### Working range

The working range of an analytical method is tested using the relative analyte 
values $x_r$ of the smallest and the largest calibration level, $j_1$ and $j_N$, 
respectively.

Relative analyte values are computed as $x_r = \frac {x_{i,j}} {\overline{x}_j}$ 
with $x_{i,j}$ being the peak area ratios of analyte and internal standard 
$x_{i,j}=\frac{A_\text{Analyte}}{A_\text{IS}}$ for each replicate $i$ and 
calibration level $j$.

For each $x_j$ in total $i=1..n$ replicate values exist and are tested:

- to follow a normal distribution (Kolmogorof-Smirnov Test, $P_{KS}$)
- to exhibit outliers (Grubbs-Test for single $P_{Grubbs1}$ and double $P_{Grubbs2}$ outliers)
- to show a trend, *i.e.* a drift associated with measurement order (Neumann-Test, $P_{Neumann}$)

Statistical test results are indicated in **Fig.V1** by colored symbols as $ns=$ 
not significant (green color), $*=$ significant at $P\le0.05$ (orange color) and
$**=$ significant at $P\le0.01$ (red color).

The two min/max calibration levels $j_1$ and $j_N$ are tested for homogeneity 
of variance using an F-Test. The user has the option to select other calibration
levels as min or max, *i.e.* $j_2$ or $j_{N-1}$. In case of a significant F-Test 
(no variance homogeneity), this allows to limit the working range to acceptable 
values.
