Reference limits

A reference limit defines a value where a given proportion of reference values are less than or equal to. A reference interval defines the interval between a lower and upper reference limit that includes a given proportion of the reference values.

The process of defining a reference interval is that reference individuals compromise a reference population from which is selected a reference sample group on which are determined reference values on which is observed a reference distribution from which are calculated reference limits that define a reference interval.

A point estimate of a reference limit is a single value that is the best estimate of the true unknown parameter; a confidence interval is a range of values and indicates the uncertainty of the estimate. It is important to remember that the width of the confidence interval is dependent upon sample size and that large sample sizes are required to produce narrow confidence intervals, particularly for skewed distributions (Linnet, 2000).

There are numerous quantile estimators that may define the reference limits. The best estimator depends heavily on the shape of the distribution.

• Normal theory quantile
  A quantile estimator derived from a normally distributed population with unknown mean and standard deviation.
• Quantile
  A distribution-free (non-parametric) quantile estimator based on the order statistics (the sorted values in the sample).
• Bootstrap quantile
  A distribution-free (non-parametric) quantile estimator that is the median of a set of quantiles calculated by re-sampling the original sample a large number of times and computing a quantile for each sample.
• Harrell-Davis quantile
  A distribution-free (non-parametric) estimator that is a weighted linear combination of order statistics. It is substantially more efficient than the traditional estimator based on one or two order statistics.
• Robust bi-weight quantile
  A quantile estimator that uses robust estimators of location and spread, which resist the effects of extreme observations.