Nonparametric models and results for two-way ANOVA with fixed effects and interactions

Abstract

Considered are balanced factorial models for two-way analysis of variance with fixed effects, interaction terms, and replication. The data are continuous and there are at least four replications. Specialized definitions, with a median orientation, are given for the constant term, for contrasts in the two kinds of main effects, and for contrasts in the interactions. For normality models and other important models, however, the parameter values yielded by the special definitions are the same as the values occurring for these models. Independence among replications is the only necessary assumption, and even this can be weakened in some cases. With only this assumption, approximate confidence intervals, tests, and median estimates are obtained for the constant term and for contrasts in the three types of effects. Exact intervals and tests are obtained for some special situations of a moderately general nature. Procedures of a sign test type are used for some of the exact results but the procedures for investigation of symmetry about zero can be used to develop exact intervals and tests for some other situations. The basis for the models and results is the linearized nonlinear regression approach.