Yates was perhaps the first person to describe the designs and analysis of split plot experiments. In a 1933 paper, reprinted in (68), he discussed the principles of orthogonality and confounding in replicated experiments. He suggested two separate analyses, one for the whole plots and one for split plots (68, pg88). Incorporating Yates ideas, this thesis explores a generalization of this two stage analysis for non-orthogonal split plot designs. This two stage approach is used in designs where runs from one experiment are the blocks for another experiment, resulting in two stages of the experiment. The blocking defines the whole plot error structure in such experiments.

Traditional definitions for resolvability and balance of block designs are modified to explain split plot design structures. Most split plot experiments in the statistical literature are resolvable in this sense. Balance in a design is often not practical as the block sizes that are physically possible require an unreasonable number of whole plots to make a 'mathematically' nice design, therefore creating a source of inefficiency. Incomplete block designs and factorial design are melded to obtain 'nice' practical unbalanced split plot designs. The two stage analysis method can be applied to non-resolvable or 'unbalanced' split plot designs. While the precision of estimates may be slightly lower than those obtained by using Restricted Maximum Likelihood Estimation (from SAS^©), they are less sensitive at the subplot level to model misspecification. Design discussion is based on whether the treatments have a factorial structure or not.

Efficiency factors at the whole plot level are calculated analogous to the definition given in block designs. We have shown that all the eigenvalues of the efficiency factor are equal to one for resolvable designs, resulting in all the estimates being orthogonal. A discussion of designs with resolvable strata is also presented. Either the traditional block design theory or computer generated optimal designs can be used to obtain optimal split plot design plans based on the experimenter's requirements. There is also an inclusion of the design recommendations with emphasis on resolvability and partial resolvability.