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Figure 2.10 shows an example in which the total steps‐per‐day walked by one subject, assessed by a pedometer worn on the hip, was recorded every day for 100 days. The observed daily total step count is subject to day‐to‐day fluctuations. There is considerable day‐to‐day variation in steps but little evidence of any trend over time. Such variation is termed within‐subject variation. The within‐subject standard deviation in this case, is SD = 4959 steps with a mean daily step count of 14 107 steps over the 100 days.

Figure 2.10 Total steps per day for 100 days for one participant in a global corporate challenge designed to increase physical activity.

If another subject had also completed this experiment, we could calculate their within‐subject variation as well, and perhaps compare the variabilities for the two subjects using these summary measures. Thus a second subject had a mean step count of 12 745 with standard deviation of 4861 steps, and so has a smaller mean but similar variability.

Successive within‐subject values are unlikely to be independent, that is, consecutive values will be dependent on values preceding them. For example, if a sedentary or inactive person records their step count on one day, then if the step count is low on one day it is likely to be low on the next day. This does not imply that the step count will be low, only that it is a good bet that it will be. In contrast, examples can be found in which high step counts are usually followed by lower values and vice versa. With independent observations, the step count on one day gives no indication or clue as to the step count on the next.

It is clear from Figure 2.10 that the daily step counts are not constant over the observation period. This is nearly always the case when medical observations or measurements are taken over time. Such variation occurs for a variety of reasons. For example, the step count may depend critically on the day of the week, whether the subject was on holiday or at work, whether the subject was on medication or unwell. There may be observer‐to‐observer variation if the successive step counts were recorded by different personnel rather than always by the same person. There may be measuring device‐to‐measuring‐device variation if the successive step counts were recorded by different pedometers rather than always the same pedometer. The possibility of recording errors in the laboratory, transcription errors when conveying the results to the clinic or for statistical analysis, should not be overlooked in appropriate circumstances. When only a single observation is made on one patient at one time only, then the influences of the above sources of variation are not assessable, but may nevertheless all be reflected to some extent in the final entry in the patient's record.

Suppose successive observations on a patient with heart disease taken over time fluctuate around some more or less constant daily step count, then the particular level may be influenced by factors within the patient. For example, step counts (and physical activity levels) may be affected by the presence of a viral infection whose presence is unrelated to the cause of the heart disease itself. Levels may also be influenced by the severity of the underlying condition and whether concomitant treatment is necessary for the patient. Levels could also be influenced by other factors, for example, alcohol, tobacco consumption and diet. The cause of some of the variation in step counts may be identified and its effect on the variability estimated. Other variation may have no obvious explanation and is usually termed random variation. This does not necessarily imply there is no cause of this component of the variation but rather that its cause has not been identified or is being ignored.

Different patients with heart disease observed in the same way may have differing average levels of step counts (physical activity levels) from each other but with similar patterns of variation about these levels. The variation in mean step count levels from patient to patient is termed between‐subject variation.

Observations on different subjects are usually regarded as independent. That is, the data values on one subject are not influenced by those obtained from another. This, however, may not always be the case, particularly with subjective measures such as pain or quality of life which may be influenced by the subject's personal judgement, and different patients may assist each other when recording their quality of life.

In the investigation of total variability it is very important to distinguish within‐subject from between‐subject variability. In a study there may be measures made on different individuals and also repeatedly on the same individual. Between‐ and within‐ subject variation will always be present in any biological material, whether animals, healthy subjects, patients, or histological sections. The experimenter must be aware of possible sources which contribute to the variation, decide which are of importance in the intended study, and design the study appropriately.