A repeated measures design involves all participants completing all levels of the independent variable. This includes designs where time is the independent variable, and participants are measured on the same dependent variable over time. Why use it? There are two key benefits: one is to increase the sensitivity or power of our experiment. By having the same participants take part in each level of the independent variable, we control for participant variables (e.g., age, personality, etc. – these should be the same across levels of the independent variable). Participant variables are usually a major source of error variance or unsystematic variation. By controlling for them, it should be easier to detect the experimental effect. A second key benefit is economy: all other things being equal, we do not need as many participants for a repeated measures design as a between-subjects design (because of the control for participant variables). At the same time, there are some limitations to this design: by using the same participants in all levels of the independent variable, the experiment becomes longer, with a greater risk of fatigue and attrition. In addition, we have to consider the possibility of increased practice effects and demand characteristics. We have to balance these drawbacks with the benefits of the repeated measures design.

We can go some way to addressing the limitations by using counterbalancing.

Counterbalancing

Counterbalancing involves changing the order of the design for different participants in order to balance out the effects of practice, learning, and so on, across participants. Complete counterbalancing means that you create all the possible combinations of order for the design. Let’s say we have three levels for our independent variable: level A, level B, and level C. All the possible orders are: ABC ACB BCA BAC CAB CBA. To implement this in our experiment, each participants would be exposed to one of these possible orders. In our statistical analyses, we might collapse across order (i.e., ignore it) and just look at the effect of the independent variable, or, we might analyze order effects. The problem with complete counterbalancing is that it creates complex designs when you have three or more levels to your independent variable.

In partial counterbalancing we use only a subset of the possible orders. One way to do this is by using a Latin square design. A Latin square design draws on the principles of the Latin square. The Latin square is an array of numbers where each number appears once in each row and once in each column. In the Latin square design, our square follows the rules: 1) the number of orders = the number of conditions; and 2) each condition appears only once in each row and once in each column. So, for example, a Latin square for a three-level design might look like this:

The orders we would use in our experiment would therefore be: ABC, BCA, and CAB (thus only three different orders of levels, instead of six!).

Randomizing

Sometimes, instead of counterbalancing, we might randomize the order of conditions, creating a new random order for each participant.