ABSTRACT
Many experiments begin with a well-thought-out plan but run into problems during execution. Sometimes experiments are intentionally unbalanced. Unbalanced experiments are more difficult to analyze than balanced ones, requiring special care for estimation and testing. Unbalanced design structures have unequal sample sizes across factor combinations. Estimation and testing of main effects in the additive model with unequal sample sizes are rather complicated, while in the full model with interaction, estimation of main effects is fairly direct. There are two main types of imbalance, one more serious than the other. Imbalance requires careful consideration of how to compare means, which becomes clearer after examining the additive model. There are several ways to extract sums of squares from the total to address hypotheses. Four types are developed which have distinct uses in testing, although they are all equivalent for the balanced experiment : Type I, Type II, Type III and Type IV.
