(98) Non-Normality and Heteroskedasticity in Linear Regression: A Practice-Oriented Summary
Date:
Contributors: Rajh-Weber, H. , Huber, S. E., Arendasy, M.
Venue: 91st Annual Meeting oft he Psychometric Society, IMPS 2026, Seoul, Republic of Korea, July 21-24, 2026
Abstract: Violating linear regression assumptions, specifically homoskedasticity, can noticeably influence the validity of null hypothesis significance tests on regression coefficients. It may seem reasonable to apply a two-step process, where alternative robust methods are used once violations are detected, and indeed, many such tests for assumption violations exist. In our studies, we, for one, assessed the performance of many well-known robust inference methods in the context of linear regression and compared well-known assumption violation tests for normality and homoskedasticity. We only chose tests or methods that are also available in the commercial software SPSS to enhance practical utility for applied researchers. Further, we simulated the aforementioned two-step approach using combinations of the assumption violation tests and robust inference methods with the best performance. Our findings show that there is no simple solution for what should be done if linear regression assumptions are violated. Which particular inference method works best, in terms of type I error rate and power, depends on the pattern of heteroskedasticity, severity of non-normality, sample size and whether the assumption violation is associated with the predictor of interest. Similar results hold true for the assessed assumption violation tests. This led to the two-step approach overall showing poor performance, namely inflated type I error rates in small samples and no benefit over always using robust methods in large samples. Thus, we can generally not recommend such a two-step approach to inference in linear regression problems.