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.

**O**: refers to an observation or measurement (i.e. the Dependent Variable). Subscripts can be used to specifically identify the observation number (e.g. O_{42}). 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. X_{7}).**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).

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`

.

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)

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.

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)

Figure 6. Pretest/posttest design

Figure 7. Pretest/posttest control group design

Figure 8. Nonequivalent control group, pretest/posttest design

Figure 9. Switching replications design

Figure 10. Solomon four group design

Figure 11. Interrupted Time-series design

Figure 12. Interrupted Time-series design with subscripts

Figure 13. Control group interrupted time-series design

Figure 14. Longitudinal design

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