Exact investigation of all effects for extensions of one-way Anova model with fixed effects

Abstract

Consider the standard one-way analysis of variance model with fixed effects. The customary assumptions of zero mean, no correlation, and equal variance are made for the random <<error>> terms in this balanced model. The usual normality assumption is also made when tests or confidence regions are desired. Extensions are made of this one-way model by addition of further <<error>> terms of one or two kinds. The extended models apply to much more general situations than does the standard model. However, exact procedures are obtained for investigating all the effects that appear in the standard model, and for investigating all the effects that appear in the standard model, and for investigating subsets of these effects. The generality level of an extension depends on what effects are investigated. For several extensions, the customary results for the standard model remain applicable. Some procedures differing from the customary ones are used for the other extensions. An application of the standard model to rejection of outlying observations is described and shown to be usable for some extensions.