Quantile
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) | Description |
|---|---|
| Np+1/2 | 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 . |
| (N+1)p | Linear interpolation of the expectations for the order statistics of the uniform distribution on [0,1]. Recommended by IFCC (1987) and CLSI (2010). |
| (N+1/3)p+1/3 | 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.
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