| Summary: | Research on language complexity has been abundant and manifold in the past two decades. Within typology, it has to a very large extent been motivated by the question of whether all languages are equally complex, and if not, which language-external factors affect the distribution of complexity across languages. To address this and other questions, a plethora of different metrics and approaches has been put forward to measure the complexity of languages and language varieties. Against this backdrop we address three major gaps in the literature by discussing statistical, theoretical, and methodological problems related to the interpretation of complexity measures. First, we explore core statistical concepts to assess the meaningfulness of measured differences and distributions in complexity based on two case studies. In other words, we assess whether observed measurements are neither random nor negligible. Second, we discuss the common mismatch between measures and their intended meaning, namely, the fact that absolute complexity measures are often used to address hypotheses on relative complexity. Third, in the absence of a gold standard for complexity metrics, we suggest that existing measures be evaluated by drawing on cognitive methods and relating them to real-world cognitive phenomena. We conclude by highlighting the theoretical and methodological implications for future complexity research.
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