L.2.1.2.1 Methods for calculating LC50

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.2.1.2.1 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.

L20

Appendix L

Statistical Methods