A Case for Nonparametrics

We provide a case study for motivating and teaching nonparametric statistical inference alongside traditional parametric approaches. The case consists of analyses by Bracht et al. who use analysis of variance (ANOVA) to assess the applicability of the human microfibrillar-associated protein 4 (MFAP4) as a biomarker for hepatic fibrosis in hepatitis C patients. We revisit their analyses and consider two nonparametric approaches: Mood’s median test and the Kruskal-Wallis test. We demonstrate how this case study enables instructors to discuss critical assumptions of parametric procedures while comparing and contrasting the results of multiple approaches. Interestingly, only one of the three approaches creates groupings that match the treatment recommendations of the European Association for the Study of the Liver (EASL). We provide guidance and resources to aid instructors in directing their students through this case study at various levels, including R code and novel R shiny applications for conducting the analyses in the classroom.