What is the goal of a matched pair design?
The goal of matched pair design is to reduce the chance of an accidental bias that might occur with a completely random selection from a population.
Suppose, for example, we wanted to test the effectiveness of some drug on a group of volunteers. Half of our test subjects would be given the drug and the other half a placebo.
Suppose we have 25,000 volunteers but for various reasons can only test 100 with the drug (and another 100 with a placebo).
We could choose our 200 candidates completely at random from the pool of volunteers.
But what if our random selection results in two test populations with different characteristics? (perhaps gender, age, race, lifestyle characteristics).
If the selection is completely random, it would be possible to have
the subgroup obtaining the drug with a female:male bias of
the subgroup obtaining the placebo with a female:male bias of
Any conclusion based on such a trial (to be valid) would need to take into account this (hidden) bias. To what extent would a positive drug outcome be the result of the drug and to what extent would it be because females recovered naturally better than males.
To avoid this kind of problem, test candidates are selected as pairs (one to obtain the drug and one the placebo in our example) with identical characteristics (age, gender, etc.) to the extent we are able to recognize such characteristics.