Estimating the 5-percentile of the species sensitivity distributions without any assumptions about the distribution.
Nelly van der Hoeven*
ECOSTAT, Vondellaan 23, 2332 AA, Leiden, The Netherlands
Nelly van der Hoeven,
2332 AA Leiden,
tel.: (+)31-(0)71-5315011; fax: (+)31-(0)842-116988;
email: NvdH @iecostat.nl
A non-parametric method is described to estimate the hazardeous concentration for p% of the species, the HCp, and the confidence limits for this value, the
HCp(α). For this method, all observed sensitivities are ordered from high to low sensitivity. The HC5 is the k-th observation were k is the largest integer below 0.05×(n+1). It is described how the
HCp(α) can be calculated. A table is presented for easy calculation of several conservative confidence limits for the HC5. For the HC5(0.05), a second table is presented which can be used to interpolate between the conservative estimate of the HC5(0.05) and the next higher observed concentration.
The non-parametric HC5 and HC5(0.05) estimation is illustrated with an example of sensitivity data on malathion. For this data set, the log-normal HC5 and HC5(0.05) estimations appear to be conservative compared with the non-parametric estimate. It is stressed that HC5 and HC5(0.05) estimates will often be much more affected by the non-randomness of the species set for which sensitivity data are available than by the choice of the statistical method.
keywords: beta distribution; hazardeous concentration
Ecotoxicology 10: 25-34, 2001