2.5 - The Study Diagram

In section 2.1 we encountered a brief description of an experiment. The description of an experiment provides a context for understanding how to build an appropriate ANOVA statistical model. All too often mistakes are made in ANOVA because of a lack of understanding the setting and procedures in which a designed experiment is conducted. Creating a study diagram is the best and most intuitive way 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 the simplest experimental setting, the study diagram may seem trivial. However, in practice and in lessons to follow in this course, the ability to create accurate study diagrams usually makes all the difference in getting the model right.

In our example, as described in Lesson 1.1, was that a plant biologist thinks that plant height may be affected by applying different fertilizers. They tested three kinds of fertilizer and also one group of plants that are untreated (the control). They kept all the plants under controlled conditions in the greenhouse. (In addition, we need to have some information about replication and randomization.) They randomly assigned the fertilizer treatment levels to individual containerized plants to produce 6 replications of each of the fertilizer applications.

Here is the data from the example that we were using in this lesson:

Control F1 F2 F3
21 32 22.5 28
19.5 30.5 26 27.5
22.5 25 28 31
21.5 27.5 27 29.5
20.5 28 26.5 30
21 28.6 25.2 29.2

So we have a description of the treatment levels and how they were assigned to individual experimental units (the potted plant), and we see the data organized in a table. But 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 way laid out. They are not typically works of art and no one should ever feel embarrassed by lack of artistic ability to draw one. For this example, I need to draw a greenhouse bench, capable of holding the 4 × 6 = 24 experimental units:

Height = Response Variable Greenhouse Bench F 1 F 1 F 3 Control 6 Reps of each TRT Level Fertilizers 1 , F 2 , F 3

I 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 CRD.

Being able to draw and reproduce a study diagram is essential for assignments in this course. To see the various options for accomplishing this, go to From Pencil & Paper to Word - Creating Study Diagrams.