Chemometrics
• "Chemometrics has been defined as the
application of mathematical and statistical
methods to chemical measurements.
" B. Kowalski, Anal. Chem. 1980, 52, 112R-122R.
• "Chemometrics is the chemical discipline that
uses mathematical and statistical methods for the
obtention in the optimal way of relevant
information on material systems." I. Frank and B.
Kowalski, Anal. Chem.,1982, 54, 232R-243R.
Chemometrics
• "Chemometrics developments and the accompanying
realization of these developments as computer software
provide the means to convert raw data into information,
information into knowledge and finally knowledge into
intelligence." M. Delaney, Anal. Chem. 1984, 261R-277R.
• ...research in chemometrics will contribute to the design
of new types of instruments, generate optimal
experiments that yield maximum information, and
catalog and solve calibration and signal resolution
problems. All this while quantitatively specifying the
limitations of each instrument as well as the quality of
the data it generates." L. S. Ramos et al., Anal. Chem.
1986, 58, 294R-315R.
Chemometrics
• "Chemometrics, the application of statistical and
mathematical methods to chemistry..." S. Brown,
Anal. Chem., 1986, 60, 252R-273R.
• "Chemometrics is the discipline concerned with
the application of statistics and mathematical
methods, as well as those methods based on
mathematical logic, to chemistry." S. Brown,
Anal. Chem. 1990, 62, 84R-101R.
Chemometrics
• "Chemometrics is the use of mathematical and
statistical methods for handling, interpreting, and
predicting chemical data."
• Malinowski, E.R.. (1991) Factor Analysis in
Chemistry, Second Edition, page 1.
• "Chemometrics is the discipline concerned with the
application of statistical and mathematical methods,
as well as those methods based on mathematical
logic, to chemistry." S. Brown et al., Anal. Chem.
1992, 64,22R-49R.
•
Chemometrics
• "Chemometrics can generally be described as the
application of mathematical and statistical
methods to 1) improve chemical measurement
processes, and 2) extract more useful information
from chemical and physical measurement data."
J. Workman, P. Mobley, B. Kowalski, R. Bro, Appl.
Spectrosc. Revs. 1996, 31, 73-124.
• "Chemometrics is an approach to analytical and
measurement science based on the idea of
indirect observation. Measurements related to the
chemical composition of a substance are taken,
and the value of a property of interest is inferred
from them through some mathematical relation."
B.Lavine, Anal. Chem. 1998, 70, 209R-228R.
Chemometrics
•
"Chemometrics is a chemical discipline that uses
mathematics, statistics and formal logic
(a) to design or select optimal experimental procedures;
(b) to provide maximum relevant chemical information by
analyzing chemical data; and
(c) to obtain knowledge about chemical systems."
Massart, D.L., et al.. (1997) Data Handling in Science
and Technology 20A: Handbook of Chemometrics and
Qualimetrics Part A, page 1.
"The entire process whereby data (e.g., numbers in a table)
are transformed into information used for decision
making."
Beebe, K. R., Pell, R. J., and M. B. Seasholtz. (1998)
Chemometrics: A Practical Guide, page 1.
Chemometrics
• “Chemometrics (this is an international definition) is
the chemical discipline that uses mathematical and
statistical methods,
(a) to design or select optimal measurement
procedures and experiments; and
(b) to provide maximum chemical information by
analyzing chemical data.”
Bruce Kowalski, in a formal CPAC presentation,
December 1997
CHEMOMETRICS IS NOT A UNITARY
SUBJECT LIKE ORGANIC CHEMISTRY
ORGANIC CHEMISTRY IS BASICALLY A
KNOWLEDGE BASED SUBJECT – certain basic
skills and then increase the knowledge.
CHEMOMETRICS IS MORE A SKILLED BASED
SUBJECT – not necessary to have a huge
knowledge of named methods, a very few basic
principles but one must have hands-on experience to
expand one’s problem solving ability.
DIFFERENT GROUPS HAVE DIFFERENT BACKGROUNDS
AND EXPECTATIONS AS TO HOW CHEMOMETRICS
SHOULD BE INTRODUCED
Statisticians want to start with distributions, hypothesis tests
etc. and build up from there. They are dissatisfied if the maths
is not explained.
Chemical engineers like to start with linear algebra such as
matrices, and expect a mathematical approach but are not
always so interested in distributions etc.
Computer scientists are often most interested in algorithms.
Analytical chemists often know a little statistics but are not
necessarily very confident in maths and algorithms so like to
approach this via statistical analytical chemistry. Difficult
group because the ability to run instruments is not necessarily
an ability in maths and computing.
Organic chemists do not like maths and want automated
packages they can use. They often require elaborate courses
that avoid matrices. The course an organic chemist would
regard is good is one a statistician would regard as bad.
Errors in quantitative analysis
• No quantitative results are of any value unless they
are accompanied by some estimate of the errors
inherent in them
• 24.69
24.73
24.77
25.39 (outlier)
X  error%
Types of errors
• Based on laboratory measurements:
–
–
–
–
Instrumental
Methodology
Theoretical
Data treatment
• Based on their effect on the evaluation of the result:
– Systematic-mostly instrumental
– Random
– Personal
– Gross
• Random errors cause replicate results to differ from
one another so that the individual results fall on both
sides of the average values even when all other
errors are allowed for.
– The deviation would be slight otherwise it could have been
investigated
– The total effects of the causes would yield a significant
deviation
• Systematic errors cause all the results to be in error
in the same sense
–
–
–
–
Instrumental errors are the most important
Insufficient chemical purity
Imperfect standard calibration and standardization
Bias of the measurement is the total systematic error (some
sources cause +ve and others cause –ve results)
• Personal errors
The results depend to some extent on the physical
peculiarities of the observer (under otherwise equal
conditions). These can be both systematic and
random.
• Gross errors
Errors that are so serious that there is no real
alternative t abandoning the experiment and making
a completely fresh start (external influences that
cause completely inaccurate results such as reading
20.0 and writing 30.0.
Absolute and relative errors

• Absolute error

• Relative error
  100 
x
• Reduced relative error
[%]

  100  ( x  x )  100  [%]
R
R
max
min
• Accuracy (according to ISO =International Standards
Organization): the closeness of agreement between
a test result and the accepted reference value of the
analyte
• Precision= reproducibility and repeatability
• Precision describes random error, bias describe
systematic error and the accuracy incorporates both
types of errors.
• Repeatability
Within-run-precision
• Reproducibility
Between-run-precision
Random and systematic errors in titrimetric analysis
It involves about 10 separate steps:
1. Making up a standard solution of one of the reactants. This involves
(a) weighing a weighing bottle or similar vessel containing some solid
material,
(b) transferring the solid material to a standard flask and weighing the bottle
again to obtain by subtraction the weight of solid transferred (weighing by
difference), and
(c) filling the flask up to the mark with water (assuming that an aqueous
titration is to be used).
2. Transferring an aliquot of the standard material to a titration flask with the aid
of a pipette. This involves
(a) filling the pipette to the appropriate marls, and
(b) draining it in a specified manner into the titration flask.
3. Titrating the liquid in the flask with a solution of the other reactant, added
from a burette. This involves
(a) filling the burette and allowing the liquid in it to drain until the meniscus is
at a constant level,
(b) adding a few drops of indicator solution to the titration flask,
(c) reading the initial burette volume,
(d) adding liquid to the titration flask from the burette a little at a time until the
end-point is adjudged to have been reached, and
(e) measuring the final level of liquid in the burette.
• In principle, we should examine each step to evaluate the
random and systematic errors that might occur.
• Amongst the contributions to the errors are the tolerances of
the weights used in the gravimetric steps, and of the volumetric
glassware
• Standard specifications for these tolerances are issued by such
bodies as the British Standards Institute (BSI) and the
American Society for Testing and Materials (ASTM).
• Tolerance for a grade A 250-ml standard flask is ±0.12 ml:
grade B glassware generally has tolerances twice as large as
grade A glassware
Handling systematic errors
• Much of the remainder of topics will deal with the
evaluation of random errors, which can be studied
by a wide range of statistical methods.
• In most cases we shall assume for convenience that
systematic errors are absent
• Many determinations have been made of the levels
of (for example) chromium in serum
– Different workers, all studying pooled serum samples from
healthy subjects, have obtained chromium concentrations
varying from < 1 to ca. 200 ng/ ml. In general the lower
results have been obtained more recently, and it has
gradually become apparent that the earlier, higher values
were due at least in part to contamination of the samples by
chromium from stainless-steel syringes, tube caps, and so
on.
• Methodological systematic errors of this kind are
extremely common - incomplete washing of a
precipitate in gravimetric analysis, and the indicator
error in volumetric analysis
•
•
•
•
•
Another class of systematic error that occurs widely arises when false
assumptions are made about the accuracy of an analytical instrument.
Experienced analysts know only too well that the monochromators in
spectrometers gradually go out of adjustment, so that errors of
several nanometres in wavelength settings are not uncommon, yet
many photometric analyses are undertaken without appropriate
checks being made.
Very simple devices such as volumetric glassware, stop-watches, pHmeters and thermometers can all show substantial systematic errors,
but many laboratory workers regularly use these instruments as
though they are always completely without bias.
Instruments controlled by microprocessors or microcomputers has
reduced to a minimum the number of operations and the level of skill
required of their operators. Yet such instruments are still subject to
systematic errors.
Systematic errors arise not only from procedures or apparatus; they
can also arise from human bias.
– Some chemists suffer from astigmatism or colorblindness (the
latter is more common amongst men than women) which might
introduce errors into their readings of instruments and other
observations.
– A number of authors have reported various types of number bias,
for example a tendency to favour even over odd numbers, or 0 and
5 over other digits, in the reporting of results.
Approaches to avoid systematic errors
• The analyst should be vigilant concerning the instruments’
functions, calibrations, analytical procedures and others.
• Handling the design of the experiment at every stage carefully.
– weighing by difference can remove some systematic
gravimetric errors:
– If the concentration of a sample of a single material is to be
determined by absorption spectrometry, two procedures are
possible. In the first, the sample is studied in a 1-cm pathlength spectrometer cell at a single wavelength, say 400 nm,
and the concentration of the test component is determined
from the A = ebc
– Several systematic errors can arise here. The wavelength
might be (say) 405 nm rather than 400 nm, thus rendering
the reference value of e inappropriate; this reference value
might in any case be wrong; the absorbance scale of the
spectrometer might exhibit a systematic error; and the pathlength of the cell might not be exactly 1 cm. Alternatively,
the analyst might take a series of solutions of the test
substance of known concentration, and measure the
absorbance of each at 400 nm.
Planning and design of experiments
•
•
•
•
Statistical tests are not used only to assess the results of completed
experiments but also they may be considered crucial in the planning
and design of experiments.
In practice, the overall error is often dominated by the error in just one stage
of the experiment, other errors having negligible effects when all the errors are
combined correctly. Again it is obviously desirable to try to identify, before the
experiment begins, where this single dominant error is likely to arise, and then
to try to minimize it.
Although random errors can never be eliminated, they can certainly be
minimized by particular attention to experimental techniques: improving the
precision of a spectrometric experiment by using a constant temperature
sample cell would be a simple instance of such a precaution.
Some times many experimental parameters should be taken into consideration,
such as sensitivity, selectivity, sampling rate, cost, etc.). So the experiment
should be designed in a way to optimize all parameters.
Calculators and computers in statistical calculations
• The rapid growth of chemometrics is due to the ease
with which large quantities of data can be handed,
and complex calculations done, with calculators and
computers.
• Personal computers (PCs) are now found in all
chemical laboratories. Most modern instruments are
controlled by PCs, which also handle and report the
analytical data obtained.