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Education And Debate

Statistics Notes: Measurement error proportional to the mean

BMJ 1996; 313 doi: https://doi.org/10.1136/bmj.313.7049.106 (Published 13 July 1996) Cite this as: BMJ 1996;313:106
  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 ICRF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, PO Box 777, Oxford OX3 7LF
  1. Correspondence to: Professor Bland.

    We often need to know the error with which measurements are made—for example, so that we can decide whether the change in a clinical observation represents a real change in a patient's condition. We have discussed previously the within-subject standard deviation as a practical index of measurement error.1 We said that this approach should be used when the measurement error was not related to the magnitude of the measurement and recommended that we plot the subject standard deviation against the subject mean to check this. Table 1 shows some duplicate salivary cotinine measurements taken from a larger study. Figure 1 shows absolute subject difference against subject mean, which is equivalent to a standard deviation versus mean plot when we have only two measurements per subject.1 If we are to use the within-subject standard deviation as an index of measurement error we need the subject standard deviation to be …

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