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In fact, we will use the transpose of this picture, so that the treatments will correspond to the columns of the data representation and the rows will corresponding to the blocking factor.Įxample 1: A company that plans to introduce a new type of herbicide wants to determine which dosage produces the best crop yield for cotton. This picture takes the following form when we add the yield:Īctually, the order of the fields within each farm is not important in the analysis, and so we can view the yields per field in the following form: In a randomized complete block design, we assign the seeds such that each of the three fields in any farm is assigned a different seed type. Note that the one-way ANOVA model corresponds to what is called a completely randomized design (CRD). As we can see from the equation, the objective of blocking is to reduce the variability of the error term, which results in a more accurate way to detect differences between the treatments.

Which is equivalent to the two-factor ANOVA model without replication, where the B factor is the nuisance (or blocking) factor. Here a block corresponds to a level in the nuisance factor. We now consider a randomized complete block design (RCBD). If the nuisance variable is known but uncontrollable we can use ANCOVA, while if the nuisance variable is unknown and/or uncontrollable then we must reply on randomization to balance out its effect. If the nuisance variable is known and controllable, then we use blocking. If, for example, we want to test the difference between different fertilizers on crop yield, we can apply a different fertilizer (the treatment) at random to different plots in the block (therefore controlling for the nuisance factors). In agriculture, a block consists of contiguous plots of land that share the same characteristics (moisture, fertility, acidity, etc.).

For the design described in CRD & RCDB, the Farm is such a nuisance factor since each farm potentially has different levels of moisture, fertility, etc. a variable which is not of interest, except that it has some influence on the variables that are of interest.