a consequence, corpus linguists should indeed abandon null-hypothesis significance testing.
Large-scale empirical evidence indicates a fascinating statistical relationship between the estimated number of language users and its linguistic and statistical structure. In this context, the linguistic niche hypothesis argues that this relationship reflects a negative selection against morphological paradigms that are hard to learn for adults, because languages with a large number of speakers are assumed to be typically spoken and learned by greater proportions of adults. In this paper, this conjecture is tested empirically for more than 2000 languages. The results question the idea of the impact of non-native speakers on the grammatical and statistical structure of languages, as it is demonstrated that the relative proportion of non-native speakers does not significantly correlate with either morphological or information-theoretic complexity. While it thus seems that large numbers of adult learners/speakers do not affect the (grammatical or statistical) structure of a language, the results suggest that there is indeed a relationship between the number of speakers and (especially) information-theoretic complexity, i.e. entropy rates. A potential explanation for the observed relationship is discussed.
Studying Lexical Dynamics and Language Change via Generalized Entropies: The Problem of Sample Size
(2019)
Recently, it was demonstrated that generalized entropies of order α offer novel and important opportunities to quantify the similarity of symbol sequences where α is a free parameter. Varying this parameter makes it possible to magnify differences between different texts at specific scales of the corresponding word frequency spectrum. For the analysis of the statistical properties of natural languages, this is especially interesting, because textual data are characterized by Zipf’s law, i.e., there are very few word types that occur very often (e.g., function words expressing grammatical relationships) and many word types with a very low frequency (e.g., content words carrying most of the meaning of a sentence). Here, this approach is systematically and empirically studied by analyzing the lexical dynamics of the German weekly news magazine Der Spiegel (consisting of approximately 365,000 articles and 237,000,000 words that were published between 1947 and 2017). We show that, analogous to most other measures in quantitative linguistics, similarity measures based on generalized entropies depend heavily on the sample size (i.e., text length). We argue that this makes it difficult to quantify lexical dynamics and language change and show that standard sampling approaches do not solve this problem. We discuss the consequences of the results for the statistical analysis of languages.
Diachrone Wortschatzveränderungen werden in der Regel exemplarisch anhand bestimmter Phänomene oder Phänomenbereiche untersucht. Wir widmen uns der Frage, ob und wie Wandelprozesse auch auf globaler Ebene, also ohne sich auf bestimmte Wortschatzausschnitte festzulegen, messbar sind. Zur Untersuchung dieser Frage nutzen wir das Spiegel-Korpus, in dem alle Ausgaben der Wochenzeitschrift seit 1947 enthalten sind. Dabei gehen wir auf grundlegende Herausforderungen ein, die es dabei zu lösen gilt, wie die Verteilung sprachlicher Daten und die Folgen unterschiedlicher Subkorpusgrößen, d.h. im konkreten Fall die variierende Größe des Spiegelkorpus über die Zeit hinweg. Wir stellen ein Verfahren vor, mit dem wir in der Lage sind, flankiert von einem „Lackmustest“ zur Überprüfung der Ergebnisse, Wortschatzwandelprozesse bis auf die Mikroebene, d.h. zwischen zwei Monaten oder gar Wochen, quantitativ nachzuvollziehen.