Matched Pairs Design — Definition, Formula & Examples
Matched pairs design is an experimental design in which subjects are grouped into pairs that share a similar characteristic, and each member of the pair is randomly assigned to a different treatment. A common special case uses the same subject for both treatments, so each person serves as their own control.
A matched pairs design is a type of randomized blocked experiment with blocks of size two, where units within each pair are matched on one or more confounding variables (or are the same unit measured under two conditions). Random assignment determines which unit in each pair receives which treatment, and the analysis is performed on the within-pair differences.
How It Works
First, identify a variable likely to affect the response and pair subjects who are similar on that variable. If practical, use each subject twice — once per treatment — with the order randomized. Then randomly assign the two treatments within each pair (for example, by coin flip). After collecting data, compute the difference in response for every pair. Finally, analyze those differences using a one-sample procedure such as a paired -test rather than a two-sample test.
Example
Problem: A researcher wants to test whether a new keyboard layout improves typing speed. She recruits 10 participants. Each participant types a passage on the standard layout and again on the new layout, with the order randomized. Their speeds (words per minute) are recorded.
Step 1 — Form pairs: Each participant serves as their own matched pair, eliminating person-to-person variability in baseline typing ability.
Step 2 — Randomize within pairs: For each participant, flip a coin to decide which layout they use first. This controls for order effects.
Step 3 — Compute differences: Suppose Participant 1 types 62 wpm on the new layout and 55 wpm on the standard layout. The difference for that pair is:
Step 4 — Analyze: After computing all 10 differences, perform a one-sample -test on the values to determine whether the mean difference is significantly different from 0.
Answer: Because each subject acts as their own control, individual differences in typing skill are removed. The researcher analyzes the set of 10 paired differences with a one-sample -test.
Why It Matters
On the AP Statistics exam, you must recognize when a matched pairs design is appropriate and distinguish it from a completely randomized or block design. In scientific research, matched pairs reduce variability caused by subject differences, giving experiments more power to detect a real treatment effect with fewer participants.
Common Mistakes
Mistake: Analyzing matched pairs data with a two-sample -test instead of a paired -test.
Correction: Because the observations within each pair are not independent, you must compute the pairwise differences and run a one-sample -test on those differences.