Assessing the Relationship Between Statistical Model Assumptions and Empirical Data Violations in Practice

Posted: Dec 22, 2021

• Brooke Stewart
• Caleb Ross
• Caroline Foster

Abstract

Statistical modeling represents a cornerstone of empirical research, providing the analytical framework through which researchers test hypotheses, estimate parameters, and draw inferences about phenomena across scientific domains. The validity of these statistical procedures hinges critically on their underlying assumptions—mathematical conditions that must be satisfied for the procedures to yield accurate results. Traditional statistical training emphasizes the importance of testing these assumptions, with textbooks and courses dedicating substantial attention to diagnostic procedures such as normality tests, homogeneity of variance assessments, and independence checks. However, a fundamental disconnect exists between the theoretical treatment of statistical assumptions and their practical manifestation in empirical research. This disconnect raises critical questions about how assumption violations actually impact research conclusions and whether current methodological practices adequately address these challenges. The conventional approach to statistical assumptions typically follows a binary framework: assumptions are either satisfied or violated, with violations prompting either data transformation, alternative analytical methods, or qualitative caveats about result interpretation. This binary perspective, while computationally convenient, fails to capture the nuanced reality of empirical data, where assumption violations exist on a continuum and often interact in complex ways. Moreover, the practical consequences of assumption violations remain poorly characterized, with limited empirical evidence about how different types and