To gain an appreciation or understanding for the title of this study we must first understand what the phrases "non-orthogonal" and "error structure" mean. With an understanding of these terms the title of this study will become clear. To obtain an understanding of the term non-orthogonal, consider an experiment where differing treatments are applied to groups of experi­mental units in order to observe the differential treatment responses. If an equal number of experimental units are in each group, then we say we have an orthogonal situation. This means that when equal numbers exist among the experimental units, that the variability associated with the individual sources of variation can be orthogonally partitioned, such that the sources of variability add to the total source of variation. However, if unequal numbers exist among the experimental units, then we say we have a non-orthogonal situation. This implies that we can no longer obtain a completely orthogonal partition, and that the sources of variability associated with the individual sources of variation do not add to the total source of variation. The phrase, error structure, can best be described with reference to the statistical technique known as the analysis of variance. For any typical analysis of variance, there exists a one to one correspondence between the mean squares and the recognized sources of variation in the underlying model.