4  Designing an Experiment

When planning an experiment we need to decide on:

• treatment factors and their levels
• the response
• experimental material / units
• blocking factors
• number of replicates

Some of these will be determined by the research question and how experimental units are assigned to treatments are determined by the design. The design that will be chosen for a particular experiment depends on the treatment structure (determined by the research question) and the blocking structure (determined by the available experimental units).

Here are two ways the treatments can be structured:

1. Single factor: the treatments are the levels of a single treatment factor.
2. Factorial: when more than one factor are of interest, then the experiment is said to be a factorial experiment. The treatments are constructed by crossing the treatment factors like we did in Figure 2.1 such that the treatments are all possible combinations of the treatment levels. For example, if factor A has \(a\) levels and factor B has \(b\) levels, there are \(a \times b\) treatments. Such an experiment would then be called an \(a \times b\) factorial experiment.

The blocking structure is determined by the set of experimental units chosen or available for the experiment. Are there any structures/differences that need to be blocked? Do I want to include experimental units of different types to make the results more general? How many experimental units are available in each block? For the block design covered in this course, the number of experimental units in each block corresponds to the number of treatments. This is called a complete block experiment and is the simplest block design. There are several other blocking structures, such as incomplete blocks and blocks with missing values, all with specific analysis which we will not cover here.

In this course, we cover two basic designs: Completely Randomized Designs (CRD) and Randomized Block Designs (RBD). For both designs, the treatment structure can be single or factorial. Where they differ is in terms of the experimental units and how randomization occurs.

Completely Randomized Designs (CRD)

When all experimental units are fairly homogeneous, a CRD is used. Treatments are randomized to all experimental units.

Randomized Block Design

This design is used when all experimental units are not homogeneous or blocking is required to control a nuisance factor. The treatments are randomized to the units within blocks.