ABSTRACT
Measuring the value of the covariate on the block, i.e., setting up blocks where all experimental units within a block have the same value of the covariate, is often used as a method of constructing blocks of experimental units. Animals are grouped by age, weight, or stage of life. Students are grouped by class, age, or by IQ. The grouping of the experimental units by the value of some covariate forms more homogeneous groups on which to compare the treatments than by not blocking. However, one must be much more concerned that there is no interaction between the levels of the treatments and the levels of the factor used to construct the blocks. An assumption of the RCB (randomized complete block), or as a matter of fact any blocked design structure, is that there is no interaction between the factors in the treatment structure and the factors in the design structure (Milliken and Johnson, 1992). It is not unusual to see researchers construct blocks by using a factor such as initial age or weight or current thickness. However, some thought should be taken into account about the possibility of interaction with the levels of the treatments. The usual approach to the analysis of such data sets is to remove the block to block variation by the analysis of variance and not consider doing an analysis of covariance, i.e., ignore the fact that a covariate was measured. That strategy is appropriate if the slopes of the treatments’ regression lines are equal, but if the slopes of the lines are unequal, a model with a covariate is required in order to extract the necessary information from the data. A block total or mean model must be used to make decisions about the slopes of the model before the analysis can continue.
