Paired data
When two types measurements, X and Y, are made from each
individual (or other unit), the data are called bivariate. Sometimes
the two measurements are of closely related quantities and
may even describe the same quantity at different times.
When the sum or difference of X and Y is a meaningful quantity,
the data are called paired data.
Hypotheses of interest
For paired data, We often want to test whether the means of the two variables
are equal,
H0 : μX = μY
HA : μX ≠ μY
Sometimes a one-tailed test is required, such as
H0 : μX = μY
HA : μX > μY
Examples
- Pre-test, post-test data
- This arises when a measurement is made from each individual, then a second
measurement of the same type is made after some kind of intervention (e.g. training
or medication). Has the intervention "improved" the measurement?
- Twin studies
- Some experiments or other studies are conducted with
identical twins, either human or animal. The members
of each pair experience different environments — either two different experimental
treatments or two other differences. Are there differences between the two treatments?
- Other types of pairing
- For example, damaged cars may each be taken to two garages for estimates
of the cost of repair. The two estimates for each car are paired data. Does one
garage overcharge?