SSD Curve Fitting
Estimate natural-log sample moments and a normal Q–Q linearity diagnostic for a species-sensitivity dataset; unlike quantile inversion, this fits data and does not claim statistical goodness-of-fit significance.
Description
Estimate natural-log SSD parameters and a normal-quantile regression diagnostic from species effect concentrations.
An SSD summarizes differences in sensitivity among species using comparable effect concentrations. Its meaning depends on which species and endpoints were selected, rather than on a distribution fit alone. Lognormal models treat the natural logarithms of those concentrations as approximately normal.1
This tool estimates the mean and sample standard deviation of natural-log concentrations and reports the number of supplied entries. It also regresses sorted log concentrations against normal quantile scores as a descriptive fit diagnostic.
Supply one consistently selected endpoint per intended species observation, all in the same concentration unit and on a comparable effect and exposure-duration basis. The calculator has no species identifiers and cannot verify independence or remove duplicate species.
When to use SSD Curve Fitting
Use it to inspect a curated species concentration set before calculating a lognormal SSD percentile, or compare parameter estimates under documented data-selection choices.
How to use SSD Curve Fitting and interpret its calculation
- Enter speciesEffectConcentrations with at least three positive finite values in one concentration unit.
- Run the fit and read logConcentrationMean, logConcentrationSampleSd, speciesCount, and normalQuantileFitRSquared.
- Review the data and diagnostic separately. If using the quantile tool, transfer the mean and sample SD without converting them to base-10 logs.
x_i = ln(C_i); μ = mean(x); s = sqrt[Σ(x_i − μ)²/(n − 1)]; z_i = Φ⁻¹[(i + 0.5)/n] for sorted entries, i = 0 … n−1 The SD uses the sample denominator n−1, not n.
The implementation sorts log values, computes their mean and sample SD, and performs an unweighted regression of sorted logs on approximate normal scores. Its R² is a quantile-plot linearity summary, not a formal goodness-of-fit probability or a likelihood-based model comparison.
{
"input": {
"speciesEffectConcentrations": [
0.36787944117144233,
1,
2.718281828459045
]
},
"output": {
"logConcentrationMean": 0,
"logConcentrationSampleSd": 1,
"normalQuantileFitRSquared": 1,
"speciesCount": 3
}
}Input order does not affect the result. Repeated concentration values are accepted if the overall log spread is positive; an all-identical list is rejected. Multiplying every concentration by a positive constant shifts the log mean by its natural logarithm and preserves the log SD and diagnostic R².
Limitations and assumptions
Three values meet the computational minimum, not a universal scientific sufficiency requirement. The tool cannot assess taxonomic coverage, endpoint relevance, test quality, or whether repeated values represent independent species.
No censored-data model, confidence interval, bootstrap, species weighting, distribution selection, or hazardous-concentration calculation is performed. A high R², especially for a small sample, does not establish a valid SSD.
Alternative or Complementary methods
Use the parameter estimates in a quantile calculation only after checking the model and selected endpoints. Exposure modeling and human reference-dose comparisons address different questions from cross-species ecological sensitivity.
References
-
Species Sensitivity Distribution (SSD) Toolbox — U.S. Environmental Protection Agency