ENBIS: European Network for Business and Industrial Statistics

On hierachical vs non-hierarchical comparisons in metrology and testing

23 September 2009, 10:45 – 11:05

Abstract

Submitted by

Franco Pavese

Authors

Franco Pavese

Affiliation

INRIM, Torino, Italy

Abstract

The type of data treatment is different depending on whether the comparison, in particular a key comparison of the MRA, is of the hierarchic or non-hierarchic type. It is not meant here the possible hierarchy between the participant laboratories, typically the National primary laboratory and accredited laboratories; nor, in the opposite sense, a non-hierarchy between them like in the MRA key comparisons or some top-level study for a new method or a new reference material in testing, but an intrinsic characteristics of the comparison measurand or design.
Typical of hierarchical comparisons is when the comparison involves artefact standards. In this case, the summary parameters of the comparison are hierarchically higher than the input dataset. It is generally to have a measure of the bias of each laboratory, and even of the differences between the bias of pairs of laboratories unless at least one of the standards is hierarchically higher in level and assigned a stipulated value.
In case of non-hierarchical comparisons, the summary parameters are generally not of a hierarchically higher level than the input dataset, because the comparison dataset can be considered drawn from a single super-population. This happens, e.g., when a single standard is circulated for measurement; when the measured samples are all drawn from a single batch of a reference material; when the standards are all realisations of a single condition –namely a physical or chemical state.
In this case, the input dataset has some similarities with the within-laboratory data under reproducibility conditions, but, for the distribution of the super-population, called mixture distribution, the pooled distribution of the populations distributions is considered instead, being the super-population the only random variable under analysis. There are basic differences with respect to the case of within-laboratory data under reproducibility conditions.
The paper will discuss in detail these two categories.

Return to programme