lc50_traditional: LC Estimation by the Traditional Linear Regression Method

In insectecol: Insect Ecology Data Analysis Toolkit

LC Estimation by the Traditional Linear Regression Method

Description

Estimates the lethal concentration by fitting an ordinary (unweighted) least-squares line to the probit-transformed mortality.

Usage

lc50_traditional(d, lc = 0.5)

Arguments

d	A data frame with the columns Concentration, Tested and Dead, as returned by lc50_read; rows with Concentration = 0 are treated as the control group.
lc	Numeric; the lethal proportion for which the concentration is estimated. The default 0.5 gives the LC50, 0.9 the LC90.

Details

The corrected mortalities are transformed to probits (y = qnorm(p) + 5) and the concentrations to common logarithms (x = log10(concentration)); the line y = a + b * x is fitted by ordinary least squares with all points weighted equally. Inverting the line at the probit that corresponds to the requested lethal proportion gives LC = 10^((y0 - a) / b) with y0 = qnorm(lc) + 5. The 95 covariance matrix of the regression coefficients on the log scale and back-transformed to the concentration scale. A Pearson chi-square goodness-of-fit test of the observed against the fitted mortalities is attached.

Mortalities are corrected for natural mortality in the control group with the Abbott (1925) formula, and concentrations with a corrected mortality of exactly 0 undefined) are dropped before fitting; at least 3 valid concentrations are required.

Value

A list with elements

method	name of the estimation method
lc	the lethal proportion used
estimate	the LC estimate
lower, upper	limits of the 95% confidence interval
intercept, slope	the regression coefficients a and b
se_slope	standard error of the slope
equation	the regression equation as a character string
r2	coefficient of determination
chisq, chi_df, p_chi	Pearson chi-square statistic, degrees of freedom and p value of the goodness-of-fit test
n_groups	number of concentration groups used in the fit
dropped	number of concentration groups dropped
fit	the fitted model object
prep	the preprocessed data

References

Finney, D. J. (1971) Probit Analysis, 3rd edition. Cambridge University Press, Cambridge.

Abbott, W. S. (1925) A method of computing the effectiveness of an insecticide. Journal of Economic Entomology 18(2), 265-267.

See Also

lc50_improved for the weighted version, lc50_probit for the maximum-likelihood version, lc50_calculate for the batch workflow.

insectecol documentation built on Oct. 5, 2026, 5:08 p.m.