# 15.1 - Overview of the Crossover Designs

15.1 - Overview of the Crossover Designs

The order of treatment administration in a crossover experiment is called a sequence and the time of a treatment administration is called a period. Typically, the treatments are designated with capital letters, such as A, B, etc.

The sequences should be determined a priori and the experimental units are randomized to sequences. The most popular crossover design is the 2-sequence, 2-period, 2-treatment crossover design, with sequences AB and BA, sometimes called the 2 × 2 crossover design.

In this particular design, experimental units that are randomized to the AB sequence receive treatment A in the first period and treatment B in the second period, whereas experimental units that are randomized to the BA sequence receive treatment B in the first period and treatment A in the second period.

We express this particular design as AB|BA or diagram it as:

 Period 1 Period 2 Sequence AB A B Sequence BA B A

Examples of 3-period, 2-treatment crossover designs are:

 Period 1 Period 2 Period 3 Sequence ABB A B B Sequence BAA B A A

and

 Period 1 Period 2 Period 3 Sequence AAB A A B Sequence ABA A B A Sequence BAA B A A

Examples of 3-period, 3-treatment crossover designs are

 Period 1 Period 2 Period 3 Sequence ABC A B C Sequence BCA B C A Sequence CAB C A B

and

 Period 1 Period 2 Period 3 Sequence ABC A B C Sequence BCA B C A Sequence CAB C A B Sequence ACB A C B Sequence BAC B A C Sequence CBA C B A

Some designs even incorporate non-crossover sequences such as Balaam's design:

 Period 1 Period 2 Sequence AB A B Sequence BA B A Sequence AA A A Sequence BB B B

Balaam’s design is unusual, with elements of both parallel and crossover design. There are advantages and disadvantages to all of these designs; we will discuss some and the implications for statistical analysis as we continue through this lesson.

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