Typical CA Results Illustrated with an Extended Example

5 Typical CA Results Illustrated with an Extended Example 

For demonstration we use the data of a cooperative test [DOERFFEL and ZWANZIGER, 1987], In this interlaboratory comparison five laboratories were involved in the analysis of slag samples three times for seven chemical elements. So the (15, 7)-data matrix consists of 5 times 3 rows and 7 columns. The raw data in % are given in Tab. 5-2. The data have been preprocessed by standardization (autoscaling). 

The result of the clustering of the objects (samples) is shown in the dendrogram of Fig. 5-14. Clearly one can identify several groups of laboratories. From the analytical results laboratory B is separated as outstanding (cut the dendrogram at a linkage distance of, say, 60). So, as a first solution we have the laboratory B values in one cluster and those from the remaining laboratories in the other cluster. 

Beside this solution we can discuss a second solution obtained by cutting at a linkage distance of about 40. Here, the inhomogenous second cluster of the former solution splits into two clusters, namely one containing the values from laboratory E and another comprising those from the rest of the laboratories. From the aspect of precision we recognize 

It is now up to the analyst to interpret the dendrogram with respect to the possible causes of the structures found. For example in the case at hand a discussion with the laboratories revealed that laboratory E optimized its determination of some elements by atomic absorption spectroscopy. If we inspect the raw data in Tab. 5-2. the special location of the 

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