Stratification, Balance, and Covariance

Some experimenters seek to avoid the need for randomized block designs by balancing the experimental units assigned to different treatments in respect of an initial quality. A particularly common instance is that of an animal nutrition experiment in which the initial mean weights of animals on the different diets are deliberately equalized by suitable allocation of animals to treatments. Apart from difficulties of maintaining an objective allocation, this procedure may achieve almost the same end as does a randomized block design, in increasing the true precision of treatment comparisons by eliminating variation associated with the factor used in balancing. What is often forgotten is that, if the statistical analysis appropriate to a completely randomized design is used, the experimental error will be overestimated; the more successful the balancing is in increasing true precision, the more seriously will the estimated precision so calculated fall below the truth. The explanation, and the manner in which the difficulty may be overcome, can be seen from comparison of four alternative experimental designs. Discussion of them will throw light on the practical utility of the balancing procedure.