ABSTRACT
Chapter 7 discusses non-parametric and robust statistical methods as essential alternatives when data violate classical assumptions. It begins by noting that real-world data are often non-normal, heteroskedastic, or contain outliers, which can mislead traditional parametric tests (e.g., t-tests and ANOVA). The chapter introduces non-parametric tests (such as the Mann–Whitney U and Kruskal–Wallis H) that operate on ranked data without assuming normality, thus maintaining valid Type I error rates even under skewed distributions. It also covers robust techniques like bootstrapping and the use of trimmed means, which increase the resilience of estimates against outliers and assumption violations. Key examples illustrate that while non-parametric and robust methods may sacrifice some power under ideal conditions, they yield more trustworthy results for non-normal or small-sample datasets. The chapter emphasizes the importance of these methods in the digital data era – researchers can confidently analyze data that do not meet textbook assumptions by using distribution-free tests and robust estimators. In summary, Chapter 7 highlights how adapting our analytical approach to the data (instead of forcing data into inappropriate models) enhances the validity and reliability of conclusions when standard assumptions are unmet.
