1. Randomized Complete Block Designs (RCBD)
The next design we'll discuss is a Randomized Complete Block Design, often abbreviated to RCBD.
2. RCBDs
In the last chapter, we conducted completely randomized experiments. One extension of that type of experiment is the RCBD, as described here. We utilize blocking in our experiments when we have a "nuisance" factor, something that may affect the outcome of the experiment, but isn't actually of interest to study in the experiment.
Blocking allows for the experimental groups to be more similar. We expect groups like those divided by metal hardness, type of crop, or gender, to have minimal differences inside the group, while across the different groups, we expect there to be much larger differences.
Sometimes, the blocking factor can be thought of not as a nuisance factor, but as something you can control as an experimenter. There's a saying in experimental design - "block what you can, randomize what you can't."
Essentially, you create blocks with your nuisance variable or variable you can control, and then run your completely randomized experiment inside each block for your desired number of repetitions.
3. RCBD workflow
In most texts or Experimental Design courses, the RCBD is demonstrated with an agricultural example. Say, for instance, you're testing a new fertilizer on your fields. Your outcome will be plant growth.
One factor that isn't of terrible interest in this experiment is the type of crop. So you block the fields: one block is corn and one soybeans. Then, inside of each block, you conduct a randomized control trial, allocating the fields randomly to either receive the new fertilizer or to use the standard method of growing the crop. Then, you measure the outcome at the specified time points and compare between the groups. This is a RCBD!
4. agricolae
While we're on the topic of agriculture, I'd like to introduce the agricolae R package. This package enables you to "draw" some of the different experimental designs possible, including an RCBD.
Let's walk through an example of using the package to draw a RCBD. We can create a treatment variable of four treatments, trt, using the R built-in lowercase letters. Then, we create an object rep, and assign it our four planned repetitions. We create our object design(dot)rcbd with the design(dot)rcbd function, which takes in our treatment, our rep, a seed, which tells the random number generator where to begin and allows for reproducibility, and set the serie input, which has to do with how the number blocks are tagged in larger experiments. If we examine the sketch object, we can see how our four repetitions with our four treatments can be randomly repeated in each run.
5. Model validation - Interaction plots
For exercises in this chapter, we would like to carry out model validations like we did in the previous chapter. In addition to the Normal QQ-plot and Residuals vs. Fitted plot, we'll also look at interaction plots.
Interaction plots help us understand the relationship between a continuous variable and a categorical variable in relation to another categorical variable. We hope to see parallel lines in an interaction plot, no matter which of the block or the treatment is on the x-axis.
The with function takes a dataset as an argument and evaluate an R expression in an environment constructed from data. Here's an example of the ToothGrowth dataset we worked with earlier. We take the dataset and ask it to plot an interactive plot between dose and length, with supplement type as a trace factor. The non-parallel lines indicates an interactive effect.
6. Let's practice!
Now that we know the basics of RCBDs and how to draw them with agricolae, let's jump in and try some examples.