Estimation of reference ranges from normal samples

Reference ranges are very widely used in medicine, and are typically computed as mean plus or minus two standard deviations. However, their precise statistical basis is rarely discussed, and is open to different interpretations. They are sometimes calculated using the Student t distribution and satisfy the condition that the expected coverage of the reference population is some nominal value such as 95 percent or 99 per cent. A case is made for using reference ranges which are based on estimating symmetric centiles of the underlying normal distribution, and appropriate formulae are given. The simplest such estimator, the sample mean plus or minus the normal-based number of sample standard deviations, is shown to have both theoretical and practical advantages.