# Learn research design notation in 2 minutes

Article by Ben Howell Research design notation

Research design notation (sometimes referred to as experimental design notation) is a succinct notation scheme for describing research designs, participant group assignment and experiment flow. Despite its simplicity, it tends to scale well and can easily describe complex experiment designs, making it particularly useful for discussing with colleagues, presenting to a class, and reasoning about your own designs.

## Syntax

• O: refers to an observation or measurement (i.e. the Dependent Variable). Subscripts can be used to specifically identify the observation number (e.g. O42). The use of subscripts is especially prevalent in notation of time-series experiment designs.
• X: refers to an experimental manipulation, intervention or treatment (i.e. the Independent Variable). As with observations, subscripts can be used to specifically identify the manipulation number (e.g. X7).
• Y: is used to refer to a second Independent Variable. Subscripts can be used to identify the manipulation number.
• R: refers to a randomly assigned participant group.
• N: refers to a non-equivalent participant group (e.g. gender, sex, smoking status). In some notations you will see that the assignment is omitted altogether when non-equivalent groups are used.
• C: refers to a participant group assigned by a cutoff score (e.g. test score, weight, age).
Design notation is read from left to right and represents the flow of time. Each column in a particular notation can be thought of as either a block of time or a step in an experiment sequence.

## Getting started

A simple posttest-only example is shown in (Figure 1) below. The notation tells us the that the experiment contains the following characteristics:

• it contains a single, randomly assigned participant group `R`.
• the first event is a manipulation of the Independent Variable `X`.
• the second event is an observation or measurement of the Dependent Variable `O`. Figure 1. Posttest-only design
The example experiment above (Figure 1) isn't very useful because we have no baseline with which to compare our observations, so let's fix that by adding a control group. Our new notation (Figure 2) tells us:
• we have two randomly assigned participant groups `R`.
• the first group is subjected to a manipulation of the Independent Variable`X`.
• both groups are subject to measurement of the Dependent Variable `O`.
With the addition of the control group, we can compare our observations across our experimental group, who were subject to manipulation and our control group, who were not. Figure 2. Posttest-only control group design (annotated)

Now that we're familiar with the notation structure, we can simplify our written notation. In (Figure 3) below we have simplified our previous notation by leaving out everything unnecessary such as lines, labels and arrows. What we are left with is a dense and concise notation describing our experiment. Figure 3. Posttest-only control group design (concise)

## Examples

In the following examples we will take a look at the notation of some common experiment designs and some subtle variations in syntax where applicable.

### Nonequivalent control group, posttest-only design Figure 4. Nonequivalent control group, posttest-only design

The example above (Figure 4) can be further simplified by leaving out the group assignment altogether (because where group assignment is absent, non-equivalence is implied) as shown in (Figure 5). Figure 5. Nonequivalent control group, posttest-only design (with implied group assignment)

### Pretest/posttest design Figure 6. Pretest/posttest design

### Pretest/posttest control group design Figure 7. Pretest/posttest control group design

### Nonequivalent control group, pretest/posttest design Figure 8. Nonequivalent control group, pretest/posttest design

### Switching replications design Figure 9. Switching replications design

### Solomon four group design Figure 10. Solomon four group design

### Interrupted Time-series design Figure 11. Interrupted Time-series design Figure 12. Interrupted Time-series design with subscripts

### Control group interrupted time-series design Figure 13. Control group interrupted time-series design

### Longitudinal Design Figure 14. Longitudinal design