A set of data consisting of observations taken on the same subject at different times (Before/After treatment) or under different conditions (Treatment/Placebo), or observations that are related on some population characteristic (heights of siblings are considered matched, because variation among siblings is likely to be smaller than that of the general population). The advantage of using paired or matched data is that the matched observations are more similar to each other than to the other observations, thus eliminating the between-subjects variance which could otherwise mask the true treatment effect.
Using paired data is a special case of blocking, where a block is a relatively homogenous set of Units. When the data are naturally correlated, estimates obtained from paired/matched data have greater precision than if the data were considered independent. However, tests based on paired data result in a loss of degrees of freedom, making them slightly less sensitive.
Some examples of situations involving paired/matched data:
1. Comparison of cholesterol levels in siblings.
2. Comparison of weight measurements of subjects before and after a weight-loss treatment.
3. Comparison of the time to perform two tasks where each operator in the group performs both tasks in random order.