Advanced Statistics 
27 
Advanced Statistics 
The statistical methods of correlation and clustering can be helpful in compar 
ing samples to find possible matches. As shown above, correlation was applied 
to find suitable matches (see “Method of data evaluation”), whitening and clus 
tering however are going to be looked at in more detail during further Investiga 
tions. The following section focuses on an unconventional but very Interesting 
approach of sample characterisation, which was suggested by René der Bruyn 
(NFI). This approach uses the GC-FID data and condenses the Individual bell 
shape and its position within the chromatogram Into a set of 2D data. 
Looking at a GC-FID chromatogram of a paraffin wax, the peak heights of 
every n-alkane (more or less) resemble a bell shape (compare Fig. 16). This 
line, described by each peak-intensity, can be seen as an analogy to a distri 
bution curve. Considering the n-alkanes abundancies under this curve as rela 
tive frequencies of a discrete probability density function, It can be used to 
derive the standard deviation (describing the variability) and the mean (as a 
weighted average, the location of the geometric balance point). These two val 
ues now represent the very unique properties of the paraffin wax composition. 
Calculation of these values can be performed following the common formulas 
(Formula 1). 
+-- sample: DelQ_1712 + 
n-Alkane 
Fig. 16: Transformation of the n-alkane profile derived from GC-FID analysis to a discrete probabil 
ity density function (PDF).