How Is This Design a Randomized Complete Block Design?

Question

I recently started learning about one-way ANOVA, multiple comparisons, and contrasts. At the moment, I have an introductory-level knowledge of these concepts.

I'm analysing an experiment that compares the effects of two preparation of hormone A (hormone treatments 1 and 2), two preparations of hormone B (hormone treatments 3 and 4), and a control (hormone treatment 5) on the growth of some food-producing plant. These plants are grown in a glasshouse, in individual pots, and the pots are arranged in three sand trays. Each treatment occurs once in each tray.

The experimenters of this experiment recorded the plant height at flowering in cm and the yield for each plant.

My introductory-level understanding of a Randomized Complete Block Design (RCBD) is as follows:

We have a non-uniform group of subjects. We then split this non-uniform group of subjects into "blocks" of uniform subjects. We now have 2 groups of subjects, each group being uniform. Call these two groups $A$ and $B$. We then select from each of these two groups at random, splitting each of $A$ and $B$ into 2 subgroups. So after splitting $A$ randomly, we have the two subgroups $A_1$ and $A_2$. And after splitting $B$ randomly, we have the two subgroups $B_1$ and $B_2$. Now, let's say we have only 2 treatments for this example. We would now apply treatments 1 and 2 to one of the randomly-selected subgroups: so, say, $A_1$ gets treatment 1, $A_2$ gets treatment 2, $B_1$ gets treatment 1, and $B_2$ gets treatment 2.

Is this understanding correct?

What I'm confused about is how the experiment I mentioned earlier is a Randomized Complete Block Design. I don't see the connection between it and the example I just gave.

I would greatly appreciate it if people could please take the time to clarify this.

Answer 1

You have one factor (independent variable) that is the treatment condition. There are five levels of this factor (four treatment and one control). You have a second factor that is a blocking factor that is the sand trays. It is a block randomized design because randomization into the five conditions is occurring within each tray (you could not have balance within trays if you did not do this). Because randomization is constrained in this way, you must take that into account when you analyze, including both the blocking factor and treatment factor in the analysis.