2.3 Paired Data
Two sets of dependent samples (x1,y1)...,(xn,yn) representing
two different treatments (conditions) X and Y. Typical examples are:
- Measurements on twin pairs. Each pair
(xi,yi) represents measurements on one sibling pair.
- Each pair (xi,yi) represents attidudes of the same
person (subject i) about
the death penalty before watching a documentary
(xi) and after watching the film (yi).
The objective is to compare the effects of the two treatments.
Typically we work with the differences di=yi-xi.
Here is an example for paired data:
Before (x) After (y) d=y-x
1 7 5 -2
2 1 1 0
3 10 9 -1
4 0 0 0
5 5 4 -1
6 3 4 1
The data gives shows for n=6 subjects their attidutes towards
legalisation of mariuana (0=strongly oppose,...,10=strongly support) before
and after being shown a documentary. To make inference about the effect
of the documentary we consider the differences d=y-x which tell
how people changed due to being shown the documentary.
Appropriate descriptive statistics are, for example, computing mean
and standard deviation for the differences d1,...,dn.
This can be done using the describe command in Minitab:
Possible graphical summaries are