Nonparametric analysis of interactions: A review and gap analysis

To improve a system, from a statistical process control approach, tools from the field of design and analysis of experiments might be used. Within this field, experimental and observational studies address the issue of finding causal relationships between potential factors and response variables. To collect data, experimental design techniques are used to obtain information about the different factors of interest. This is followed by an analysis typically performed with ANOVA or regression techniques, where normality of residuals is frequently assumed. Nevertheless, many processes are not prone to having normally distributed errors, outliers might be present, and observations might be heteroscedastic, which diminish the power of detecting effects on the response variable. To address this issue, nonparametric procedures have been developed. However, most techniques are focused on detecting main effects; and only a few of them take into account interactions. This paper discusses the problem of assessing interactions with the fixed effects model, presents a literature review of nonparametric approaches to interactions testing, and concludes with a gap analysis to identify future research avenues. Practitioners looking for nonparametric alternatives to ANOVA, especially when dealing with interactions, may find these research results useful.