Matched Pairs Design vs Random Assignment
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Matched pairs design
Collecting data and study design
A matched pairs design compares two treatments within pairs of similar units, or one unit measured twice, then analyzes the difference inside each pair.
A matched pairs design controls for variation between units by comparing treatments inside pairs that are alike, or on the same unit under both conditions. Because each pair serves as its own comparison, differences between individuals cancel out and the test focuses on the within-pair difference. For example, you measure each runner's time in old shoes and new shoes, then analyze the 20 time differences. The analysis is a one-sample procedure on the paired differences, using , where is the mean difference, its standard deviation, and the number of pairs.
Random assignment
Collecting data and study design
Random assignment uses chance to sort experimental units into treatment groups, so the groups start out similar and confounding is balanced out.
Random assignment is how an experiment builds comparable groups. Because a coin flip or random number decides who gets which treatment, no systematic difference in age, health, or motivation piles up in one group, so a later difference in outcomes can be credited to the treatment. For example, flipping a coin for each of 40 patients to assign a drug or a placebo balances the other traits across the two groups on average. Random assignment builds the groups, while random selection picks the sample; assignment supports cause-and-effect claims, and selection supports generalizing to a population.