Study design for a hypothetical agricultural experiment

[Clyde Schechter]

I'm sorry that this topic is a little outside the domain of the Stata forum, but I really don't know where else to turn for advice. It is about how certain types of agricultural experiments are normally conducted. It is tangentially related to statistics, not at all to Stata.

I am tutoring some high school students for the AP statistics exam. One of the practice questions we reviewed asks the examinee to set out a study design to test the effects of three different fertilizers on the growth of certain agricultural plants. The question specifically asked for detailed focus on assigning plots to treatments.

One student proposed that the plots first be grouped into larger contiguous units, and then the larger units should be randomized to receive one of the three treatments.

I countered that I thought that the plots should not be so grouped but should be directly randomized to receive one of three treatments. My rationale was that randomization would reduce the likelihood of confounding treatment with things like sunlight exposure, shade, soil quality and access to ground water that would, I thought, likely be somewhat homogeneous over a large group of contiguous plots.

But the student countered that if the plots were randomized individually, the fertilizer would migrate from plot to adjacent plot, carried by wind, itinerant animals, rain, or irrigation water. So individual plot randomization would actually end up treating each plot with an unknown mixture of all three treatments.

I think we are both right here. But I have been an urban dweller all my life, and my experience with agriculture is limited to a small number of house plants that all quickly died under my care. So what do I know?

Does anybody know how this dilemma gets resolve in actual agricultural experiments? I know modern statistics got its start in agriculture, so I imagine these problems have been somehow solved. But I can't find it in any references that are readily available to me.

[Carole J. Wilson]

Hmm, very interesting issue. I have very little knowledge of agriculture, but I would guess this is somewhat similar to assigning multiple treatments and control groups in geographic areas. We are careful to avoid assignments in contiguous municipalities/counties because people may cross borders to access programs. So, in the agriculture case, I would leave empty plots (or not analyze the plots) between the plots receiving treatment.

[Steve Samuels]

The student has the right idea. From reading DR Cox's book "Planning of Experiments" , I gather that there are almost always gradients in soil composition and in other factors. Your student's design, called a randomized block design, will adjustt for some of these problems, but not all. One design that will control for twoway gradients is the Latin Square. With three treatments, one needs a number 3 x 3 squares. Each square will provide 2 degrees of freedom for error. As your student points out, choice of location and size of plots is also an important part of the design, although one I know nothing about. I can only suggest consultation with specialized texts. I do recommend Cox's book as a fine introduction to experimental design.

[Andrew Musau]

Another good reference is Agricultural Field Experiments: Design and Analysis by Roger Peterson.

http://www.amazon.com/Agricultural-F.../dp/0824789121

In page 48, he notes

The randomized block design (RBD), or more correctly, the randomized complete block design, is the design used most often in agricultural research. It is nearly as easy to use as the controlled randomized design (CRD), yet it provides an opportunity for increased precision over the CRD. In the RBD the plots (experimental units) are first classified into groups, or blocks, of plots that are as nearly alike as possible.The treatments are then assigned to the plots within blocks in such a way that each treatment occurs the same number of times, usually once within each block. The object is to make the variation from plot to plot as small as possible within the blocks while maximizing the variation among blocks...

It appears that the motivation for the RBD is to reduce variation caused by factors such as soil quality, amount of sunshine, etc., and not so much contamination as the student argues. Of course in cases where the likelihood of contamination is high, the student's point is valid... but the cost is the loss of precision.