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Research Methods & Reporting

Random measurement error and regression dilution bias

BMJ 2010; 340 doi: (Published 23 June 2010) Cite this as: BMJ 2010;340:c2289
  1. Jennifer A Hutcheon, postdoctoral fellow1,
  2. Arnaud Chiolero, doctoral candidate, fellow in public health23,
  3. James A Hanley, professor of biostatistics2
  1. 1Department of Obstetrics & Gynaecology, University of British Columbia, Vancouver, Canada
  2. 2Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Purvis Hall, 1020 Avenue des Pins Ouest, Montreal QC, Canada H3A 1A2
  3. 3Institute of Social and Preventive Medicine (IUMSP), University Hospital Centre and University of Lausanne, Lausanne, Switzerland
  1. Correspondence to: J A Hanley james.hanley{at}
  • Accepted 2 February 2010

Random measurement error is a pervasive problem in medical research, which can introduce bias to an estimate of the association between a risk factor and a disease or make a true association statistically non-significant. Hutcheon and colleagues explain when, why, and how random measurement error introduces bias and provides strategies for researchers to minimise the problem

Summary points

  • The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease)

  • Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null

  • Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant

  • Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable


Random measurement error is a pervasive problem in medical research and clinical practice.1 It occurs when measurements fluctuate unpredictably around their true values and is caused by imprecise measurement tools or true biological variability, or both. For instance, when blood pressure is assessed with a sphygmomanometer, random error may arise from imprecise measurement due to rounding error or from true diurnal or day to day variation in pressure.2 3 Hence, a blood pressure reading obtained at a single occasion may differ by an unpredictable (random) amount from an individual’s usual blood pressure.3

Random measurement error differs from systematic measurement error.4 Systematic error occurs when the measurement error, after multiple measurements, does not average out to zero. The measurements are consistently wrong in a particular direction—for example, they tend to be higher than the true values. …

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