Blocking Field Trials and the First Law of Geography

I’m studying for my prelims this semester, which involves going back over the classes I’ve taken over the last 4 years, reviewing my research proposal, and just generally refreshing my memory about the topics a person with a PhD in agronomy should know. I’m focusing on traditional statistics and experimental designs this week, which reminded me that I’ve never actually blogged about some of my favorite ANOVA resources. Today I’ll share some blocking and experimental design tips, and next week I’ll get into more mixed-model analysis resources.

Treatments in small-plot agronomic studies are usually arranged in a randomized complete block design (RCBD), a type of restricted randomization pattern. Other common small-plot trial designs are factorial and split-plot designs, which are also usually blocked.

Most spatial blocking patterns are just an extension of the first law of geography (things that are closer together are more similar to each other than things that are further apart). When we are using an ANOVA to determine if there are significant differences in yield between treatments (as is most common in my work), blocking plots based on location helps account for the variation in yield that is due to spatial variability in yield.

A sketch of a field layout of a randomized complete block design small plot trial with 4 treatments, and 5 replicates or blocks. The first block is in the area of lowest elevation, and the fifth block is in the area of highest elevation.

When we block plots, we want our blocks to run perpendicular to a known gradient in the field (see sketch to the left). In this example, accounting for the variation in yield due to elevation improves our ability to detect differences in yield due to treatment. Sarah Mueller has a great explanation of blocking as part of the conceptual introduction to her R package plotdesignr, and the gradient maps and yield distributions help visualize what happens when you don’t block, or block incorrectly.

For any experimental design, it’s important to understand the model that the ANOVA is actually fitting. In the model statement for an RCBD experiment, the grand mean, effect of treatment, effect of block, and residuals are summed. But, since treatments are not typically replicated within blocks, there is not a term for treatment*block interactions. This differs from other two-way ANOVAs, and I highly recommend reading Lukas Meier’s explanation of block designs to learn more. I’ve long recommended his comparison of multiple testing techniques, especially for people who like lots of examples and code chunks, but somehow I didn’t come across his blocking chapter til now.

As much as I’d love to keep rambling about blocking, I really should go study some more. Thanks for reading, and subscribe to the blog if you want a notification for the upcoming ANOVA post!

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