Matched Pairs Design in AP Statistics

In AP Statistics, a matched pairs design is an experiment comparing two treatments in which each unit receives both treatments in random order, or similar units are paired and the two treatments are randomly assigned within each pair. It is a special case of a randomized block design.

What is Matched Pairs Design?

A matched pairs design is an experimental design for comparing exactly two treatments. It comes in two versions.

1. Each unit gets both treatments. For example, each subject tries Drug A and Drug B, and a coin flip decides which comes first.
2. Similar units are paired up. For example, twins, or two students with the same prior test score. Within each pair, a random process decides which unit gets which treatment.

Either way, you compare the two treatments inside each pair, where the units are as alike as possible. Think of it as blocking taken to the extreme. In CED terms (1.13.B.2), a randomized block design groups units by a blocking variable so the units in each block are similar. A matched pairs design is that same idea with blocks of size two. Differences between people (or plants, or fields) get cancelled out, so the treatment effect is easier to see. Randomization still matters. You randomize the order of treatments or which unit in the pair gets each one, and that is what keeps the design a true experiment.

Why Matched Pairs Design matters in AP® Statistics

Matched pairs design lives in Unit 1, Topic 1.13 (Experimental Design). It directly supports AP Stats 1.13.B (identify experimental designs) because you need to recognize it next to completely randomized and randomized block designs. It also supports AP Stats 1.13.C (justify the appropriateness of a design). Per 1.13.C.1, one design can beat another depending on the study's goals and the units involved. Matched pairs wins when units vary a lot on something that affects the response and you only have two treatments. It ties into AP Stats 1.13.A as well, because pairing is a form of direct control of extraneous variation (1.13.A.1.iv). It also ties into AP Stats 1.13.D, because random assignment within pairs is still what lets you make cause-and-effect conclusions (1.13.D.1). The design pays off again in Unit 4, where matched pairs data gets analyzed with paired procedures.

How Matched Pairs Design connects across the course

Randomized Block Design (Unit 1)

A matched pairs design is a randomized block design where every block holds exactly two units, or one unit measured twice. If you understand why blocking reduces variability, you already understand why pairing works. Pairs are just the tightest possible blocks.

Dependent Samples and Paired t-Procedures (Unit 4)

The design you choose in Unit 1 decides the test you run in Unit 4. Matched pairs produces dependent samples, so you analyze the differences within each pair as a single sample, not as two independent groups. Picking a two-sample t-test for paired data is a classic way to lose points.

Causal Relationship (Unit 1)

Pairing alone does not earn you a cause-and-effect conclusion. Randomly assigning treatments within each pair (or randomizing the order) is what reduces confounding, per 1.13.D.1. A pairing with no randomization is a comparison, not an experiment.

Response Variable and Experimental Unit (Unit 1)

Pairing works because the matching variable is related to the response variable. Matching twins on height is pointless if you are measuring reading speed. Always pair experimental units on something that actually affects the response.

Is Matched Pairs Design on the AP® Statistics exam?

On the exam, matched pairs design shows up in three main ways.

• Identify the design. Multiple-choice stems describe a study and ask which design it uses or which design is most appropriate. You will often see matched pairs listed next to completely randomized, randomized block, and factorial designs. One clue that points away from matched pairs is a study with three or four treatments (three teaching methods, four fertilizers). A pair can only hold two.
• Justify the choice (1.13.C). You may need to explain why a design fits. A strong answer for matched pairs names the variable you are pairing on, explains that it affects the response, and says that comparing within pairs reduces variability so treatment differences are easier to detect.
• Spot the weaknesses. When each unit gets both treatments, watch for carryover effects, where the first treatment still influences the second measurement. Questions about carryover test whether you know to randomize order or switch to a design where each unit gets only one treatment.

No released FRQ has used the exact phrase "matched pairs design," but experimental design FRQs regularly ask you to describe a design, explain how to randomize it, and justify its benefits. That is exactly the skill set this term needs. In free response, always describe the randomization concretely (for example, flip a coin for each pair to decide which unit gets Treatment A).

Matched Pairs Design vs Randomized Block Design

These are not rivals. Matched pairs is a special case of a randomized block design. A randomized block design can have blocks of any size and any number of treatments, such as blocking a field by soil quality and testing four fertilizers in each block. A matched pairs design has blocks of exactly two (or one unit used twice) and compares exactly two treatments. If a question has more than two treatments, it can't be matched pairs. You'd need a general block design.

Key things to remember about Matched Pairs Design

• A matched pairs design compares exactly two treatments, either by giving each unit both treatments in random order or by randomly assigning treatments within pairs of similar units.

• Matched pairs is a randomized block design where each block has size two, so it reduces variability caused by differences between units.

• Randomization is still required, because randomizing the order or the assignment within each pair is what allows cause-and-effect conclusions.

• When the same unit gets both treatments, carryover effects are a real risk, and randomizing the order helps balance them out.

• Data from a matched pairs design are dependent, so in Unit 4 you analyze the differences with a paired t-procedure instead of a two-sample test.

• To justify a matched pairs design, name the matching variable, explain how it affects the response, and say that comparing within pairs makes the treatment effect easier to detect.

Frequently asked questions about Matched Pairs Design

What is a matched pairs design in AP Stats?

It's an experiment comparing two treatments where each unit receives both treatments in random order, or similar units are paired and the treatments are randomly assigned within each pair. It is covered in Topic 1.13 (Experimental Design) in Unit 1.

Is a matched pairs design a type of randomized block design?

Yes. A matched pairs design is a randomized block design with blocks of size two, or a single unit that serves as its own block. The goal is the same, which is to group similar units so that differences between units don't hide the treatment effect.

Does a matched pairs design still need random assignment?

Yes. You must randomly decide which unit in each pair gets which treatment, or randomly decide the order when one unit gets both. Without that randomization, you can't make the cause-and-effect conclusion described in 1.13.D.1.

Can you use a two-sample t-test on matched pairs data?

No. Matched pairs data are dependent samples, so you compute the difference within each pair and run a one-sample t-procedure on those differences. This is the paired t-test from Unit 4.

How is a matched pairs design different from a completely randomized design?

In a completely randomized design, treatments are assigned to units completely at random with no grouping (1.13.B.1). In a matched pairs design, you first pair similar units, or use each unit twice, and then randomize within the pair. Pairing usually gives more precise comparisons when units differ a lot on something related to the response.