In eCerto: Statistical Tests for the Production of Reference Materials

Statistics on the distribution of lab means

The distribution of lab means is evaluated using a variety of recommended tests. Normality of the distribution is tested using the KS-Test. Besides mean and sd the robust alternatives median and MADare provided. Columns which end on _p provide P-values of the respective tests. Skewness and Kurtosis are computed additionally and grouped with their respective tests (Agostino and Anscombe).

**Tab.C2** Statistics on the lab mean distribution

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

Bartlett s-test of the null hypothesis that the variances in each of the labs is the same.
ANOVA tests if labs are significantly different from each other (which is almost always the case). Note! Should the ANOVA P-value be not significant you can select the pooling option for this analyte.
KS -test performs a one-sample (Kolmogorov) test, which is carried out of the null that the distribution of lab means is similar to a normal distribution with parameters $\mu$ and $\sigma$ estimated from the analyte data.
Skewness computes the skewness of the distribution.
Agostino performs the D'Agostino test for skewness in normally distributed data.
Kurtosis computes the estimator of Pearson's measure of kurtosis.
Anscombe performs the Anscombe-Glynn test of kurtosis for normal distributed samples. Note! Skewness and Kurtosis are computed using a two-sided alternative.

Note! Some tests need a minimum number of replicates and will not yield a result if this criteria is not met (i.e. Agostino).

The is used to compare the distribution of Lab means against a normal distribution. Besides the KS test P-value, deviation of the data from a normal distribution can also be visually investigated by opening a QQ-plot using the respective link.