Associated Hypothesis in Linear Models with Unbalanced Data

Abstract

In a two-way linear model one can test six different hypotheses regarding the effects in this model. Those hypotheses can be ranked from less specific to more specific. Therefore the more specific hypotheses are nested in the less specific ones. To test those nested hypotheses sequential sums of squares are used. Searle sees a problem with these since they test an associated hypothesis that has the same sums of squares but involve the sample sizes. Hypotheses should be generic and not dependent on the data. The proof he uses in his book Linear Models for Unbalanced Data is not easy to understand. Therefore this thesis verifies his equations for the associated hypothesis for the nested hypotheses 'Only A present' given 'No interaction' with an unpublished theorem of Beder. It also shows a way to derive Searle’s equations for the associated hypothesis from this theorem.