Chapter 2 ANOVA-unbalanced, no blocking 2.1
Introduction
In this section we consider the situation where not all the treatments have the same number of replications, yet we wish to test whether there are differences amongst treatments. Ofter experiments start with balanced deisgns but for some reason or another units are lost. Consider the situation where 2 car batteries (battery A and battery B) with 4 replications are tested over a year. At some point during the year one of battery A starts to leak and it has to be dismissed from the experiment- the experiment now consists of an unblanced design since we are left with 3 replictions of battery and 4 from group B. The techniques developed below will address how to deal with unbalanced designs in non blocked experiments.
2.2
Unbalanced designs
The model used is similar to the model used for balanced designs, this time however treatment i is restricted to ri replications. Mathematically let Yij be the response variate, τi the treatment, µ the mean and Rij the random error, then: (2.1)
Yij = µ + τi + Rij
where i = {1, 2, ..., t}, j = {1, 2, ..., ri }
As before a restraint is required on the τi s: X ri τ i = 0 i
Under this model: 9