L.2.1.2.2 Analysis of example data

Logistic methods. In this manual, we recommend the use of untransformed

mortality for simplicity and consistency. However, LC50 estimates using other

scales can easily be calculated for comparison.

L.2.1.2.2 Analysis of example data

The data from Table L-3 were analyzed using several different LC50

methods, including the Probit procedure in the SAS program WATTOX

(Section L.4.1.1). In the Probit output (Section L.4.1.2), the chi-square

goodness-of-fit statistic (shown in bold) is not significant (?2 = 1.7558, P =

0.4157), indicating acceptable fit to the Probit model (i.e., no significant lack of

fit). The LC50 is obtained from the second output table of probabilities, where

probability = 0.50 (shown in bold). Other lethal effects concentrations may be

obtained from the same table, e.g., LC10 or LC5. The SAS Probit plot of

observed and predicted mortalities is given in Figure L-3.

Table L-5 provides LC50 estimates calculated by several different methods

using the example data in Table L-3. The data from the five replicates for each

concentration may be pooled and entered as the number responding (dying) out

of 100. Because pooling over replicates ignores any additional variance in

survival among replicates (i.e., beyond the expected error from sampling the

binomial distribution), the confidence limits provided by the programs may not

be accurate and should not be reported or used. Because the LC50 is required

only for use in the mixing model (Appendix H), confidence limits are not

needed.

Table L-5

Calculated LC50 Values for Example Water Column Toxicity Test

Data

Method

LC50 Estimate (percent v/v)

Probit

52.6

Linear Interpolation - untransformed mortality -

44.9

arcsine-transformed mortality

45.1

Trimmed Spearman-Karber

48.4

Logistic

52.6

The Probit LC50 was calculated with the EPA PROBIT program and was

almost identical to the Logistic LC50 calculated using the SYSTAT LOGISTIC

program (the same estimates are obtained using the SAS PROBIT procedure).

The LC50 estimated by Linear Interpolation, with untransformed mortality, was

almost identical to the LC50 calculated using arcsine-transformed mortality. The

TSK LC50 was calculated using a program modified from an original program

described in Hamilton, Russo, and Thurston (1977), and was intermediate

between the Linear Interpolation and regression (Probit and Logistic) estimates.

L24

Appendix L

Statistical Methods