In paired data, two related measurements, X and Y, are made
from each sampled individual and we are interested in testing whether their means
are equal.
Groups of 3 or more values
The idea of paired data can be extended to situations in which 3 or more related
measurements are made from each 'individual'. Two important situations that give
rise to this type of data are:
- Experiment with blocks
- Paired data can arise when the experimental units are grouped into blocks of
size 2 (e.g. matched pairs) and two treatments are used. This can be extended to g treatments
with blocks of g experimental units and the treatments randomised within
each block.
- Repeated measure data
- Several comparable measurements may be made from each individual, often measurements
of the same quantity at different times.
Example (randomised blocks)
In an experiment to assess the effect of codeine and acupuncture
for relieving dental pain, 32 subjects were grouped into
blocks of 4 according to an initial assessment of their tolerance to pain. Four treatments
were randomly given to the four subjects in each block and pain relief scores were
recorded.
|
Pain relief score |
Tolerance
group |
Control |
Codeine
only |
Acupuncture
only |
Codeine +
Acupuncture |
|
0.0
0.3
0.4
0.4
0.6
0.9
1.0
1.2 |
|
0.6
0.7
0.8
0.9
1.5
1.6
1.7
1.6 |
|
0.5
0.6
0.8
0.7
1.0
1.4
1.8
1.7 |
|
1.2
1.3
1.6
1.5
1.9
2.3
2.1
2.4 |
|
Example (repeated measures)
An experiment investigated the use of nicotine to control tics in patients with
Tourette's syndrome. For each patient, the number
of tics was recorded before a nicotine gum was chewed and at different times afterwards.
|
Number of tics during 30-min period |
Patient |
Baseline |
Chewing gum |
0-30 min after |
30-60 min after |
|
249
1095
83
569
368
326
324
95
413
332 |
|
108
593
27
363
141
134
126
41
365
293 |
|
93
600
32
342
167
144
312
63
282
525 |
|
59
861
61
312
180
158
260
71
321
455 |
|