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
1
2
3
4
5
6
7
8
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  
1
2
3
4
5
6
7
8
9
10
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