The Violating Assumptions Series: Simulated demonstrations to illustrate how assumptions can affect statistical estimates

Abstract

When teaching and discussing statistical assumptions, our focus is oftentimes placed on how to test and address potential violations rather than the effects of violating assumptions on the estimates produced by our statistical models. The latter represents a potential avenue to help us better understand the impact of researcher degrees of freedom on the statistical estimates we produce. The Violating Assumptions Series is an endeavor I have undertaken to demonstrate the effects of violating assumptions on the estimates produced across various statistical models. The series will review assumptions associated with estimating causal associations, as well as more complicated statistical models including, but not limited to, multilevel models, path models, structural equation models, and Bayesian models. In addition to the primary goal, the series of posts is designed to illustrate how simulations can be used to develop a comprehensive understanding of applied statistics.