In eCerto: Statistical Tests for the Production of Reference Materials

Homogeneity boxplot

Statistical differences between groups are nicely visualized using boxplots. While the ANOVA allows to calculate a probability testing the hypothesis that the mean values of different groups are similar or not, the boxplot visualizes the distribution of values within each group.

The box comprises 50% of the measured values of a group (from 25% to 75% quartile) and highlights the median (50% quartile). Overlapping boxes indicate that a t-test would not yield a significant P-value.

Within Fig.H1 dashed black and grey lines indicate $\mu$ and $s$ of the distribution of specimen means from Tab.H2.

Especially when several analytes are tested in a material using a small number of replicates per specimen, ANOVA might result in P-values below the alpha-level. Observing such a P-value does not automatically render the material non homogeneous. Due to multiple testing such observations might be False Positive results. However, they require a more careful inspection of the data to identify a potential systematic bias. To this end, eCerto offers several options:

• apply bonferroni correction to account for multiple testing (if adjusted P-values are above the alpha level, the material can be considered as homogeneous)
• check z-scores plot of all analytes (to check if there are specimen which deviate from the poupulation mean systematically, i.e. in one direction)
• overlay Fig.H1 with numbers indicating the replicate (to check if for a suspicious specimen always the same replicate over all analytes causes a severe deviation, which might be a reason to exclude this single measurement)

eCerto documentation built on April 12, 2025, 9:13 a.m.