In eCerto: Statistical Tests for the Production of Reference Materials

Table of certified values

The table of certified values (Tab.C3) combines all data collected within a certification trial to provide for each measured entity within the certified material the certified mean $\mu_c$ and the certified uncertainty $U_{abs}$.

**Tab.C3** Table of certified values

Note! Only for analytes which have been visually inspected by the user certified values will be transfered to this table to ensure that inspection took place. The reported mean is similar to the value obtained in Fig.C1 but will be different to Tab.C2 when Labs are filtered for an analyte.

Several columns of the material table can be edited by the user by clicking in an individual cell and entering a new value.

Table column descriptions:

mean and sd give the arithmetric mean $\mu$ and standard deviation $s$ for n analytical values of this analyte similar to Fig.C1
n is dependent on pooling and gives the number of values used for calculting $\mu$ and $s$. To this end, n is either similar to the number of finite measurement values (pooling allowed) or similar to the number of labs included in the analysis (poolingnot allowed).

Example: We have an arbitrary analyte measured in three laboratories with five replicates each. We can calculate $\mu$ from all three laboratory averages (poolingnot allowed, n=3). If a laboratory is filtered, it will be grayed-out in the plot and not considered for $\mu$ (n=2). If the user decides to allow pooling than n will reflect the number of finite measurement values from all labs for this analyte (n = 2 x 5 = 10). - F columns can be added/edited and may contain correction factors $f_i$ to adjust $\mu$ and obtain the certified mean by $\mu_c = \mu \times \prod f_i$ - u columns can be added and may contain relative uncertainty contributions (e.g. from homogeneity or stability modules)

Note! u columns containing different uncertainty contributions should always be provided relative to the mean to allow an easy combination of the individual terms. Only U_abs is expressed as an absolute value.
u_char describes the characteristic uncertainty, calculated as $u_{char}=\frac{s}{\sqrt{n} \times mean}$
u_com is the combined uncertainty from all u columns, where all relative uncertainty components $u_i$ are combined using formula $u_{com}=\sqrt{\sum{u_i^2}}$
k is an additional expansion factor for the uncertainty $U=u_{com} \times k$
$U_{abs}$ specifies the absolute uncertainty and is calculated by $U_{abs}=U \times \mu_c$

Note! Numeric values of $\mu_c$ and $U_{abs}$ are rounded to the number of digits specified by the user at the analyte selection panel (Precision µ~c~). A precision according to DIN 1333 based on $U_{abs}$ is suggested. However, all relative u columns are depicted with fixed 4 digits precision.

Tab.C3 can be exported within a report using the download section on top of the page.