Nonparametric results for two-way ANOVA with fixed effects, no interactions, and unequal subclasses

Abstract

Considered are unbalanced cross-classification models for two-way analysis of variance with fixed effects and no interaction terms. At least one observation occurs for each combination of factor levels, each factor has at least four levels, and the data are continuous. Special definitions with a median basis are used for contrasts in each of the two types of effects and for the constant term. However, the parameter values resulting from the special definitions are the same as occur for normality models and other important kinds of models. Subject only to independence among the error terms, approximate tests, confidence intervals, and median estimates are developed for stated contrasts in each of the kinds of effects. In general, an exact median estimate occurs for the constant term (the only procedure for this parameter). Exact tests and intervals are developed for some cases of a moderately general nature. Sign test types of procedures provide the basis for some of the exact results, but others can be based on the numerous procedures developed for investigating symmetry about zero. The models and investigation methods presented are based on the linearized nonlinear regression approach.