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Statistics notes: Measurement error

BMJ 1996; 312 doi: (Published 29 June 1996) Cite this as: BMJ 1996;312:1654
  1. J Martin Bland, professor of medical statisticsa,
  2. Douglas G Altman, headb
  1. a Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
  2. b IRCF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, PO Box 777, Oxford OX3 7LF
  1. Correspondence to: Professor Bland.

    Several measurements of the same quantity on the same subject will not in general be the same. This may be because of natural variation in the subject, variation in the measurement process, or both. For example, table 1 shows four measurements of lung function in each of 20 schoolchildren (taken from a larger study1). The first child shows typical variation, having peak expiratory flow rates of 190, 220, 200, and 200 l/min.

    View this table:
    Table 1

    Repeated peak expiratory flow rate (PEFR) measurements for 20 schoolchildren

    Let us suppose that the child has a “true” average value over all possible measurements, which is what we really want to know when we make a measurement. Repeated measurements on the same subject will vary around the true value because of measurement error. The standard deviation of repeated measurements on the same subject …

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