4.6 - The Study Diagram

In Lesson 1.1 we encountered a brief description of an experiment. The description of an experiment provides a context for understanding how to build an appropriate statistical model. All too often mistakes are made in statistical analyses because of a lack of understanding of the setting and procedures in which a designed experiment is conducted. Creating a study diagram is one of the best and intuitive ways to address this. A study diagram is a schematic diagram that captures the essential features of the experimental design. Here, as we explore the computations for a single factor ANOVA in a simple experimental setting, the study diagram may seem trivial. However, in practice and in lessons to follow, the ability to create an accurate study diagram usually makes a substantial difference in getting the model right.

In our example in Lesson 1.1, a plant biologist thinks that plant height may be affected by the fertilizer type and three types of fertilizer were chosen to investigate this claim.  Next, 24 plants were randomly chosen and 4 batches of 6 plants each were assigned to the 3 fertilizer types and as well as a control (untreated) group. The individual plants were randomly assigned the treatment levels to produce 6 replications within each level. The researchers kept all the plants under equivalent conditions in a single greenhouse throughout the experiment. Here is the resulting data:

We have a description of the treatment levels, how they were assigned to individual experimental units (the potted plant), and we can see the data organized in a table... What are we missing? A key question is: how was the experiment conducted? This question is a practical one and is answered with a study diagram. These are usually hand-drawn depictions of a real setting, indicating the treatments, levels of treatments, and how the experiment was laid out. For this example, we need to draw a greenhouse bench, capable of holding the 4 × 6 = 24 experimental units:

The diagram identified the response variable, listed the treatment levels, and indicated the random assignment of treatment levels to these 24 experimental units on the greenhouse bench.

This randomization and the subsequent experimental layout we would identify as a Completely Randomized Design (CRD). We know from this schematic diagram that we need a statistical model that is appropriate for a one-way ANOVA in a Completely Randomized Design (CRD).

Furthermore, once the plant heights are recorded at the end of the study, the experimenter may observe that the variability in the growth may be influenced by additional factors besides the fertilizer level (e.g. position on the bench). A careful examination of the layout of the plants in the study diagram may perhaps reveal this additional factor. For example, if the growth is higher in the plants placed on the row nearer to the windows, it is reasonable to assume that sunlight also plays a role. In this case, an experimenter may redesign the experiment as a randomized completely block design (RCBD) with rows as a blocking factor. Note that design aspects of experiments (such as CRD and RCBD) are covered in Lessons 7 and 8. 

Being able to draw and reproduce a study diagram is very useful in identifying the components of the ANOVA models.