lod(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default")
lm
or
rlm
with model formula y ~ x
or y ~ x - 1
,
optionally from a weighted regression.
The decision limit (German: Nachweisgrenze) is defined as the signal or analyte concentration that is significantly different from the blank signal with a first order error alpha (one-sided significance test). The detection limit, or more precise, the minimum detectable value (German: Erfassungsgrenze), is then defined as the signal or analyte concentration where the probability that the signal is not detected although the analyte is present (type II or false negative error), is beta (also a one-sided significance test).
- The default values for alpha and beta are the ones recommended by IUPAC.
- The estimation of the LOD in terms of the analyte amount/concentration
xD from the LOD in the signal domain SD is done by simply inverting the
calibration function (i.e. assuming a known calibration function).
- The calculation of a LOD from weighted calibration models requires
a weights argument for the internally used predict.lm
function, which is currently not supported in R.
Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, Chapter 13.7.8
J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules. Web edition.
Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995). Analytica Chimica Acta 391, 105 - 126.
$x [1] 0.08655484 $y 1 3317.154# The critical value (decision limit, German Nachweisgrenze) can be obtained # by using beta = 0.5: lod(m, alpha = 0.01, beta = 0.5)$x [1] 0.0698127 $y 1 3155.393