Design of Experiments > Counterbalancing

## What is Counterbalancing?

Counterbalancing removes confounding variables from an experiment by giving **slightly different treatments to different participant groups.** For example, you might want to test whether people react positively or negatively to a series of images. They use a left-hand clicker for positive, and a right-hand clicker for negative. Potential problems with this design include the fact that left-handed people might be more inclined to click left and vice-versa. You can remove this potential confounding variable by having a counterbalanced experiment: assigning one group right-hand clickers for positive and a second group left-hand clickers for positive.

## Across Subjects Counterbalancing

When one set of treatments is given, but many sequences are used overall, it’s called **across subjects counterbalancing**. Your participants receive **all combinations of treatments in different orders**. This is to guard against *order effects *(the possibility that the position of the treatment in the order of treatments matters) and **sequence effects** (the possibility that a treatment will be affected by the treatment preceding it). For example, let’s say your study for depression had two treatments: counseling and meditation. You would split your treatment group into two, giving one group counseling, then meditation. The second group would receive meditation first, then counseling.

## Reverse Counterbalancing

In a **reverse counterbalanced design**, all participants receive all treatments twice: first in one order and next in another order. For example: counseling, meditation, meditation, counseling.

## Complete Counterbalancing

With this method, each possible sequence is used and each sequence is used the exact same amount of times. For example, let’s say you had treatments 1,2,and 3. There are six possible sequences: 123,231,312,321,213,and 132. You could use the sequence on 6 groups, 12 groups, 18 groups…and so on, as long as you had a multiple of six (so that each sequence is run the same number of times). If you don’t have enough participants to do this (let’s say you had 17 groups instead of 18), it’s called **partial counterbalancing**. Another possibility is to randomize the allocation of those 6 treatments to your 17 groups: if you do that, then you’re using a **randomized partial counterbalanced** design.

## Latin Square Counterbalancing

This method, which also controls order effects, uses a square to ensure that each treatment only occurs once in any order position (i.e. 1st, 2nd, 3rd). Let’s say you had three treatments 1,2,3. Your square would be:

1st sequence: 1 2 3

2nd sequence: 2 3 1

3rd sequence: 3 1 2.

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