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).

```
lod(
object,
...,
alpha = 0.05,
beta = 0.05,
method = "default",
tol = "default"
)
```

- object
A univariate model object of class

`lm`

or`rlm`

with model formula`y ~ x`

or`y ~ x - 1`

, optionally from a weighted regression.- ...
Placeholder for further arguments that might be needed by future implementations.

- alpha
The error tolerance for the decision limit (critical value).

- beta
The error tolerance beta for the detection limit.

- method
The “default” method uses a prediction interval at the LOD for the estimation of the LOD, which obviously requires iteration. This is described for example in Massart, p. 432 ff. The “din” method uses the prediction interval at x = 0 as an approximation.

- tol
When the “default” method is used, the default tolerance for the LOD on the x scale is the value of the smallest non-zero standard divided by 1000. Can be set to a numeric value to override this.

A list containig the corresponding x and y values of the estimated limit of detection of a model used for calibration.

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.

Examples for `din32645`

```
m <- lm(y ~ x, data = din32645)
lod(m)
#> $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
#>
```