Associated Hypothesis in Linear Models with Unbalanced Data

Rica Wedowski
MS Student
University of Wisconsin-Milwaukee

“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 hypothesis are nested in the less specific ones. To test those nested hypotheses sequential sums of squares are used. Searle sees a problem with those 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this thesis verifies his associated hypothesis for the nested hypotheses Only A present given No interaction with an unpublished theorem of Beder.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 this associated hypothesis from this theorem”.

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