Linear Interpolation Method

The data do not fit the Probit (or Logistic) models.

The Linear Interpolation method should also be used when LC50s are

calculated and compared over an extended time series (i.e., for tracking reference

toxicant results), because inevitably, one or more data sets will fail to meet the

requirements for the Probit, TSK, or Logistic methods. Linear Interpolation may

also be used if programs for the other methods are unavailable, but we strongly

recommend that investigators have programs available for one or more of the

other methods.

The Linear Interpolation method calculates an LC50 by interpolation between

the two concentrations with mortality nearest to, and on either side of 50 percent.

The interpolation is made on a log concentration scale, using the following

formula:

(50 - M L )( logCU ) + ( M U - 50)( logC L )

LC 50 = antilog

(L-15)

MU - M L

where

CL = concentration with mortality nearest to and below 50 percent

CU = concentration with mortality nearest to and above 50 percent

ML = percent mortality at CL

MU = percent mortality at CU.

If there are no partial mortalities, the formula simplifies to:

LC 50 = ( CU ) ( C L )

(L-16)

For the example data given in Table L-3, CL = 25 percent elutriate

(log = 1.398); ML = 28 percent mortality; CU = 50 percent elutriate (log = 1.699);

and MU = 54 percent mortality. Therefore:

(50 - 28) (1.699) + (54 - 50) (1.398)

LC 50 = antilog

(L-17)

54 - 28

or 44.9 percent.

The formula and example given above express mortality on an arithmetic

(untransformed) scale. Some computer programs or investigators may use

arcsine-transformed mortalities (Stephan 1977; see Section L.2.1.1.1, Tests of

Assumptions). One could also express mortality on a probit or logit scale, if

there were one partial mortality on each side of 50 percent. In those cases, the

Linear Interpolation should produce the same LC50 estimate as the Probit or

L23

Appendix L

Statistical Methods