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Education And Debate

# Statistics Notes: Measurement error and correlation coefficients

BMJ 1996; 313 (Published 06 July 1996) Cite this as: BMJ 1996;313:41
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

Measurement error is the variation between measurements of the same quantity on the same individual.1 To quantify measurement error we need repeated measurements on several subjects. We have discussed the within-subject standard deviation as an index of measurement error,1 which we like as it has a simple clinical interpretation. Here we consider the use of correlation coefficients to quantify measurement error.

A common design for the investigation of measurement error is to take pairs of measurements on a group of subjects, as in table 1. When we have pairs of observations it is natural to plot one measurement against the other. The resulting scatter diagram (see figure 1 may tempt us to calculate a correlation coefficient between the first and second measurement. There are difficulties in interpreting this correlation coefficient. In general, the correlation between repeated measurements will depend on the variability between subjects. Samples containing subjects who differ greatly will produce larger correlation coefficients than will samples containing similar …

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