One of the main goals of statistical modelling is to understand the dependence of a response variable, Y, with respect to another explanatory variable, X. This type of dependence can be studied through nonparametric regression models, where the relationship between Y and X is modelled without specifying in advance the function that links them. Within this framework, the study of the regression curves can be useful in the comparison of two or more groups, which is an important problem associated with statistical inference. In particular, the topic of hypothesis testing the equality of mean functions has been widely investigated in the literature, see, for instance, the review that González-Manteiga and Crujeiras (2013) offers about this topic. Relevant papers on this topic are Hall and Hart (1990); King et al. (1991); Delgado (1993); Kulasekera (1995); Young and Bowman (1995); Dette and Neumeyer (2001); Pardo-Fernández et al. (2007); Srihera and Stute (2010), among others. Furthermore, in order to compare the values of a response variable across several groups in the presence of a covariate effect, nonparametric analysis of covariance or factor-by-curve interaction test can be used. Young and Bowman (1995) generalized the one-way analysis of variance test to the nonparametric regression setting, and Dette and Neumeyer (2001) proposed to use Young and Bowman's test also in the situation of a heteroscedastic error. In addition, Park and Kang (2008) developed a SiZer tool based on an analysis of variance type test statistic that is capable of comparing multiple curves based on the residuals. The evolution of this procedure is based on the comparison using the original regression curves (Park et al., 2014).