A distribution-free (non-parametric) quantile estimator based on the order statistics (the sorted values in the sample).
There are several definitions for the quantile estimator useful in defining reference limits.
|Formula (N is the sample size and p is the quantile)
||Piecewise linear function where the knots are the values midway through the steps of the empirical distribution function. Recommended by Linnet (2000) as having the lowest root-mean-squared-error .
||Linear interpolation of the expectations for the order statistics of the uniform distribution on [0,1]. Recommended by IFCC (1987) and CLSI (2010).
||Linear interpolation of the approximate medians for the order statistics. Has many excellent properties and is approximately median-unbiased regardless of the distribution.
A 95% reference interval (0.025 and 0.975 quantiles) requires a minimum sample size of 39. A
90% confidence interval for a 95% reference interval requires a minimum sample size of 119.