Paired data

Paired data can arise in two ways:

Blocked data with two treatments
Experimental units are grouped into pairs of similar units. Two treatments are randomly allocated to the two units in each pair.
Repeated measure data
Two comparable measurements are made from each individual, often measurements of the same quantity at two different times (e.g. pre-test and post-test).

In both situations, the recorded values arise in pairs. By analysing the differences between the values in each pair, we remove the variability between different pairs.

Groups of 3 or more values

We now extend the above scenarios to data in which the values come in groups of 3 or more.

Blocked data with several treatments
Experimental units are grouped into blocks whose size equals the number of treatments. The treatments are randomly allocated to the units in each block.
Repeated measure data
Several comparable measurements are made from each individual, often measurements of the same quantity at different times.

Acupuncture and Codeine for dental pain relief (randomised blocks)

An anaesthetist conducted an experiment to assess the effects of codeine and acupuncture for relieving dental pain. The experiment used 32 subjects who were grouped into blocks of 4 according to an initial assessment of their tolerance to pain.

The four treatment combinations of (codeine or a sugar capsule) and (active or inactive acupuncture points) were randomly given to the four subjects in each block. Pain relief scores were recorded from each subject two hours after dental treatment. The experiment was double blind since neither the subjects nor the person assessing pain relief knew which treatment had been administered.

  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

Have codeine or acupuncture affected the mean pain relief score? If so, by how much?

Effect of nicotine on tics (repeated measures)

An experiment was conducted on 10 patients with Tourette's syndrome, a neurological disorder that results in tics (rapid involuntary muscle movements). In these patients, the tics were inadequately controlled by the drug haloperidol.

The experiment investigated the use of nicotine to control the tics. The number of tics was recorded during an initial 30-minute period (baseline), then during 30 minutes of chewing nicotine gum (containing 2 mg nicotine), from 0 to 30 minutes after chewing, and finally from 30 to 60 minutes after chewing.

  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

These are repeated measures data with a baseline measurement for each patient against which the other measurements can be compared.

Has the mean number of tics been affected by the nicotine? If so, by how much?