In eCerto: Statistical Tests for the Production of Reference Materials

Laboratory statistics to identify potential outliers for lab means and lab variances

For an analyte selected in Tab.C3 various statistical tests regarding lab means and variance will be performed according to ISO 17025 and outlying values will be indicated if observed at the .05 and .01 level respectively. The displayed values n.s. and . indicate either that the test probability was >0.05 or that this lab was not tested because it did not contain an extreme value.

Note! eCerto performs outlier tests at the lower and upper end of the value distribution independently (i.e. two one sided tests). This might lead to confusion as P-values for both independent tests are displayed within the same column of Tab.C1. However, it allows to keep the output compact. Please always use results of Tab.C1 in parallel with Fig.C1 to decide on the removal of Labs.

**Tab.C1** Laboratory statistics

Except for Cochran, which tests for outliers with respect to variance, all other columns indicate potential outliers regarding lab means.

To compute the statistical tests eCerto uses functions from different packages available for R. Details regarding the conducted statistical test (implementation, parameters) can be found using the following links:

Scheffe Note! Similar letters indicate similar group and hence no difference. The test is performed at two $\alpha$ levels (.01 and .05) and re-implemented following the code provided in the agricolae package.
Dixon Note! The Dixon-Test was originally developed for small sample sizes of $3 \le n \le 30$. We use tabulated critical values for Dixon up to $n=100$ obtained from different tables in this website. Different tables are used according to $n$.
Grubbs Note! Test is performed as single (only the most extreme value at each end of the distribution is tested) as well as double version (the two most extreme values are tested against the rest). In accordance with ISO 17025 the double Grubbs Test is only conducted in case that the single Grubbs Test is not significant. Critical values for double Grubbs are obtained from the provided link for $4 \le n \le 30$ and are estimated for $31 \le n \le 100$ based on this paper.
Cochran Note! The Cochran test is performed consecutively, i.e. the Lab showing the highest variance is tested first. If significant, it is removed and the procedure is repeated. excl indicates that the sd of a lab was too low and the lab was removed from the testing procedure.

Note! Most tests require at least 3 data points (Labs) and finite differences in Lab means and Lab variances. If these conditions are not fulfilled Error might be reported instead of a P-value.