364
12.3.3 Lead Isotope Ratios: Measurement Challenges
Whichever methodology is selected, the natural or ‘common lead’
204
Pb isotope is
measured as a reference to calculate the original (primordial) level of the other
(mainly radiogenic) Pb isotopes, so accurate measurement of
204
Pb is essential
(Taylor et al. 2015). Unfortunately, for measurements made using inductively coupled plasma mass spectrometry (ICP-MS),
204
Pb suffers an isobaric interference
from
204
Hg (an isobaric overlap is where isotopes of different elements occur at the
same nominal mass) meaning that any mercury present as a contamination or as a
component of the sample would bias the measurement of
204
Pb.
12.4 Chemometric Tools
12.4.1 Multivariate Analysis
Multivariate statistical analysis (MSA) has been present in science for almost a
century. However, its application in the natural sciences began only in the late 50s
of the 20th century. Over time, multivariate analysis applications have become more
common as they have been increasingly appreciated by both scientists and business
people. Before the advent of MSA, most studies used analyses that processed a
maximum of two variables simultaneously. This analysis is based on measures of
central tendency (arithmetic mean and median), measures of variation (variance,
standard deviation and quarters), confidence intervals and tests based on normal
distribution, t-distribution, etc. The farthest reach in the study of the relationship
between the two phenomena was the correlation coefficient. MSA has provided
much more powerful techniques that have allowed researchers to discover patterns
of behaviour in the interrelationship of a large number of variables, patterns that
would otherwise be hidden or barely noticeable. In addition, most techniques are
precise enough to use a statistical significance test to determine whether a particular
interdependence is really relevant or whether it is the result of data fluctuations in
sample. These techniques have significantly increased the amount of usable information that can be extracted from the observed statistical data. Today, with the help
of high-tech computers and available statistical software, the results of multivariate
statistical analysis take only a few seconds. A variable or variable in the context of
MSA is any phenomenon that varies freely in such a way that these variations can
be identified and measured. When MSA is applied in research, we come across an
inexhaustible set of phenomena that can be analysed, such as, for example, imports,
exports, sales, costs, customer preferences, social product, national income, etc.
A multivariate technique can analyse the interrelationships between several variables (more than two), simultaneously according to the appropriate model on which
the technique is based. Most techniques identify patterns (patterns) of concordance
or relationships between many variables, assess the relative importance of each
L. Fan et al.
12.3.3 Lead Isotope Ratios: Measurement Challenges
Whichever methodology is selected, the natural or ‘common lead’
204
Pb isotope is
measured as a reference to calculate the original (primordial) level of the other
(mainly radiogenic) Pb isotopes, so accurate measurement of
204
Pb is essential
(Taylor et al. 2015). Unfortunately, for measurements made using inductively coupled plasma mass spectrometry (ICP-MS),
204
Pb suffers an isobaric interference
from
204
Hg (an isobaric overlap is where isotopes of different elements occur at the
same nominal mass) meaning that any mercury present as a contamination or as a
component of the sample would bias the measurement of
204
Pb.
12.4 Chemometric Tools
12.4.1 Multivariate Analysis
Multivariate statistical analysis (MSA) has been present in science for almost a
century. However, its application in the natural sciences began only in the late 50s
of the 20th century. Over time, multivariate analysis applications have become more
common as they have been increasingly appreciated by both scientists and business
people. Before the advent of MSA, most studies used analyses that processed a
maximum of two variables simultaneously. This analysis is based on measures of
central tendency (arithmetic mean and median), measures of variation (variance,
standard deviation and quarters), confidence intervals and tests based on normal
distribution, t-distribution, etc. The farthest reach in the study of the relationship
between the two phenomena was the correlation coefficient. MSA has provided
much more powerful techniques that have allowed researchers to discover patterns
of behaviour in the interrelationship of a large number of variables, patterns that
would otherwise be hidden or barely noticeable. In addition, most techniques are
precise enough to use a statistical significance test to determine whether a particular
interdependence is really relevant or whether it is the result of data fluctuations in
sample. These techniques have significantly increased the amount of usable information that can be extracted from the observed statistical data. Today, with the help
of high-tech computers and available statistical software, the results of multivariate
statistical analysis take only a few seconds. A variable or variable in the context of
MSA is any phenomenon that varies freely in such a way that these variations can
be identified and measured. When MSA is applied in research, we come across an
inexhaustible set of phenomena that can be analysed, such as, for example, imports,
exports, sales, costs, customer preferences, social product, national income, etc.
A multivariate technique can analyse the interrelationships between several variables (more than two), simultaneously according to the appropriate model on which
the technique is based. Most techniques identify patterns (patterns) of concordance
or relationships between many variables, assess the relative importance of each
L. Fan et al.