Document ID: chunk:federal_register_of_legislation:F2013C00288:reg:3:p9
Version: federal_register_of_legislation:F2013C00288
Segment Type: reg
Provision Reference: reg 3 (pt 9/21)
Character Range: 1368403–1371299

of shapes that BT III distributions can have is large (Shao 2000), including the log-logistic distribution and approximations of the log-normal and log-triangular distributions. Thus, attempting to fit a BT III distribution to any given toxicity data set has a greater probability of success than attempting to fit only the log-logistic distribution.

This method is guaranteed to fit a statistical distribution to the toxicity data at least as well as the Aldenberg and Slob method because the log-logistic distribution is a BT III distribution (Shao 2000). Greater detail about the BT III method is provided in Shao (2000).

3.2.2         How do SSD methods work?
The main difference between the various SSD methods is the statistical distribution that they fit to the data. For that reason, the following explanation of how SSDs work is generic.

In SSD methods, each species is given equal weighting and a single value is used to represent the sensitivity of each species. However, there is usually multiple toxicity data for each species which requires some manipulation. The rules governing this manipulation were presented earlier in this Schedule. The data is then entered into SSD software such as ETx (Aldenberg & Jaworska 2000) or BurrliOZ (Campbell et al. 2000). The SSD calculates the cumulative frequency of the species sensitivity data by ranking the data from lowest to highest and then using the formula:
cumulative frequency = rank * [100/(n + 1)]             (equation 12)

The cumulative frequency for each species is then plotted against the concentration that represents the sensitivity of each species. A typical SSD plot is shown in Figure 5 below. In the case of the Stephan et al. (1985), Wagner and Løkke (1991), Aldenberg and Slob (1993), and Aldenberg and Jaworska (2000) methods that fit one specific distribution to the toxicity data, statistical tests (for example, the Kolmorogorov Smirnov test or the Anderson-Darling test) are used to determine if the toxicity data fits the selected distribution. The more flexible SSD methods, for example,  BT III and the approach adopted by Maltby et al. (2003) and Kwok et al. (2007), use statistical methods (for example, maximum likelihood methods, Anderson-Darling test) to determine which particular statistical distribution best fits the toxicity data. In doing this, the SSD methods estimate the parameters that mathematically describe the selected distribution. Because the equation that describes the selected distribution is known, it is very simple to calculate the concentration that should theoretically protect any chosen percentage of species or permit any chosen percentage of species to experience toxic effects. To do this, the cumulative frequency that corresponds to the percentage of species to be protected is entered into the equation for the distribution that best fitted the toxicity data. Thus, the