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We provide a discussion of some of the challenges in using statistical methods to investigate the morphology-syntax distinction cross-linguistically. The paper is structured around three problems related to the morphology-syntax distinction: (i) the boundary strength problem; (ii) the composition problem; (iii) the architectural problem. The boundary strength problem refers to the possibility that languages vary in terms of how distinct morphology and syntax are or the degree to which morphology is autonomous. The composition problem refers to the possibility that languages vary in terms of how they distinguish morphology and syntax: what types of properties distinguish the two systems. The architecture problem refers to the possibility that languages vary in terms of whether a global distinction between morphology and syntax is motivated at all and the possibility that languages might partition phenomena in different ways. This paper is concerned with providing an overarching review of the methodological problems involved in addressing these three issues. We illustrate the problems using three statistical methods: correlation matrices, random forests with different choices for the dependent variable, and hierarchical clustering with validation techniques. [ABSTRACT FROM AUTHOR]