Topic 3.6 Selecting an Experimental Design: compare completely randomised, randomised block, and matched pairs designs, and explain how blocking and pairing control a known source of variation to make treatment effects clearer.

What this topic is asking

The College Board (Topic 3.6) wants you to compare the main experimental designs, completely randomised, randomised block, and matched pairs, and to explain how blocking and pairing control a known source of variation so that the treatment effect stands out more clearly.

Three designs

The progression is one of increasing control over a known source of variation. The completely randomised design controls nothing in advance and relies on randomisation alone to balance everything. The block design takes one large, predictable source of variation out of the comparison by handling it explicitly. The matched pairs design takes this to its limit, pairing on as much similarity as possible.

What blocking does

The purpose of blocking is not to balance the block variable (random assignment already tends to do that) but to reduce variability so a real treatment effect is easier to detect. Suppose a drug's effect is small but sex strongly affects the response. In a completely randomised design, the large male-female differences inflate the overall variation and can swamp the drug's effect. Blocking on sex compares the treatments within men and within women separately, where the sex variation is absent, so the drug's effect emerges clearly. You block on a variable you know matters; you randomise within blocks to handle everything you do not know.

Matched pairs as the extreme

A matched pairs design is the tightest form of blocking, with blocks of size two. There are two common versions. In the first, you pair similar subjects (twins, or people matched on age and weight) and randomly give one of each pair each treatment. In the second, common and powerful, each subject receives both treatments, in a randomly chosen order, and serves as their own control, as in the running-sole example where each runner wears both soles. Because the comparison is made within a pair (or within a person), all the variation between people, weight, fitness, habits, simply cancels out, leaving a much cleaner read on the treatment difference. The price is that you must still randomise within each pair (which subject or which order gets the new treatment) so that a pairing artefact, such as a left-right foot difference or an order effect, does not confound the result. This is why matched pairs questions always reward randomising the within-pair assignment, usually by a coin flip per pair.

Choosing the right design on the exam

The exam expects you to justify a design choice, so reason from the source of variation. If there is a known variable likely to affect the response and you can group units by it, a randomised block (or matched pairs) design gives a more precise comparison than a completely randomised design of the same size. If no such dominant variable is apparent, or pairing is impractical, the completely randomised design is appropriate and simplest. When each unit can sensibly receive both treatments without one affecting the other, matched pairs (within-subject) is often the most powerful choice. In every case the analysis still rests on random assignment for its validity; blocking and pairing are about sharpening the comparison, not about whether causation can be claimed. Articulating "block what is known, randomise what is not" is the reasoning Topic 3.6 wants to see.

Try this

Q1. What is the purpose of blocking in an experiment? [2 points]

• Cue. To remove the variation due to a known variable by comparing treatments within similar groups, making the treatment effect more precise and easier to detect (not to enable causation, which randomisation already does).

Q2. In a matched pairs design where each subject takes both treatments, what must still be randomised, and why? [1 point]

• Cue. The order (or which treatment comes first) for each subject, so an order or position effect does not systematically favor one treatment.