In eCerto: Statistical Tests for the Production of Reference Materials

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) |