### Symbol and formula collection

This is the collection of abrreviations and formulas used in the method validation
module of *eCerto*. While the calculations follow generally the recommendations
given in DIN 32645:2008-11, we hope that this redundancy may serve as a quick
reference when using *eCerto*.

| Symbol | Description                                                         |
|-------:|:--------------------------------------------------------------------|
| $N_j$  | total number of calibration levels with $j$ denoting the j-th level |
| $n_i$  | (minimal) number of replicates within a calibration level with $i$ denoting the i-th replicate |
| $x_{i,j}$ | denoting the normalized analyte value, the ratio of analyte and internal standard (IS) peak areas in replicate $i$ of level $j$ calculated as $x_{i,j}=\frac{A_\text {Analyte}}{A_\text {IS}}$ |
| $\overline{x}_j$ | mean of normalized analyte values at concentration $j$ |
| $x_r$ | denoting the relative analyte level $x_r = \frac {x_{i,j}} {\overline{x}_j}$ |
| $b_0, b_1, (b_2)$ | denoting the coefficients (intercept, slope, ...) of a linear (quadratic) model fitting the data |
| $e$   | denoting the residuals (error) of a model |
| $k$   | denoting the result uncertainty specified by the user |
| $t_{f,\alpha}$ | denoting the $t$ distribution with $f$ degrees of freedom and probability $\alpha$ |
| $s_{x,y}$ | denoting the standard error of estimate of a linear model of $N$ levels with residuals $e$ calculated as $s_{x,y}=\sqrt{\frac{\sum e^2}{N-2}}$ |
| $\text {LOD}$ | limit of detection of a linear model of $N$ levels with $n$ replicates having slope $b_1$ and residuals $e$ calculated as $\text {LOD} = k \times \frac {s_{x,y}} {b_1} \times t_{f,\alpha} \times \sqrt {{\frac {1} {n}} + {\frac {1} {N}} + \frac {\overline{x}^2} {\sum (x-\overline{x})^2}}$ where $f = N-2$ and $\alpha$ is specified by the user |
| ... | (to be completed) |
