In eCerto: Statistical Tests for the Production of Reference Materials

Analyte options

For analytes under inspection (i.e. which are selected in Tab.C3), several analyte specific parameters can be set and will be stored also in the backup file.

**User Options** Possible options which can be set per individual analyte

Pooling

pooling means that calculations in the material table (mean, sd and uncertainty columns) are not based on the lab means, but rather on all measured values. This is justified when the between lab variance is smaller than the within lab variance (check if the ANOVA P-value is insignificant in Tab.C2, if so pooling might be allowed).

Selecting this option will also affect n in Tab.C3 being either the number of included labs or the number of finite data points from these labs.

Filtering

Individual Samples can be filtered by ID (select show IDs in Fig.C1 to identify outlying IDs). These samples will not be used in any calculations. They are removed from downstream processing right after import. However, information of this filtering step is preserved and included in reports.

Labs can be excluded by Lab-ID. Please note, that this is done after statistical testing for mean and variance outliers (in Tab.C1 and Tab.C2). Filtered labs are depicted in Fig.C1 (using grey color), but excluded from calculating the certified value of the analyte in Tab.C3.

Rounding

Note! Internally, all calculations are performed on non-rounded values (as imported). Only the visual output to the user is rounded to improve readability. Because analytes within an RM might be measured at very different scales it is possible to define analyte specific precision values for rounding. The Precision (Tables) value is used for most values displayed in tables.

The only exception is Tab.C3. Here, Precision (µ_c) is used to round $\mu_c$ and $U_{abs}$ to allow to comply with DIN/ISO regulations on rounding and columns containing relative uncertainties are rounded to fixed 4 digit precision.

The user can decide the rounding precision for $\mu_c$ and $U_{abs}$ and even specify negative numbers for Precision (µ_c) to indicate a desired rounding digit left of the decimal separator (i.e. $-1$ to round an uncertainty of 13.1 up to 20). If the uncertainty is even larger, the user should consider to upload data using a different (more appropriate) unit and, for instance, switch from mg/L to g/L.

DIN1333

eCerto suggests the rounding precision for $\mu_c$ and $U_{abs}$ according to DIN 1333. The appropriate value is displayed right over the input box of Precision (µ_c). It's background is colored green if it is in accordance with the user selected value and red otherwise.

The significant digit is determined based on the first non-zero digit in $U_{abs}$. The position will be shown above the analyte parameter Precision (µ_c) upon selection of an analyte in Tab.C3. Once found, the respective digit will be rounded up for $\mu_c$ if the consecutive digit is $\ge 5$ and down otherwise. For $U_{abs}$ the rounding procedure is a bit more complicated. If the respective digit is 1 or 2, than the consecutive digit will be rounded up. If the respective digit is $\ge 3$, than it will be rounded up itself.