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L.2.1.2 Calculating median lethal concentration
Figure L-2. LC50 decision tree
in the lowest elutriate concentration must be at least 50 percent (1); otherwise
the test must be repeated using lower concentrations (2). An LC50 should not be
calculated unless at least 50 percent of the test organisms die in at least one of
the serial dilutions (3). If there are no mortalities greater than 50 percent, then
the LC50 is assumed to be $100 percent elutriate (4).
If the conditions in (1) and (3) are met, then replicate mortality data for each
concentration are pooled (5) for calculation of LC50 (6). The Probit method (7)
can be used if the data meet the requirements of the Probit method listed below
and fit the probit model (8). The Trimmed Spearman-Karber (TSK) and Logistic
methods (described below) are acceptable substitutes for the Probit method,
provided that these data meet the requirements of these alternative methods. If
these data do not meet the requirements of the Probit method or alternatives,
then the Linear Interpolation method should be used (9). When an LC50 value
has been determined, 1 percent of that value is entered into the mixing model
(10) provided in Appendix E for mixing zone evaluation.
Calculation of LC50 values is also recommended for reference toxicant tests
to determine the relative health of the organisms used in toxicity and bioaccumu-
lation testing.
L. Methods for calculating LC50
Stephan (1977) and Gelber et al. (1985) provide careful reviews of LC50
estimation procedures. In addition, USEPA (1985) discusses in detail the
mechanics of calculating LC50 using various methods and contains, as an
appendix, computer programs for each statistical method. The most commonly
used methods are the Probit, Trimmed Spearman-Karber (TSK) and Linear
Interpolation. This Appendix recommends use of the Probit, TSK or Logistic
methods if the data are appropriate; otherwise the Linear Interpolation method
may be used (Figure L-2). In general, results from different methods should be
similar. Programs commonly used to calculate LC50 are PROBIT, developed for
and available from the USEPA (Environmental Monitoring and Support Labora-
tory, Cincinnati, OH), and several programs developed by Dr. C.E. Stephan, the
USEPA Environmental Research Laboratory, Duluth, MN. SAS program
statements for the Probit procedure are included in WATTOX (Section L.4.1).
Probit. The Probit method is based on regression of the probit of mortality
on the log of concentration. A probit is the same as a z-score; for example, the
Probit corresponding to 70 percent mortality is z0.70 or .0.52. The LC50 is
calculated from the regression, and is the concentration associated with z = 0
(mortality = 50 percent). The Probit method can be used whenever the following
conditions are met:
There are at least two concentrations with partial mortality (i.e., >0 and
<100 percent).
These data points fit the probit regression line reasonably well.
Appendix L
Statistical Methods

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