This chapter discusses the nonparametric models, hypotheses, and test statistics for analysis of variance (ANOVA) and analysis of covariance (ANCOVA) designs, with independent and dependent ordinal data. This chapter presents the nonparametric models for two-way ANOVA and one-way ANCOVA. These are the simplest designs where all features of the nonparametric modeling can be appreciated. An important advantage of the nonparametric models is that these hypotheses and the procedures for analyzing them are unchanged by monotone transformations in the response. Decomposition for two-way ANCOVA that displays the covariate adjusted main effects and interactions of the two factors are easily obtained by replacing the single index. The nonparametric hypothesis of no interaction is equivalent to the statement that the mean of any transformation of the response can be decomposed in an additive fashion.
All Science Journal Classification (ASJC) codes